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1 Introduction

1. since the List destructor calls up this method liste delete all 4 2 Client and Server The Server class is derived from the Socket class It allows the user to quickly implement a server capable of handling several requests When the class is initialized the user enters a name for the server When initializing a Client type object the server s name is entered if a Postmaster is being Microb User s Manual 21 Chapter 4 Utilities used or a host name and port The server provides ServerFcn type functions The Server class offers the following default services StartRecordDemand PrintRecordedDemand DeleteRecordedDemand and StopRecordDemand These services allow the user to begin recording service requests printing them out deleting the list or stopping the input process Example 13 Services Matrix fonctionl Server amp Message printf Service 1 was called n Matrix fonction2 Server amp Message printf Service 2 was called n Server main Server simple server Simple server simple server register service Servicel fonctionl simple server register service Service2 fonction2 simple server loop Client main Connected to server Client my client Simple server Request list of services available from server client get_service Print out list of available services printf Service disponible n client service pri
2. 7121107 712109 7121121 71213 T 5 101 FBIM 71812 7BB1B Note that a homogenous matrix is in fact made up a rotation matrix and a position vector x y Z 34 Microb User s Manual Chapitre 5 Vectmath R 0 0 REO R O 2 _ REJO REE 211112 RE2J 0 RP R 2 2 0 0 0 vo NS amp 5 4 2 Creating a Transform Since the homogenous matrix is always 4x4 the dimensions should not be specified when the matrix is being created 5 4 2 1 Creating the matrix without specifying the dimensions Transform A Dimensions do not need to be defined 5 4 3 Initializing a Transform A homogenous matrix can be initialized in several ways 5 4 3 1 By specifying one term at a time Creating a homogenous matrix Initializing the element 0 0 ransfor 0 0 oud it uot it tones PLOO0OOO0OPORPOp T A A A A A A A A A ber SE KEEN EG Des NACRE Ww DDP Dp H Ww 1 amp D 5 N Ww H ine Se 5 4 3 2 By calling up a function that returns a 4x4 homogenous matrix Transform A A mc_identity 4 The 4x4 matrix is a homogenous matrix 5 4 3 3 By copying one 4x4 homogenous matrix into another Transform A B A mc identity 4 B A A will be copied into B 5 4 3 4 By copying the product of an operation Transform A B C Microb User s Manual 35 Chapter 5 Vectmath A mc identity 4 B 0 0 1 B 0 1 0 B 0 2 0
3. HD conv Convention Paul or Craig Robot type HD nb gen coord x 1 Type of joint 0 gt Angular or 1 gt Prismatic Robotnb gen coord 1x1 Size of generalized coordinate vector Robotnb gen forces 1x1 Size of generalized force vector Robot gen_coord_min HD nb_gen coord x 1 degrees Lower boundaries of generalized coordinates if type Angular Robot gen_coord_max HD nb gen coord x 1 degrees Upper boundaries for generalized coordinates if type Angular Robot base 6x1 degrees m Transform between the robot base and starting referential for the HD convention Robot world 6x1 degrees m Transform between the world referential and robot base Robot tool_mount 6x1 degr s m Transform between the last referential and the location where the tool is installed It is the end effector which cannot be described using Craig s HD convention and which cannot always be fully described using Paul s convention Robot master_slave Type of robot 0 for master slave 1 for slave and 2 for master Microb User s Manual 77 Chapter 10 Exception Handling Robot gen forces limit HD nb gen coord x 1 n m Maximum generalized force which can be sent to each joint Robot flag_ feedback 1x1 NO FEEDBACK PD_NUM I NUM or PID NUM defined in Robot robot h Robot flag_ dynamic 1x1 NO DYNAMIC STATIC_FORCES INV DYN MODEL BASED INV DYN MESURED FORCES ou INV_DYN_ADAPTATIVE def
4. int i for i 0 i lt nb data i Create input signal data_in i sin i 2 M PI nb data Add a step in the middle if i gt nb_data 2 data_in i 1 5 and two pulses data_in nb_data 5 2 data_in nb_data 3 4 7 0 3 5 for i 0 i lt nb data i data outf i median process data infi mc _transpose data_in print Input mc transpose data_out print Output 6 4 Lagrange derivative The Derivative class is a Lagrange derivative filter of width 3 The constructor is used to specify the time lag between two samples while the process method is used to calculate the signal derivative Exemple 16 include Signal processing derivative h include Vectmath vectmath h const int nb data 32 const double delta t 2 M PI nb data Derivative derivative delta t Vector data in nb data Vector data out ob data int i for i 0 i lt nb data i Create input signal data infi sin i delta t for i 0 i lt nb data i data outfi derivative process data infi 58 Microb User s Manual Chapitre 6 Signal processing mc transpose data in print Input mc transpose data out print Output 3 T T T T T T 0 20 40 60 80 100 120 140 Figure 4 Effect of Butterworth filter 6 5 Integration The Integration class is used to integrate a signal using the trapezoid method The constructor is used to s
5. 16 07 p2 1 3 0 pSl11131 18 0 p1 21 3 8a 07 pzz 6 07 63121131 iow al toi a tou a ou us So int main int char ETrajectory etraj const double period 5 Transform TO T1 Position p generate TO0 p T1 Angle_axis_xyz A TO etraj set_from T0 etraj set_middle_target p etraj set_target T1 Vector3 v max 4 4 4 rad sec et m sec Vector3 a_max 1 1 1 rad sec sec et m sec sec etraj set max speed v max etraj set max accel a max mc transpose A print while etraj done A etraj get next pose period mc transpose A print return 1 9 4 PID Compensator The Control module also contains a PID compensator The gains for each type of control may be configured separately The PID class performs the numerical derivative and integral on the signal using the Signal processing module which includes these functions To not use the integral torque the gain should be left at 0 There is also a function for using a threshold on the integrator Moreover the compensation method is overloaded to act on doubles Vectors Quaternions or Quaternion_xyzs Based on the type of parameter passed to the get command method the compensation will take place in the joint or Cartesian domain In the latter case the error used in the algorithm is calculated using the quaternion theory 9 5 Compensator for adaptive control The Adaptive module contains the adaptati
6. 2 3 Matrix m try ms T v Incompatible type catch Warning error error print catch Fatal error error error print exit 1 catch Generic error error error print exit 1 CAC ace printf Unknown error n exit 1 In the above examples only one line was contained in the try block In normal applications several lines will be included that may even contain function calls In fact a single try block may be used for any application for all exception handling 76 Microb User s Manual Appendice 1 Configuration Files When users wish to control a new manipulator with the Microb library they need to first define the robot s physical properties using parameters Each parameter is identified by a specific label Some of these parameters are mandatory while others are optional They are designed to initialize certain class attributes related to the robot The table below presents the configuration parameters used by Microb Table 2 Configuration parameters Parameters Dimensions Unit Description note HD a HD nb_gen_coord x 1 m HD a parameters HD d HD nb_gen_ coord x 1 m HD d parameters HD alpha HD nb_gen_coord x 1 degree HD alpha parameters HD theta HD nb_gen coord x 1 degree HD theta parameters HD d_min HD nb_gen_coord x 1 m Upper boundaries of d if type Prismatic HD d_max HD nb_gen coord x 1 m Lower boundaries of d if type Prismatic
7. B 1 0 0 B 1 1 0 B 1 2 1 B 2 0 0 B 2 1 1 B 2 2 0 B 0 3 2 0 B 1 3 3 4 B 2 3 1 4 C A B The product of A B will be inserted into C 5 4 4 Matrix functions 5 4 4 1 Transposition NOTE The rotation part is transposed while NOTE the position part is lost A mc_transpose B 5 4 5 Modifying the Transform 5 4 5 1 Orthonormalization Orthonormalization applies to the rotation part of the Transform See the note in section 5 3 6 1 Orthonormalizes T using the singular value d composition T OfEhO Orthonormalizes T using the vectorial product T ortho fast Orthonormalizes T by converting it to an Angle axis then back to a Transform T ortho very fast 5 5 Position 5 5 1 Introduction The Position class is derived from the Vector class It supports special vector position cases All of the Vector functions are available if applicable In addition some of them may have been optimized to take advantage of the position vector specialization Position vectors have a length of 3 and form of x y z They can still be used as homogenous vectors of form x y z 1 There are two types of position vectors column position vectors and row position vectors The referencing of the nth element in a given row or column P is notated P x 1 since indexing begins at 0 36 Microb User s Manual Chapitre 5 Vectmath X P y column position
8. Robot 8 5 Mobile robot class The Mobile robot class performs operations similar to those of the Serial_ robot class However the generalized coordinates in this case are defined by cartesian degrees of freedom 8 6 Wheeled_robot class The Wheeled_robot class contains conventions for the terminology used to design generic controllers for wheeled mobile robots In more concrete terms these conventions take the form of direct and inverse kinematic virtual methods and I Os for the position of each wheel 8 7 Rigid_body class The Rigid_body class contains the parameters required to define a mobile robot which can be seen as a rigid body of arbitrary shape moving in cartesian space see the document on the underwater inspection controller for more information on these concepts This class is used to calculate the forces and moments shared by all rigid bodies and determine their position in space It is thus possible to use the Rigid body class to model any type of mobile robot without any non holonomic constraints For a specific application which should normally contain a controller and motor able to use a virtual model the Rigid_body class consists in creating a derived class which models the forces and moments which must be added to those already present in the base class For instance for a helicopter model the forces and moments generated by the helicopter s blades will have to be calculated as well as those caused by the motion of the
9. User s Manual Chapitre 3 OSDL Client Include OSDL socket h short sl s2 3 double d Int 15 15 char str 20 Socket S test client Initialization with the Postmaster recv amp sl S S recv amp d S send s2 S recv i5 5 S recv str 3 2 Postmaster The Postmaster is an application that can be used to establish communication between the server and client on different hosts without the latter knowing where the server actually is The Postmaster ensures that communication is established The use of the Postmaster is not mandatory but it greatly facilitates the development and use of the client server applications To use this type of connection the hosts must be correctly registered with the name server DNS The MICPOSTMASTER environment variable must be initialized in the name of the host on which the Postmaster is running MICPOSTMASTER uses valid addresses in the following formats e amadeus e amadeus ireq ca e 204 19 60 17 3 2 1 Use in Unix Under Unix Postmaster is a daemon controlled by inetd It is not started up manually inetd opens the socket to communicate with the clients launches Postmaster and establishes a connection between the client and Postmaster To add this service the user must be in root mode All of the following operations must be done on the host where the postmaster is running rlogin MICPOSTMATER The following line is added in etc services mic
10. absolute time to be obtained Sandglass absolute or relative Sandglass delta With the exception of SunOS you can expect to have good accuracy since Posix approved functions are being used Exemple 5 include OSDL time h Sandglass timer double t0 timer absolute Absolute time Some code double dt timer delta Time since last call of absolute or delta 3 4 Semaphore synchronization Data synchronization or protection mechanism between processes or threads For SunOS the semaphores only work between threads For the other OS they work between threads and processes In Microb users may specify at the time the semaphore is being created or initialized whether it is to be made available By default the semaphores are not available when being created users must perform a give to make them available Exemple 6 ex_semaphore C include OSDL semaphore h include OSDL thread h Semaphore sem int entiers 30 Place the 4 lines which begin with sem as comments For the 2nd test if the Semaphore is removed the program output is no longer the same each time each time it is run Main does not wait for thread to be finished writing to fill in the vector gt at the end the vector will consist of a undefined combination of 1 and 0 E void functionl void sem take printf functionl I have the semaphore n for int 3 0 3 lt 30 3 entiers j 1 mc_t
11. in the compute gravity and compute_inertial dynamic_forces methods are added those specific to the derived class model The derived class must use the variable gen forces to transmit these values to Rigid body The variable gen_forces is a 6 element vector with the following form N N N F F E where all the values are measured in the local reference frame The derived class must call up the model_integration method at each control loop iteration This method uses the forces calculated by the basic class and the additional forces included in gen forces in order to calculate the accelerations and velocities angular and linear and the body s position It performs a dual integration by using the 4th order Runge Kutta integration method provided by Microb The methods that define the acceleration and velocity equations for purposes of using the Runge Kutta method are respectively dynamic_equation which calls up dynamic model and kinematic equation which calls up kinematic model The accelerations velocities and body position are all measured in the local reference frame attached to the body The following are the main operations that need to be done for the derived class e Initialize the rigid body parameters call up Rigid_body read and add the parameters to the configuration file inertia matrix position of the centre of mass and initial conditions e Calculate the external forces acting on the body at each it
12. nb data i for 0 j lt 6 data_out j i p_mean 3 process data_in 3 i 60 Microb User s Manual Chapitre 6 Signal processing Microb User s Manual 20 40 60 80 100 120 140 Figure 6 Result of Exemple 18 61 Configuration The Configuration library is used to read and write configuration files It is also used to extract configuration subsets The configuration files used to provide the parameters of a given robot are presented in section 1 Configuration files are made up of parameters and comments A comment is a line that begins with the number sign These lines are ignored when the file is read Parameters are made up of four parts a label a type a string of characters and data which vary based on the type MC MATRIX or MC_LIST The following figure shows the different parts that make up a parameter Type du param tre tiquette du param tre Group name MC MATRIX Cha ne de caract re X String 2 3 Gan Dintensions de la matrice 12 3 Matrices de donn es my 456 Figure 7 Definition of a parameter 7 1 Label The label defines the name of the parameter It begins the definition of a parameter and is made up of one or more words separated by a period The convention used for Microb is that the first word represents the class for which the parameter is intended while the second word is the name of the attribute where the parameter will be stored
13. 1 Il RN Create function pointer p_fonc amp fonct Evaluate the results using the two integration methods result_euler euler Compute p fonc initial t0 pas nb nb equations result RK4 rk4 Compute p fonc initial t0 pas nb nb equations Print out results printf Result of yl integrated using euler f n result_euler 0 printf Result of y2 integrated using euler f An result _euler 1 printf Result of yl integrated using runge kutta f An result_RK4 0 printf Result of y2 integrated using runge kutta f An result_RK4 1 Vector fonct double t Vector value int nb equations 2 Vector yp nb equations double y0 double yl yO valeur 0 yl valeur 1 yp 0 4 cos y0 pow y1 3 1 t 0 001 yp 1 4 t yl return yp Microb User s Manual 45 Chapter 5 Vectmath 5 10 Interaction between classes 5 10 1 Introduction One of the major advantages of the Vectmath library is the interaction between the different classes of objects Examples include the multiplication of a matrix and vector and the addition of a rotation and a position vector Operator overloading was used as often as possible and in a way we thought to be natural Users should still pay attention and make sure that the behavior of an operator applied to the classes is in fact what they are expecting 5 10 2 Type conversion Converting one type to another can be done in two
14. 1 By specifying one term at a time Vector V1 3 Create a vector of length 3 v1 0 1 Initialize element 0 v1 1 2 v1 2 3 Vector V2 mc_transpose 2 Vector of length 2 V2 0 4 V2 1 5 5 2 3 2 By calling up a function that returns a vector Vector V Matrix A mc_identity 3 2 5 V mc_diag A mc diag A returns the diagonal of A 5 2 3 3 By copying one vector into another Vector V1 2 V2 v1 0 1 v1 1 2 V2 V1 V1 will be copied into V2 Microb User s Manual 31 Chapter 5 Vectmath 5 2 3 4 By copying the result of an operation Vector V1 2 V2 double d 3 0 The product of V1 d will be inserted in V2 5 2 3 5 Using the constructor available for VectorX only Vector3 V1 1 2 34 45 Vector4 V2 1 2 34 45 03 Vector3 V3 1 5 All the elements will be 1 5 Vector4 V4 1 5 All the elements will be 1 5 5 2 4 Vectorial functions 5 2 4 1 Inversion VI VI mc pinv V2 1 V2 5 2 4 2 Transposition V1 mc transpose V2 5 2 4 3 Extracting an element double V A get x Extract element x 5 2 4 4 Scalar product and vectorial product double d mc scalar product A B C mc vectorial product A B 5 3 Rotation 5 3 1 Introduction The Rotation class is used to perform matrix calculations on rotation matrices The rotation matrics are orthonormal 3x3 matrices All of the Matrix functions are available In addition s
15. 4x4 matrices vectors quarternions etc An A nrow ncol matrix will have nrow lines and ncol columns The referencing of the element found on the 3rd line and in the 2nd column of matrix A is notated A 2 1 since the lines and columns are numbered starting from 0 26 Microb User s Manual Chapitre 5 Vectmath A 0 0 ATOM A O fncol I ATI Al Allffncol 1 Afnrow 11 0 Aaron UI A nrow 1 ncol 1 5 1 2 Creating matrices There are two ways to create a matrix 5 1 2 1 Without specifying the dimensions Matrix A Dimensions should be defined later 5 1 2 2 By specifying the dimensions Matrix B 2 3 Create a 2x3 matrix 5 1 3 Initializing a matrix A matrix can be initialized in several ways 5 1 3 1 By specifying one term at a time Matrix A 2 A 0 0 A 0 1 A 0 2 A 1 0 AILLE A 1 2 3 Create a 2x3 matrix Initialize the element 0 0 Su EN 5 1 3 2 By calling up a function that returns a matrix Matrix A A mc identity 2 A will be a 2x2 matrix Position p 1 2 3 A mc _diag p A will be a 3x3 diagonal matrix A mc jordan s 6 A will be a 5x5 Jordan matrix with 6s on the diagonal 5 1 3 3 By copying one matrix into another Matrix A B A mc_identity 3 B A A will be copied into B 5 1 3 4 By copying the result of an operation Matrix A B 2 2 E LA A mc identity 2 Microb User s Manual 27 Ch
16. Microb User s Manual Chapitre 5 Vectmath The Euler angle is converted into Angle axis without any loss of information and so as to express the same transformation in space 5 10 2 22 2 From Angle _ axis to Euler angle The rotation part of the Angle axis is converted into an Angle axis while the position part is lost 5 10 3 Operations involving different classes An object from a given class that expresses pure rotation in space Rotation Quaternion Euler angle may be combined with a Position using a operator to create an object from a class that expresses an orientation and a position Transform or Angle axis Transform T Rotation R Position P Transform T Quaternion Q Position P Transform T Euler angle E Position P Angle_axis A Rotation R Position P Angle_axis A Quaternion Q Position P Angle_axis A Euler angle E Position P 5 10 4 Examples of interaction between classes Exemple 10 Creating a rotation Euler angle E 75 1 57 0 0 Rotation R E Rotation R Angle axis 4 5 6 1 2 3 Exemple 11 Creating a Transform Position P 3 1 2 04 Quaternion Q 0 741713 0 130604 0 594085 0 282607 Transform T Q P Transform T2 Euler angle 1 2 3 Position 3 4 5 Transform T3 Angle axis 2 4 3 4 4 5 6 Transform T4 Angle axis 4 1 0 0 4 5 6 Exemple 12 Extracting the rotation part of a Transform Posi
17. air drag and lift and added to those calculated by Rigid body The main Rigid body methods used to calculate the forces and moments and to position the body in space are model_integration kinematic_model dynamic_model compute_gravity and compute_inertial dynamic_forces The compute_gravity and compute inertial dynamic forces methods are used to calculate the forces that act on all rigid bodies First compute_gravity calculates the force of gravity then compute_inertial dynamic_forces calcules the inertial forces and moments which act on the body due to its mass as well as the moments due to the Coriolis force Note that it is possible to include coefficients of mass added to the inertia matrix when reading the configuration file to model certain additional forces acting on the body The kinematic_model and dynamic_model methods respectively correspond to the rigid body s kinematic and dynamic models The kinematic model uses the quarternion law of propagation and the derivative of the position vector in the local reference frame to determine the body s velocities in the local reference frame The dynamic model uses the F ma and J M laws to determine Microb User s Manual 69 Chapter 8 Robot the body s acceleration To do so an inertia matrix must be correctly initialized and inverted which is done when reading the configuration file In addition to the forces and moments calculated by Rigid_body
18. days by using the equal operator or by type casting Table 2 lists the possible conversions by indicating the section where they are found An X means that the conversion cannot be done or does not have any specific properties Table 2 Type conversion Vector Rotation Transform Position Quaternion Euler_angle Angle_axis Matrix 5 10 2 1 5 10 2 2 5 10 2 3 5 10 2 4 5 10 2 5 5 10 2 6 5 10 2 7 Vector X x 5 10 2 8 5 10 2 9 5 10 2 10 5 10 2 11 Rotation X 5 10 2 12 1 x 5 10 2 13 1 5 10 2 14 1 5 10 2 15 1 Transform X 5 10 2 12 2 5 10 2 16 2 5 10 2 17 1 5 10 2 18 1 5 10 2 19 1 Position 5 10 2 8 X 5 10 2 16 1 X X X Quaternion 5 10 2 9 5 10 2 13 2 5 10 2 17 2 X 5 10 2 20 1 5 10 2 21 1 Euler_angle 5 10 2 10 5 10 2 14 2 5 10 2 18 2 x 5 10 2 20 2 5 10 2 22 1 Angle axis 5 10 2 11 5 10 2 15 2 5 10 2 19 2 X 5 10 2 21 2 5 10 2 22 2 5 10 2 1 Matrix and Vector Vector to Matrix conversion is done without any loss of information The process is as follows Matrix nrow x ncol becomes a Vector of 1 x ncol if ncol gt nrow otherwise it becomes a Vector of nrow x 1 Matrix A 4 1 Vector V A O 0 5 46 Microb User s Manual Chapitre 5 Vectmath V will be a row vector since A nrow gt A ncol V Conversion using A V Matrix R print Vector Conversion by type casting Vector A print A 5 10 2 2 Matrix and Rotation Rotation t
19. exist the value of 1 must be returned const char get_name void const this method is used to return a unique name for the class or peripheral 5 Implement the access methods in the client and server class see the class diagram above In Microb the Device class already inherits from the Record class Refer to the Utilities Tests test_record C file for an example of how the Record class is used 24 Microb User s Manual Vectmath The Vectmath module has a series of classes used to create and manipulate matrices and vectors The Matrix class covers the general case of MxN matrices while the Vector class is used to handle Mxl or 1xN vectors It inherits from the Matrix class The other classes have set dimensions and inherit from either a Matrix or Vector They express for the most part a pure orientation Angle_axis Rotation Quaternion Euler angle pure position Position or both Transform Angle axis xyz Quaternion_xyz et Euler angle xyz Vector3 Vector4 Vector6 and Vector are generic classes for given vectors with dimensions of 3 4 6 or 7 They have no specific properties Figure 1 shows these relationships in UML language Table 1 shows the dimensions of each class and their use Mic Buber Func Euler iil Wectar Again Transom Figure 1 Relationship between the Vectmath module classes Table 1 Information on cl
20. inverse T v print Inverse kinematics For robots which do not have six degrees of freedom or which are not wrist partitioned users must overload the inverse kinematic methods if they wish to use a controller that requires this function cartesian controllers Users may also wish to overload the inverse and direct kinematic methods in order to optimize calculations as required 8 3 Robot class The Robot class uses all the parameters that apply to all the robots in the configuration object This class is designed to simplify the user interface since all users must use the terminology used in this class and the terminology applies to all serial and mobile robots In addition this convention is used in the design of generic controllers 8 4 Serial_robot class The Serial robot class inherits from the Robot Kinematic and HD classes It uses the HD parameters to overload the methods related to the generalized coordinates In short it creates the gen_coord vector by using theta for the rotary joints and d for the prismatic joints It also checks the joint boundaries by taking into account the nature of each joint Exemple 23 Serial robot my robot Puma760 cnf Vector6 v 1 57 0 3 14 0 1 57 v print Initial joint values my robot set_gen_coord v Transform T my robot get_Q T print Direct kinematics v my robot inverse T v print Inverse kinematics 68 Microb User s Manual Chapitre 8
21. special quaternion vector cases All of the Vector functions are available if applicable In addition some of them may have been optimized to take advantage of the quaternion vector specialization Quaternion vectors have a length of 4 and form of q0 q1 q2 q3 There are two types of quaternion vectors column quaternion vectors and row quaternion vectors The referencing of the nth element in a given quaternion row or column Q will be notated Q x 1 since indexing begins at 0 010 Ol Oo 013 column quaternion vector Q Q OQ 0 Q0 Q 2 OU row quarternion vector Unit quaternions The unit quaternion is a special case It is also known as Euler s parameters or Euler s Quaternion and is especially useful for expressing rotation in space Most of the library constructors return a unit quaternion with the exception of the direct initialization of the vector elements Following algebraic addition subtraction etc or other types of calculations it is up to the user to render the unit quarternion when needed see the unit method 38 Microb User s Manual Chapitre 5 Vectmath 5 6 2 Creating quaternion vectors Since the quaternion vector is always of length 4 its dimensions should not be specified when it is being created 5 6 2 1 Creating a quaternion vector without specifying its dimensions Quaternion Q1 Column quaternion vector Quaternion Q2 mc _transpose 4 Row quaternion vecto
22. to obtain the table where the data are entered while the save_record method is used to save the data in a file The following example illustrates the use of this function An engine is created that calls up a periodic function This function displays the time elapsed between two iterations The record method is used to record three data during eight iterations The three data are the time elapsed since the last iteration a counter and the period requested This last parameter is a pointer passed as an argument to the record method A pointer to the controller s class is normally used to access relevant data Exemple 9 Inputing data include OSDL osdl h include lt stdio h gt static void periodic func void static Sandglass my clock static int cpt 0 printf 3d This message must be displayed periodically period g n cpt my clock delta void rec func void p arg double p record static Sandglass my clock static int i 0 p_record 0 p_record 1 p_record 2 my clock delta i double p_arg void main void Engine engine const double per 5 seconds const double laps 5 0 seconds Sandglass my clock int nb data 3 nb iter 8 engine init AUXILIARY per periodic func 0 0 5 engine record rec func void amp per nb data nb iter engine start Microb User s Manual 17 Chapter 3 OSDL Engine left to run for 5 seconds dou
23. 17 M ma tre de poste 7 Ma tre de poste 9 matrice initialisation 23 matrices analyse 24 cr ation 23 op rations 23 Matrix 22 mc random 16 mc seed 16 Mean 47 Median 48 M moire partag e 16 P PID 65 Position 31 Q Quaternion 33 R Record 18 Microb User s Manual Rigid body 61 robot mobile 60 mobiles roues 60 s riel 60 Robot 59 Rotation 28 S Chapitre 10 Exception Handling T Sandglass 10 Semaphore 11 Serial robot 60 Server 17 Shmem 16 Signal processing 47 Socket 7 Microb User s Manual Thread 12 traitement de signal 47 trajectoire g n ration de domaine articulaire 63 domaine cart sien 64 elliptique 64 Trajectory 63 Transform 29 U Utilities 17 V vecteur 26 Vectmath 21 conversion de types 40 Vector 26 81
24. 2 18 2 From Euler_angle to Transform The Euler_angle is converted into a Rotation then the latter is converted into a Transform see 6 10 2 13 Microb User s Manual 51 Chapter 5 Vectmath 5 10 2 19 Transform and Angle avis 5 10 2 19 1 From Transform to Angle axis The Transform is converted into an Angle axis without any loss of information 5 10 2 19 2 From Angle_axis to Transform The Angle axis is converted into a Transform without any loss of information 5 10 2 20 Quaternion and Euler_angle 5 10 2 20 1 From Quaternion to Euler_angle The Quaternion is converted into a Euler_angle without any loss of information and so as to express the same transformation in space Note that this conversion is not unique i e a Quaternion may yield different Euler_angle vectors representing the same transformation 5 10 2 20 2 From Euler_angle to Quaternion The Euler_angle is converted into a Quaternion without any loss of information and so as to express the same transformation in space 5 10 2 21 Quaternion and Angle_axis 5 10 2 21 1 From Quaternion to Angle_axis The Quaternion is converted into Angle axis without any loss of information and so as to express the same transformation in space 5 10 2 21 2 From Angle_axis to Quaternion The rotation part of the Angle_axis is converted into a Quaternion while the position part is lost 5 10 2 22 Euler_angle and Angle_axis 5 10 2 22 1 From Euler_angle to Angle_axis 52
25. 5 Vectmath 5 3 5 2 Vect Vector v mc_vect R Return the vect of matrix R 5 3 6 Modifying a rotation matrix 5 3 6 1 Orthonormalization There are three orthonormalization methods The first one that gives the best theoretical solution uses singular value decomposition R U S transpose V Rortho U transpose V where U and V are orthogonal and S is diagonal The other two methods are much faster but give a slightly different solution than the best theoretical solution The ortho_very_fast method gives excellent results for most applications Orthonormalizes R using singular value decomposition R ortho Orthonormalizes R using the vectorial product R ortho fast Orthonormalizes R by converting it to an Angle axis then back to a Transform R ortho very fast 5 4 Transform 5 4 1 Introduction The Transform class is used to perform matrix calculations on 4x4 homogenous matrices All of the Matrix functions are available In addition some of them may have been optimized to take advantage of the specialization of the homogenous matrix For instance a homogenous matrix inversion will be much faster than that of an ordinary matrix A homogenous matrix T will have 4 rows and 4 columns The referencing of the element found on the 3rd row and in the 2nd column of homogenous matrix R will be notated R 2 1 since the rows and columns are numbered starting from 0 TOO 701111 710112 TEOL 711110 ZED 71022 711115
26. A a A a ane a 63 KEE PR Seager vc EAEE acess seers au os Pe wes AC aS GaSe oe ead ve dae eens saeco A 63 EELER EE 64 PE DA nt ne eegene RS A R tir ts nv eg 64 AA a Need ne ta ne 64 T 6Obtaminga A e e nn e 65 Pet Obtaining US daa 65 FS Robot CONT UA O A A A nn date de en dau 66 De ODO iii A AR A adi 67 O 67 8 2 Kinematic AA is 67 EE A screenees 68 FSC O O IN 68 8 5 Mobile TEE 69 GO Eege A ee 69 NN a ne 69 COMO AA EE 71 9 1 Trajectory generation in the joint domain sstetnnisbar disc 71 9 2 Trajectory generation in the Cartesian domain 72 9 3 Generation of elliptical trajectOri s a oi T2 E PID Compensatot en r RS lo 73 9 3 Compensator for adaptive control ses dus 73 10 Traitement des CET E 75 LOT ee ee E EE 75 EE Elei 75 2 Microb User s Manual Introduction Microb is a library of functions that can be used to develop controllers for either mobile or serial robots One of Microb s main characteristics is its modular architecture In fact Microb consists of a group of reusable modules characterized by a hierarchy of classes created using the C programming language Each module may therefore be used independently of the others depending on the type of robot involved and the level of complexity of the controller being developed To control most robots users need only define a class representing the robot and containing the methods for accessing the robot inputs outputs Microb already has the direct kinematic algori
27. For instance the parameter Robot base is used to initialize the basic attribute of the Robot class It is recommended that users use the same convention for attributes specific to their robots 7 2 Type The type which is optional is located immediately after the label and specifies the nature of the parameter When there is a type a colon is used to separate the label from the type Two types are currently supported MC MATRIX and MC LIST The default type is MC MATRIX Microb User s Manual 63 Chapter 7 Configuration 7 3 Character string The character string is used to insert a comment that is to remain with the parameter not to be confused with the comments that begin with the number sign which are not read The character string is marked off by brackets 7 4 Data 7 4 1 MC_MATRIX The data matrix is made up of two dimensions and data The two dimensions are the number of rows and the number of columns Exemple 19 Robot HD MC_MATRIX example 24 234 56 7 in a 7 4 2 MC_LIST The data are made up of a set of character strings The first word in each string serves as an index to reference the string Exemple 20 Server script MC LIST other example length 1 weight 10 3 name Test Comment This is a test 7 5 Reading a file To read a configuration file the filename is entered when the constructor is called up or the read method is used tinclude Configuration configu
28. Table of Contents 1 Introduccion ami ia 3 2 Microb s general structure sessicsisecesssscecscadsscdsscscancacedsseusseasnsseedascasnesassisvetsoassnecenvse 5 a EA ce nee 6 e En dre 6 2 3 VI uns nn ad dt ae nue 6 ZA E 6 A E E R E acme ease 6 20 ROGOL PP E E O E OO o EEE 7 A on ER E E N aa A 7 Y COST EEN 9 KSE 9 3 2 POStMASte EN 11 E SR nee nn arr se 13 SEN EE ne ann one 13 3 9 A ennemis sine rien 14 3 6 Periodic function BUE E 15 3 7 Random number Pen tia 18 3 8 Shared memory Shen EE 18 4 Dt TE iaa 21 SR a en dla nn dia 21 42 Chent EE 21 43 EE 22 Ye E ss isssiivscsvsnscescsuniasasennsubissascwasseus ieeasusbanassaansabeugedapessrtnnuisaaniencansess eededuesceers 25 5l M tik DE RE ee 26 5 2 Vector Vector3 Vector4 Vector6 Vector 0 0 0 eeeecececeeesseeseesseeeseesseeeseeeseeeseeeeees 30 5 3 TR OT ATOM ne on O OOO Er ie no een 32 54 ek e EE 34 5S POSTON nn nn anna tte 36 5 6 Quaternion and Quaternion AVES ere nent 38 5 7 Euler_angle and Euler angle Zi 40 5 8 Angle axis and Angle_axis_XyZ ns 42 5 9 Integrating differential equation systems v lt ssciasisscaccsanesserisncsuatssusseeatassndeinndduieienedentivneess 44 3 10 Interaction between CAS iria 46 Microb User s Manual 1 Chapter 1 Introduction O Signal e E 55 EE ee ia 55 6 2 Median UE locnadangncaeatv aneyanouieadaeiiasuontuataa panes 56 6 3 Eeer 57 6 4 Lagrange O nn aaa aaia 58 A ee Mes dr ue 59 6 6 Multiple signal processes haine its 60 A A 63 TD A
29. angle 5 7 3 3 By copying a euler_angle into another Euler_angle El E2 El 0 0 741713 E1 1 0 130604 El 2 0 594085 Microb User s Manual 4 Chapter 5 Vectmath E2 El El will be copied into E2 5 7 3 4 By copying the result of an operation Euler angle El E2 E3 El 0 0 741713 El 1 0 130604 El 2 0 594085 E2 El E3 El E2 The product of El E2 will be inserted into E3 5 7 3 5 Using the constructor Euler angle V1 1 2 34 45 Euler angle V2 1 5 All the lements will be 1 5 5 8 Angle_axis and Angle_axis_xyz 5 8 1 Introduction The Angle axis class is derived from the Vector class It supports specific angle axis vector cases All of the Vector functions are available if applicable In addition some of them may have been optimized to take advantage of the angle axis vector specialization The angle axis vectors have a length of 6 or 7 and form of tnx tny tnz pl p2 p3 or theta nx ny nz pl p2 p3 The Angle_axis vector has a length of 6 by default the first three elements of the vector represent the orientation while the last three represent the position If the user wishes to work with an Angle_axis of length 7 the first 4 elements represent the orientation while the last 3 represent the position this must be specified in the statement see 6 8 2 1 In addition to their length Angle axis vectors may be broken down into two categories column Angle axis
30. apter 5 Vectmath B 0 0 1 B 0 1 2 B 1 0 3 B 1 1 4 C A B The product of A B will be put in C 5 1 4 Matrix functions 5 1 4 1 Addition A B C Of 2 matrices A B s Of a matrix and a scalar A s B Of a scalar and a matrix A B A Si 5 1 4 2 Subtraction A B C Of 2 matrices A B Si Of a matrix and a scalar A s B Of a scalar and a matrix A B A s 5 1 4 3 Multiplication A B C Of 2 matrices A B s Of a matrix and a scalar A s B Of a scalar and a matrix A B A s 5 1 4 4 Division A B C Of 2 matrices gt inv C B A B s Of a matrix and a scalar A s B Of a scalar and a matrix A Ze B A s 5 1 4 5 Inversion A A mc_inv B 1 B 5 1 4 6 Transposition A mc_transpose B 5 1 5 Analyzing a matrix 5 1 5 1 Dimensions number of columns A ncol number of rows A nrow 28 Microb User s Manual Chapitre 5 Vectmath 5 1 5 2 Determinant d mc det A 5 1 5 3 Eigenvalues mc_eigen values A double complex vp Find eigenvalues if mc eigen values A 1 Check whether eigenvalues are positive 5 1 5 4 Trace t mc_trace A 5 1 5 5 Minimum and maximum values min max A min A max 5 1 6 Binary tests 5 1 6 1 Equality if LE gt gt UI UI B s If A is 1x1 and a value of s 5 1 6 2 Difference if A Bi if A s Tf A is n
31. ary contains certain utility classes such as List which implement linked lists It also offers the tools required to develop a client server type communication It also contains the Record class which allows data to be input for the plotting of graphs 2 3 Vectmath The Vectmath library is a set of matrix classes specifically developed for robotics The following classes are found Matrix Vector Vector3 Vector4 Vector6 Vector7 Transform Position Angle axis Euler angle Euler angle xyz and Quaternion 2 4 Signal_processing The Signal processing library offers classes that allow data to be filtered This is particularly useful when the robot is equipped with sensors with unstable data e g potentiometers force sensors etc The available filters are Mean Median Butterworth and Derivative 2 5 Configuration The Configuration library contains functions to read and write configuration files It also allows configuration subsets to be extracted The Configuration class is described in Section 8 while the configuration files used in Microb are presented in Section 1 6 Microb User s Manual Chapitre 2 Microb s General Structure 2 6 Robot The Robot class along with the Control and Controllers classes constitute the very essence of Microb This class is used to define a robot using its HD parameters direct and inverse kinematics dynamics etc 2 7 Control The Control module contains the trajectory generation m
32. as to express the same transformation in space 5 10 2 15 Rotation and Angle_ axis 5 10 2 15 1 From Rotation to Angle_axis The Rotation is converted into an Angle axis without any loss of information and so as to express the same transformation in space 5 10 2 15 2 From Angle_axis to Rotation The rotation part of the Angle axis is converted into a Rotation while the position part is lost 5 10 2 16 Transform and Position 5 10 2 16 1 From Position to Transform The Transform is made up of the identity rotation part 3x3 matrix located in the upper right hand side and the position vector 3 element column vector located in the upper right hand side The Ath row is made up of vector 0 0 0 1 50 Microb User s Manual Chapitre 5 Vectmath S ro e o 5 10 2 16 2 From Transform to Position The Position is made up of the position part 3x1 vector located in the upper right hand side of the Transform R P Le 00 0 1 5 10 2 17 Transform and Quaternion 5 10 2 17 1 From Transform to Quaternion The rotation part of the Transform is converted into a Quaternion see 6 10 2 13 5 10 2 17 2 From Quaternion to Transform The Quaternion is converted into a Rotation then the latter is converted into a Transform see 6 10 2 13 5 10 2 18 Transform and Euler_angle 5 10 2 18 1 From Transform to Euler_angle The rotation part of the Transform is converted into a Euler_angle see 6 10 2 13 5 10
33. asses Class Dimension Expresses Inherits from Matrix MxN General matrix Microb User s Manual 25 Chapter 5 Vectmath Vector MxlorlxN General vector Matrix Vector3 3xlorlx3 Vector of length 3 Vector Vector4 4xlorlx4 Vector of length 4 Vector Vector6 6xlorlx6 Vector of length 6 Vector Vector7 7xlorlx7 Vector of length 7 Vector Transform 4x4 Orientation and position Matrix Rotation 3x3 Orientation Matrix Position 3xlorlx3 Position Vector3 Quaternion 4xlorlx4 Orientation Vector4 Euler_angle 3xlorlx3 Orientation Vector3 Angle axis 3x1 1x3 4xlorlx4 Orientation Vector Quaternion_xyz 7xlorlx7 Orientation and position Vector7 Euler angle xyz 6xlorlx6 Orientation and position Vector6 Angle axis xyz 6x1 1x6 7xlorlx7 Orientation and position Vector The following sections describe each of these classes The Vector Vector3 Vector4 Vector6 and Vector7 classes are described in the same chapter given their considerable similarities The same applies for classes with the extension _xyz which are described in the same section as classes without extensions 5 1 Matrix 5 1 1 Introduction The Matrix class is used to perform basic matrix calculations such as multiplication addition division inversion etc The matrices can be of any given dimension Since the Matrix class methods are general in nature they are not optimized for special cases such as homogenous
34. axis A1 7 A2 A1 0 0 741713 A1 1 0 130604 A1 2 0 594085 A1 3 0 282607 A2 Al Al will be copied into A2 5 8 3 4 By copying the result of an operation Angle axis Al 7 A2 A3 A1 0 0 741713 A1 1 0 130604 A1 2 0 594085 Microb User s Manual functionx returns an angle axis 43 Chapter 5 Vectmath A1 3 0 282607 A2 Al A3 Al A2 The product of A1 A2 will be inserted into A3 5 9 Integrating differential equation systems Different numeric integration methods can be used to integrate a differential equation system Microb has two Euler s method and the 4th order Runge Kutta method The first is simple easy to use and has a geometric interpretation that is easy to understand The Runge Kutta method is also easy to use but is much more precise However it requires more extensive calculations 5 9 1 Using the functions The user must first define a time step T and a number of iterations N which will indicate the integration period For instance 1f the user wishes to integrate the equation system for a duration of one second he may choose T 0 01 and N 100 or T 0 001 and N 1000 To obtain greater precision it is preferable to choose a smaller time step In fact the larger the time step the more erroneous the approximation However when an overly small time step is chosen there is a very high number of iterations Once the step and number of iterations have bee
35. ay occur in a try block set off by brackets Following the block one or more catch blocks must be placed The catch operator uses as argument the type of error which the user wishes to catch and a name for the object optional The block is also set off by brackets The user may place more than one catch block after a try block only the first catch block with a type that corresponds to that of the error or to one of its basic types will be executed The following code provides a simple example of exception handling The line contained in the try block attempts to add two matrix classes with different dimensions The operator will detect the problem and launch a Fatal_error object As this object inherits from Generic_error the catch block Generic_error error will catch the object The object s print method is called up to display the error message Exemple 24 include Vectmath vectmath h tinclude OSDL error handling h Microb User s Manual 75 Chapter 10 Exception Handling Transform T mc identity 4 Vectors vd 2 3 Matrix m try m T v Incompatible type catch Generic error error error print The following is another example where several catch blocks are used to handle errors Note that the last catch block catches all of the errors that were not handled Exemple 25 include Vectmath vectmath h include OSDL error handling h Transform T mc identity 4 Vector3 vil
36. ble t0 my clock absolute while my clock absolute t0 lt laps mc thread yield Engine is stopped engine stop Data on screen are printed out double p record engine get_record printf Test for record n for int i 0 i lt nb iter i for int j 0 j lt nb data printf sg p_record i j prier er on Data are recorded in a file engine save record foo xyz 3 7 Random number generator The functions mc seed and mc random provide a standard interface for the generation of random numbers regardless of the type of operating system used In the following example 10 numbers are generated between 0 5 and 0 5 Example 10 Random number generator include OSDL random h double d mc_seed for int i 0 i lt 10 i d mc_random 0 5 0 5 printf d g n d 3 8 Shared memory Shmem The Shmem class has a mechanism for sharing data between processes running on the same host through a shared memory area The class is initialized using a key and the size of the memory area that is to be allocated The Shmem addr method is used to obtain a pointer for the allocated memory address If the allocation fails the pointer will be nil Example 11 Data sharing used a shared memory Process 1 18 Microb User s Manual Chapitre 3 OSDL Shmem data 1234 10 sizeof double double d double data addr AS O ase fo
37. configuration Robot Matrix base robot conf get matrix base Microb User s Manual 65 Chapter 7 Configuration 7 8 Robot configuration The Mobile robot and Serial robot classes used to define a robot contain a configuration type attribute known as conf The read method from the Mobile robot class calls up the Kinematic read method which calls up the HD read method which in turn calls up the read method of the conf attribute after which it initializes some of its attributes to the values of the configuration file parameters The read method used for derivative classes also initializes certain attributes Users may if they wish include their own parameters in the configuration file and overload the read method of the Serial_robot However they must directly call up Serial_robot read to ensure that the other classes have been properly initialized Parameter initialization is similar for mobile robots It is recommended to use the robot s name as prefix in the configuration file to ensure that the file is clear e g Puma760 enc offset 66 Microb User s Manual Robot The Robot module along with the Control and Controllers modules is the very essence of Microb The Robot module is used to define a robot using its HD parameters direct and inverse kinematics dynamics etc 8 1 HD class The HD class for Hartenberg and Denavit is used to define the kinematic properties of serial robots Most of the attribute
38. data i Create the input signal data inli sin i 2 M PI nb data Add a step in the middle of the signal if i gt nb data 2 data_in i 1 5 and two pulses data_in nb_data 5 2 data _in nb_data 3 4 7 0 3 5 for i 0 i lt nb data 1 data out i mean process data_in i mc transpose data in print Input mc transpose data out print Output Microb User s Manual 55 Chapter 6 Signal processing Wi A 20 ac Di Eb ict 120 al Figure 2 Effect of mean filter 6 2 Median filter The Median class implements a filter that returns the median value among the last N values provided This filter behaves similarly to a mean filter but its advantage is that it maintains the steps while eliminating short duration pulses In the example that follows the median filter will be used to eliminate noise from a sinusoidal signal The signal contains 128 data while the filter has a width of 5 The constructor is used to specify the width of the filter while the process method is used for the actual filtering Exemple 14 include Signal processing median h include Vectmath vectmath h const int nb data 128 const int filter width 5 Median median filter width Vector data in nb data Vector data out ob data int 1 for i 0 i lt nb data i Create input signal data_in i sin i 2 M PI nb data Add a step in the middle o
39. e loops running at different frequencies The Engine module is built such that each instance of the class is entered in a static table The initialization method of each real time loop may then establish the basic period shared by all the registered loops and make it its main period Then at each iteration of the main loop the functions of each loop are called up in turn One of the disadvantages of this is the delay caused by the time required to execute the function Thus if three functions are registered and the execution time of the first two is not constant the period of the third method will not be very consistent 3 6 1 Starting up a periodic loop A periodic loop is started up in two stages initializing using the constructor or init method and the actual startup using the start method A loop can be stopped using the stop method and started up again as desired In the following example my function will be called up at a frequency of 50 Hz 1 02 sec Exemple 8 Using an Engine tinclude OSDL engine h Microb User s Manual 15 Chapter 3 OSDL Engine engine double period 02 In seconds double priority 5 Between 0 and 1 void arg void engine engine init REAL period my function arg priority engine start mc thread sleep 5 Allowed to run for 5 seconds engine stop Engine is stopped The function that is called up will have the following syntax void my function void
40. eration calculate the forces and moments originating from the motors etc and include them in gen_forces e Update the accelerations velocities and position of the body at each iteration call up the model_integration method 70 Microb User s Manual Control The Control module contains the trajectory generators It includes three types of trajectories The Trajectory class discretizes a given value and is used for trajectories in the joint domain CTrajectory is used for the Cartesian domain The ETrajectory class is used to define elliptical trajectories The set_from and set_target methods are used to specify the starting and ending points while the get_next_pose method gives intermediate values The joint or cartesian movements follow a velocity profile with a trapezoid shape acceleration constant velocity deceleration The velocity profile is determined by the maximum velocities and maximum accelerations which must be defined using the set_max_speed and set_max_accel methods For elliptical trajectories a pose must be specified for the starting point and ending point as well as for an intermediate point It is always preferable to use a trajectory generator in robotics applications Otherwise the gains need to be modified based on the desired specifications For instance the response time tr increases with the gains module Trajectory generation frees up part of the work to the PID compensator The trajectory generato
41. f the signal 56 Microb User s Manual Chapitre 6 Signal processing if i gt nb data 2 data ini 1 5 and two pulses data_in nb_data 5 2 0 data_in nb_data 3 4 3 5 for i 0 i lt nb data i data_out i median process data infi mc transpose data in print Input mc transpose data out print Output Figure 3 Effect of median filter 6 3 Butterworth filter Microb also has a class that allows data to be filtered using a Butterworth filter The Butterworth filter is a filter where all the poles are located on a half circle with a radius of 1 in the left hand complex half plane The Butterworth class requires discretized transfer function coefficients obtained from the desired cutoff frequency and the filter order These coefficients may be found using a software program such as Octave e g b a butter 2 0 09 and must be specified when the constructor is called up The filter is then used in the same way as the median filter shown in the previous example Microb User s Manual 57 Chapter 6 Signal processing Exemple 15 include Signal processing butterworth h include Vectmath vectmath h const int nb data 32 const int filter width 3 Cutoff frequency of 0 09 order 2 Vector3 a 0 1 6041 0 6705 Vector3 b 0 0166 0 0332 0 0166 Butterworth butterworth filter width a b Vector data in nb data Vector data_out nb data
42. hen calling up the constructor The set_from and set target methods use Transforms as arguments The set max speed and set_max_accel methods use vectors with units related to the Cartesian domain as arguments rad sec rad sec rad sec m sec m sec m sec and rad sec2 rad sec2 rad sec2 m sec2 m sec2 m sec2 include Control ctraj h include Vectmath vectmath h CTrajectory ctra const double period 5 sec Transform TO Euler angle xyz 0 0 0 1 2 3 Transform Tl Euler angle xyz 1 57 0 3 14 0 3 4 Angle axis xyz A TO ctraj set from TO ctraj set target T1 Vector6 v_max 1 1 1 2 2 2 rad sec and m sec Vector6 a_max 2 2 2 3 3 3 rad sec sec and m sec sec ctraj set max speed v max ctraj set max accel a max mc transpose A print while ctraj done A ctraj get next pose period mc transpose A print Note that even if there is a discontinuity in the desired accelerations due to the velocity trapezoid in the generation of trajectories there will be no problems with an actual robot since the robot s actual trajectory does not contain any unevenness 9 3 Generation of elliptical trajectories include Control Etraj h include Vectmath vectmath h void generate Transform amp pl Position amp p2 Transform amp p3 pl mc Rz 1 p3 mc Rz 2 72 Microb User s Manual Chapitre 9 Control p1 0 3 p2 0 p3 0 3 14 0 p1 1 1 3
43. hread_sleep 5 0 printf functionl I give back the semaphore n sem give Microb User s Manual 13 Chapter 3 OSDL int main int char int i Thread th functionl 0 8192 Functionl 0 5 printf main I give the semaphore n sem give sem take printf main I have taken back the semaphore n for i 0 1 lt 30 it integers i 0 printf main The vector is n for i 0 1 lt 30 it printf d n integers i return 0 To make the semaphore available from the start the following must be added sem init Semaphore Full and sem give must be removed in main 3 5 Thread The Thread class has a function parallelization mechanism It allows a task to start up other tasks in parallel without having to stop the program The threads of a process share the same resources e g memory Exemple 7 ex_threads C BRK KKK KKK I KK KI IK I I KAR I IA I I I I KK MICROB Modules Int gr s pour le Contr le de ROBots Copyright C 1996 2002 Hydro Qu bec nstitut de recherche d Hydro Qu bec IREQ 800 boul Lionel Boulet Varennes Qu bec Canada J3X 1S1 microb robotique ireq ca http www robotique ireq ca This library is free software you can redistribute it and or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation either version 2 1 of the License or at your option any later version This library i
44. ialization Euler_angles have a length of 3 and form of roll pitch yaw There are two types of euler_angle vectors column euler_angle vectors and row euler_angle vectors The referencing of the nth element of a euler_angle row or column E is notated E x 1 since indexing begins at 0 El0 E Efi column vector El2 E E 0 Eli 2 row vector The Euler_angle xyz class is equivalent to the Euler_angle class but also contains a Position vector 40 Microb User s Manual Chapitre 5 Vectmath El0 EI El2 E E 3 column vector EA El5 LET6T E E 0 E Z 2 3 4 Eis 6 row vector 5 7 2 Creating euler_angle vectors Since the euler_angle vector is always of length 3 its dimensions should not be specified when it is being created 5 7 2 1 Creating a euler_angle vector without specifying its dimensions Euler angle Q1 Column euler angle vector Euler angle Q2 mc _transpose 3 Row euler angle vector 5 7 3 Initializing a euler_angle A euler_angle can be initialized in several ways 5 7 3 1 By specifying one term at a time Euler_angle El Create a euler angle column E1 0 1 Initialize element 0 E1 1 0 E1 2 0 Euler angle E2 mc_transpose 3 Euler angle row E2 0 0 68825 E2 1 0 555325 E2 2 0 21525 5 7 3 2 By calling up a function that returns a euler_angle Euler angle E E functionx functionx returns a euler
45. ined 5 10 2 12 Rotation and Transform 5 10 2 12 1 From Rotation to Transform The Transform consists of the rotation part 3x3 matrix located in the upper left hand side and a nil position vector 3 element column vector located in the upper left hand side The 4th row is made up of vector 0 0 0 1 7 5 10 2 12 2 From Transform to Rotation The Rotation consists of the rotation part 3x3 matrix located in the upper left hand side of the Transform 5 10 2 13 Rotation and Quaternion 5 10 2 13 1 From Rotation to Ouaternion The Rotation is converted into a Quaternion without any loss of information and so as to express the same transformation in space Note that each rotation may be represented by 2 quarternions q and q 5 10 2 13 2 From Quaternion to Rotation Microb User s Manual 49 Chapter 5 Vectmath The Quaternion is converted into a Rotation without any loss of information and so as to express the same transformation in space 5 10 2 14 Rotation and Euler _angle 5 10 2 14 1 From Rotation to Euler angle The Rotation is converted into a Euler angle without any loss of information and so as to express the same transformation in space Note that this conversion is not unique i e a Rotation may yield different Euler_angle vectors representing the same transformation 5 10 2 14 2 From Euler_angle to Rotation The Euler_angle is converted into a Rotation without any loss of information and so
46. ined in Robot robot h Robot gen coord_ error max HD nb_gen coord x 1 degrees Maximum allowable error for each joint Robot velocity max HD nb_gen_coord x 1 degrees sec Maximum allowable velocity for each joint Robot acceleration_max HD nb_gen coord x 1 degrees sec2 Maximum allowable acceleration for each joint Graph draw HD nb_gen coord x 3 Whether the links A D and the joints are drawn or not Graph link_color HD nb_gen_coord x 3 Link color Graph joint_color HD nb_gen_coord x 3 Joint color Graph link_diameter HD nb_gen coord x 1 m Link diameter Graph joint_diameter HD nb_gen_ coord x 1 m Joint diameter Graph type_link HD nb_gen_coord x 1 0 gt cylinder shape 1 gt box shape 78 Microb User s Manual Appendice 2 Class Diagram Microb User s Manual 79 Chapter 10 Exception Handling Index A H Adaptative 65 HD 59 al atoire g n ration de nombre 16 Angle axis 36 B Butterworth 49 Cc Chronom tre 10 Client 17 compensateur PID 65 Configuration 55 Control 63 contr le adaptatif 65 CTrajectory 63 D Derivative 50 d riv e 50 E Engine 13 p riodicit 14 quations diff rentielles int gration 38 erreurs traitement des 67 ETrajectory 63 Euler angle 35 exceptions 67 F filtre de Butterworth 49 d rivatif 50 m dian 48 moyenneur 47 80 Int gration 51 K Kinematic 59 L List
47. n Socket communication is done using a server which listens on a specific port on a given host Clients can thus transmit and receive data on the host s port The Socket class includes both server and client functions Only the initialization method is different With respect to the server users can choose to specify the port number or not It is not recommended that a port number be specified since it may already be used by another program With respect to the client the host name and server port number must be specified The server program must thus display on screen the port number and name of the host being used so that the user can enter them as arguments in the client process These operations can be avoided by using a Postmaster In this respect the server selects the port then registers it with the Postmaster which then communicates it to the client process In such a case the user need only specify a name to identify the server Refer to Section 3 2 for information on how to use a Postmaster Exemple 1 Socket initialization while specifying the port number For the server example on the amadeus host Microb User s Manual 9 Chapter 3 OSDL Socket S S init 1715 Port number assigned For the client Socket S S init amadeus 1715 Exemple 2 Socket initialization with automatic port assignment For the server example on the amadeus host Socket S S init Automatic port selection in
48. n selected a function must be defined that contains the differential equation system Note that this function should accept values of y in the form of vectors and should also return results in the form of a Vector or a class which inherits from the Vector class Lastly the user should define initial conditions for each of the system s equations 5 9 2 A simple example The following is a simple example containing two equations to be solved In this example y designate the points calculated in curve y t while y represent the first derivatives from the two equations The equation system to be solved is as follows yo t 4 cos yo y 1 y 1 40 2 44 Microb User s Manual Chapitre 5 Vectmath include rk4 h include euler h include lt stdio h gt include lt stdlib h gt include lt assert h gt include lt iostream h gt include lt math h gt include Vectmath vectmath h Vector fonct double Vector main int nb equations 2 Number of equations to solve Vector initial nb equations Initial conditions Vector result euler nb equations Vector result RK4 nb equations double pas 0 00001 int nb 200000 Euler euler RK4 rk4 double t0 0 Vector p_fonc double Vector Initialization of integration results and initial conditions result _euler 0 0 result _euler 1 0 result_RK4 0 0 result_RK4 1 0 initial 0 initial
49. nt 0 Call up services client execute Servicel client execute Service2 Ask server to end client close server 4 3 Record This class allows the user to record the data from variables over a desired period of time By using tools such as Gnuplot or Excel users can plot graphs and analyze the data recorded 22 Microb User s Manual Chapitre 4 Utilities The following is the class diagram Record register_var Engine Record refresh a Record 1 N Device 4 get_name recora get_recora 1 1 Server Record set_rec_var Record get_registered_var 1 1 SetRecordChoice StartRecord Client GetRecordChoice GetRecord 1 N The following procedure is used for the Record class 1 Add include Utilities record h 2 Inherit from the Record class public inheritance 3 When initializing the class record the class variables in Record by calling up Record register_var this varname for each recordable variable 4 Implement the two virtual Record methods Microb User s Manual 23 Chapter 4 Utilities double rec const char name this method is used to compare the variable name passed as a parameter with the names of the recordable class variables and return the value of the variable if it exists When the variable being sought does not
50. o Matrix conversion or vice versa is always done without any loss of information Matrix to Rotation conversion is only possible if a 3x3 Matrix is used Matrix A mc_identity 3 Rotation R A 0 0 5 NOTE R may be other than orthonormal R A Conversion by A R Matrix R print R Conversion by type casting Rotation A print A 5 10 2 3 Matrix and Transform Matrix to Transform conversion or vice versa is always done without any loss of information Matrix to Transform conversion is only possible if a 4x4 Matrix is used Matrix A mc identity 4 Transform T A 0 0 A 0 3 BT 1 NOTE The T rotation part may be other than NOTE orthonormal T A Conversion by A T Matrix T print T Conversion by transtyping Transform A print A 5 10 2 4 Matrix and Position Position to Matrix conversion is done without any loss of information Matrix to Position conversion can only be done ifa 3x1 or 1x3 Matrix is used In all cases the type of vector column or row is maintained Microb User s Manual 47 Chapter 5 Vectmath 5 10 2 5 Matrix and Quaternion Quaternion to Matrix conversion is done without any loss of information Matrix to Quaternion conversion is only done if a 4x1 or 1x4 Matrix is used In all cases the type of vector column or row is maintained 5 10 2 6 Matrix and Euler_angle Euler_angle to Matrix conversion is done withou
51. odules and different types of PID compensators Microb User s Manual 4 OSDL The Operating System Dependent Library OSDL allows Microb to run under different operating systems This library provides an interface for all functionalities which can vary from one operating system to another The following classes are found Sandglass clock Socket inter process and inter CPU communication Thread parallel execution threads Engine peridodic call or invocation of a function Semaphore synchronization and certain functions related to the operating system random number generator task management etc When Microb is migrated to a new operating system this is the only library that must be modified Users are strongly urged to use OSDL classes so that their code can be reused more easily To date OSDL supports SunOS Solaris 2 6 Linux QNX Irix VxWorks and WindowsNT 3 1 Socket The Socket class is used to establish fast communication between two threads whether they are found on the same host or not The class takes into account the possible difference in the order of bytes on the different operating systems Communication can thus be established between a program running on WindowsNT and another on Solaris The Socket class allows low level communication by socket The Client and Server classes see section 4 2 are derived classes which implement a client server paradigm with the notion of services 3 1 1 Socket initializatio
52. olumn vectors and row vectors Column vectors are a special case of a nrow x 1 matrix and row vectors are a special case of a 1 x ncol matrix The referencing of the nth element of a row vector or column V vector is notated V x 1 since indexing starts at 0 30 Microb User s Manual Chapitre 5 Vectmath 5 2 2 Creating vectors There are two ways to create a vector 5 2 2 1 Without specifying the dimensions Vector V Row or column vector dimensions will have to be defined Vector3 V1 Column vector of length 3 Vector4 V2 Column vector of length 4 Vector6 V3 Column vector of length 6 Vector V4 Column vector of length 7 5 2 2 2 By specifying the dimensions Vector V1 3 Column vector of length 3 Vector V 4 Column vector of length 4 Vector V2 mc_transpose 4 Row vector of length 4 Vector3 mc_transpose 3 Row vector of length 3 Vector4 mc transpose 4 Row vector of length 4 NOTE Vector3 V x Will create a vector of length 3 NOTE using all the elements initialized at x NOTE Vector4 V x Will create a vector of length 4 NOTE using all the elements initialized at x NOTE Vector6 V x Will create a vector of length 6 NOTE using all the elements initialized at x NOTE Vector6 V x Will create a vector of length 6 NOTE using all the elements initialized at x 5 2 3 Initializing a vector A vector can be initialized in several ways 5 2 3
53. ome of them may have been optimized to take advantage of the specialization of the rotation matrix For instance a rotation matrix will have a much faster inversion than a regular matrix will A matrix with a rotation R will have three rows and three columns The referencing of the element located on the 3rd row and in the 2nd column will be notated R 2 1 since the rows and columns are numbered starting from 0 32 Microb User s Manual Chapitre 5 Vectmath R 0 10 OI R O 2 R ROJO RHIN RUIZ R 21 01 RIT R22 5 3 2 Creating a rotation matrix Since the rotation matrix is always 3x3 the dimensions are not specified when the matrix is being created 5 3 3 Creating a matrix without specifying the dimensions Rotation A Dimensions do not need to be defined 5 3 4 Initializing a rotation matrix A rotation matrix can be initialized in several ways 5 3 4 1 By specifying one term at a time tion A Create a rotation matrix Initialize the element 0 0 O NNNRARROOOct w c SRE SAS AO E DS pp Sp a 9 IOON POoD0oororo 5 3 4 2 By calling up a function that returns a rotation matrix Rotation A A mc_identity 3 The 3x3 matrix is a rotation matrix 5 3 5 Matrix functions 5 3 5 1 Eigenvalues Find the eigenvalues mc eigen values A double complex vp Check whether the eigenvalues are positive if mc eigen values A 1 Microb User s Manual 33 Chapter
54. on law which calculates the value of the parameters to be calibrated on line The method that calculates the value of these parameters must be called up at each iteration of the control using the module Other methods can also be used to enter the initial estimated values of the parameters the gains from the adaptation law etc Microb User s Manual 73 Exception Handling Microb uses the exception handling function from C based on the concept of the try and catch blocks and the throw operator When an exception occurs in a library an object is thrown and the application is responsible for catching it If no catch block takes care of the problem the application ends with an error message This situation is not desirable in a robot control context 10 1 Error objects When an error occurs in Microb an object representing the type of error is launched The object also contains a message providing information on the error that occurred The object classes are defined in the OSDL error_handling h file The classes are Generic_error Warning and Fatal error The Generic_error class is a basic class from which other classes inherits The print method for these classes is used to display the message contained in the object while the get error_type and get message methods return the type of error and the message respectively 10 2 Try and catch blocks To catch one of the error objects the code must be placed where the error m
55. ot 1x1 or a value of s 5 1 7 Creating submatrices 5 1 7 1 Deleting a column A mc del col B col Delete column col 5 1 7 2 Deleting a row A mc del row B row Delete row 5 1 7 3 Deleting a row and a column A mc sub matrix B row col Delete column col and row 5 1 7 4 Extracting a region Only keep submatrix which extends from column x1 to column x2 and from row yl to row y2 A mc sub matrix B yl xl y2 x2 Microb User s Manual 29 Chapter 5 Vectmath 5 1 7 5 Extracting a column Vector V A col x Extracting column x 5 1 7 6 Extracting a line Vector V A row y Extracting row y 5 1 7 7 Absolute value matrix B mc abs A 5 1 7 8 Modifying matrices 5 1 7 9 Swapping columns A swap_col xl x2 5 1 7 10 Swapping rows A swap_row yl y2 5 1 8 Matrix file operations 5 1 8 1 Save A save MyMatrix mat Saved in MyMatrix mat 5 1 8 2 Read A load MyMatrix mat Read in MyMatrix mat 5 2 Vector Vector3 Vector4 Vector6 Vector 5 2 1 Introduction Vector Vector3 Vector4 Vector6 and Vector are classes derived from the Matrix class They support special vector cases All of the Matrix functions are available if applicable In addition some of them may have been optimized in order to take advantage of the vector s specialization The Vectors may be of any length whereas VectorX is of lengh X There are two types of vectors c
56. pecify the time lag between two samples while the process method is used to calculate the signal derivative The set method is used to specify the initial value of the integrator Exemple 17 include Signal processing integration h include Vectmath vectmath h const int nb data 32 const double delta t 2 M PI nb data Integration integration delta_t Vector data in nb data Vector data out ob data int i for i 0 i lt nb data i Create input signal data infi sin i delta t integration set 1 0 for i 0 i lt nb data i data_out i integration process data_in i Microb User s Manual 59 Chapter 6 Signal processing mc transpose data in print Input mc transpose data out print Output 1 05 0 5 0 20 40 60 80 100 120 140 Figure 5 Effect of Lagrange derivative 6 6 Multiple signal processing Users may wish to process a signal with multiple dimensions e g the values of a robot s potentiometers The functions mc new mean mc new median mc new butterworth and mc new derivative are used to allocate a list of operations of variable length The following example shows how this function is used for a 6 element vector Certain parts of the code have been omitted for the sake of clarity Exemple 18 Mean p mean filter width p_ mean mc new median 6 nb data Matrix data in 6 nb data Matrix data out 6 nb data for i 0 i lt
57. postmaster 12459 tcp Microb Postmaster 12459 can be replaced with any short greater than 3400 Microb User s Manual 11 Chapter 3 OSDL The following line is added in etc inetd conf micpostmaster stream tcp nowait microb PATH postmaster postmaster tmp postmaster log PATH is the directory where the postmaster binary is found In some operating systems a make must be performed in var yp or the SIGHUP signal sent to the inetd process 3 2 2 Use in WindowsNT inetd is not standard in WindowsNT Postmaster must therefore be running at all times as with a daemon In the Services file which is found in C Winnt system32 drivers etc the following line must be added at the end of the file micpostmaster 12459 tcp Microb Postmaster It can be launched in WindowsNT Startup as follows In the directory c Winnt Profiles All Users Start Menu Programs Startup Create a link to the target Target C PATH postmaster exe c tmp postmaster log Start in C PATH Run Minimized Where PATH is the directory where the postmaster exe program is located 12 Microb User s Manual Chapitre 3 OSDL 3 3 Clock Sandglass This class allows users to obtain the time in seconds as accurately as possible The accuracy varies based on the OS Generally you can expect a maximum error of 10 milliseconds for a non real time OS For a real time OS the accuracy rate is less than 1 millisecond The class methods allow
58. ptr where the pointer ptr is the 4th argument passed to the Engine init method In the example above it is the Engine object s address 3 6 2 Detecting non periodicity During robot control control loop periodicity is often crucial The Engine class uses two methods to check whether the periodicity is met at each iteration First Engine checks that the function called up is of a duration less than the period requested Then Engine ensures that the last period has not been overly long thanks to the following algorithm if last_period tolerance gt desired_period The warning function is called The last_period variable represents the time elapsed from the start of the periodic function during the previous iteration to the start of this function during the current iteration This period may differ from the desired period if the time required to execute the periodic function is greater than the desired period and or if another task has higher priority on the system than the control loop The value of the tolerance variable must be found between 0 and 1 where 1 represents perfect periodicity The Engine get_tolerance and Engine set_tolerance methods are used to read and modify this value The acceptable tolerance level will obviously depend on the application In addition on a non real time system most of the time this value will have to be decreased For instance the Solaris operating system will not allow any interr
59. r 5 6 3 Initializing a quaternion A quaternion can be initialized in several ways 5 6 3 1 By specifying one term at a time Quaternion Q1 Create a column quaternion Q1 0 1 Initialize the element 0 Q1 1 0 Q1 2 0 Q1 3 0 Quaternion 02 transpose 4 Row quaternion 02 0 0 68825 Q2 1 0 555325 Q2 2 0 21525 02 3 0 414239 5 6 3 2 By calling up a function that returns a quaternion Quaternion Q Q functionx functionx returns a quaternion 5 6 3 3 By copying a quaternion into another Quaternion Q1 02 Q1 0 0 741713 Q1 1 0 130604 Q1 2 0 594085 Q1 3 0 282607 Q2 Q1 Q1 will be copied into Q2 5 6 3 4 By copying the result of an operation Quaternion Q1 02 03 Q1 0 0 741713 Q1 1 0 130604 Q1 2 0 594085 Q1 3 0 282607 Q2 Q1 03 Q1 Q2 The product of Q1 Q2 will be inserted into Q3 Microb User s Manual 39 Chapter 5 Vectmath 5 6 4 Vector functions 5 6 4 1 Square V1 mc square v2 5 6 5 Analyzing a quaternion 5 6 5 1 Norm double d Q norm 5 6 5 2 Absolute value double d Q abs 5 7 Euler_angle and Euler_angle_xyz 5 7 1 Introduction The Euler angle class is derived from the Vector class It supports specific Euler angle cases All of the Vector functions are available if applicable In addition some of them may have been optimized to take advantage of the Euler angle spec
60. r int i 0 125 d i Process 2 Shmem data 1234 10 sizeof double double d double data addr for int i 0 i lt 10 i printf d d g An i diil Note that the size of the allocated memory is taken into account only at the first initialization This allows a process to allocate a variable amount of memory and to send this size information to another shared memory process Note also that the class destructor does not free up the memory The Shmem free method must be called up specifically by one of the processes Microb User s Manual 19 _ Utilities This library contains certain utility classes such as List which implement the chained lists 4 1 List The List class allows the user to create and manipulate a list of pointers Different methods are used to add insert remove remove or retrieve get_ptr elements It is also possible to print print the list or delete it delete all Example 12 include Utilities list h List lise double iteml 1 2 item2 3 4 item Add 2 elements in the list list insert First item void iteml list insert Second item void amp item2 Print out the list list print s Get an item item double list get_ptr Second item printf Item g n item Remove an item list remove First item Print out the list again list print Delete the list optional in this example
61. r requires the robot to follow a trajectory by constantly moving in small increments D to reach the desired pose see Figure 9 The compensator gains can thus be adjusted to obtain an acceptable response time tr and overtravel d for this type of motion The time required to attain the final desired pose is then adjusted by selecting the maximum velocity and acceleration The overall performance is also improved since the robot decelerates before reaching the desired pose 9 1 Trajectory generation in the joint domain When in the joint domain the number of joints must be specified in the constructor The methods set_from set target set max speed and set_max_accel use as arguments vectors with units associated with the joint domain usually rad rad sec and rad sec2 include Control traj h include Vectmath vectmath h Trajectory traj 4 const double period 5 sec Vector4 VO 0 0 1 57 1 57 rad Vectort V1 1 57 1 57 149 077 rad Vector4 V VO traj set_from V0 traj set_target V1 Microb User s Manual 71 Chapter 9 Control Vector4 v max l 5 1 2 rad sec Vector4 a max 2 2 2 3 rad sec sec traj set max speed v max traj set max accel a max mc transpose V print while traj done V Vector4 traj get next pose period mc transpose V print 9 2 Trajectory generation in the Cartesian domain In the Cartesian domain no elements need to be specified w
62. ration h Configuration conf file cnf 64 Microb User s Manual Chapitre 7 Configuration or tinclude Configuration configuration h Configuration conf conf read file cnf 7 6 Obtaining a parameter The get comments get_matrix and get list methods are used to obtain the comment matrix and list of one parameter char string conf get comments HD convention Matrix mat conf get matrix Robot base List Wist conf get list Server script Users can also check whether an element is found in the configuration with the item exists method if conf item exists Robot tool mount tool mount conf get matrix Robot tool mount The get_matrix Conf_item method is more efficient by avoiding having to search through the list twice tool mount conf get matrix item x y Configuration Error 7 7 Obtaining a subset The Configuration class is used to group the parameters into subsets to increase the efficiency of the search and the coherence of the configuration file For instance let s assume that the conf Configuration object contains the following parameters HD a HD d HD alpha HD theta Robot base Robot tool mount Robot velocity max The get configuration method is used to extract the two subsets HD and Robot Configuration hd conf conf get configuration HD Matrix a hd conf get matrix a Matrix d hd conf get matrix d Configuration robot conf conf get
63. s distributed in the hope that it will be useful but WITHOUT ANY WARRANTY without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE See the GNU Lesser General Public License for more details You should have received a copy of the GNU Lesser General Public License along with this library if not write to the Free Software Foundation Inc 59 Temple Place Suite 330 Boston MA 02111 1307 USA RA A RRA A A A RRA A A A oe oe He Oe A Ka Ka Ka Ka Ka Ka Ka Ka Ka Ka L Ka Ka Ka Ka Ka Ka include lt stdio h gt include OSDL thread h void functionl void printf functionl startin mc thread sleep 2 printf functionl end n 14 Microb User s Manual Chapitre 3 OSDL void function2 void printf function2 startin mc thread _sleep 1 printf function2 end n int main int char printf main startin Thread filsl functionl 0 8192 Functionl 5 Thread fils2 function2 0 8192 Function2 5 mc thread _sleep 4 printf main end n return 0 3 6 Periodic function Engine This module is used to append a function that will be called up periodically at a frequency specified by the user On a real time OS the period will be guaranteed For other operating systems the period will be met insofar as possible This class is the core of Microb controllers The Engine class allows to have several real tim
64. s of this class are defined using a robot s configuration file see section 1 The read method is used to read a configuration file and initialize the attributes The print method is used to display the class values These values will be used by the Kinematic and Serial_robot classes as well as the class which inherits from them Note that Microb supports two versions of the HD convention i e Paul and Craig The HD convention parameter is used to define the version used in the file Microb uses the Paul version by default Exemple 21 HD hd hd read Puma760 cnf hd print y Users do not usually have to call up the read method of the HD class directly since it is overloaded by the Serial_robot class 8 2 Kinematic class This class provides direct and inverse kinematic generic functions for serial robots Direct kinematics can be used for any type of serial robot while inverse kinematics are used for serial six DOF wrist partitioned robots In the following example a Kinematic type object is declared which is initialized using a configuration file During normal Microb use users do not need to handle this class directly this is a basic class which Serial_robot inherits Exemple 22 Kinematic kin Puma760 cnf Microb User s Manual 67 Chapter 8 Robot Vector6 v 1 57 0 3 14 0 1 57 v print Initial joint values Kin ser theta v Transform T kin get_Q T print Direct kinematics v kin
65. t any loss of information Matrix to Euler_angle conversion is done only ifa 3x1 or 1x3 Matrix is used In all cases the type of vector column or row is maintained 5 10 2 7 Matrix and Angle_axis Angle_axis to Matrix conversion is done without any loss of information Matrix to Angle_axis conversion is done only ifa 6x1 1x6 7x1 or 1x7 Matrix is used In all cases the type of vector column or row is maintained 5 10 2 8 Vector and Position Position to Vector conversion is done without any loss of information Vector to Position conversion is done only ifa 3x1 or 1x3 Matrix is used In all cases the type of vector column or row is maintained 5 10 2 9 Vector and Quaternion Quaternion to Vector conversion is done without any loss of information Vector to Quaternion conversion is only done ifa 4x1 or 1x4 Matrix is used In all cases the type of vector column or row is maintained 5 10 2 10 Vector and Euler_angle Euler_angle to Vector conversion is done without any loss of information Vector to Euler_angle conversion is only done ifa 3x1 or 1x3 Matrix is used In all cases the type of vector column or row is maintained 48 Microb User s Manual Chapitre 5 Vectmath 5 10 2 11 Vector and Angle avis Angle axis to Vector conversion is done without any loss of information Vector to Angle axis conversion is only done if a 6x1 1x6 7x1 or 1x7 Vector is used In all cases the type of vector column or row is mainta
66. t port S get_port For the client Socket S S init amadeus port port is the value returned by the server s S get_port Exemple 3 Socket initialization using the Postmaster For the server Socket S S init MyServer server Automatic port selection and recorded with Postmaster as server For the client Socket S S init MyServer client The client obtains the name from the host and the port number via the Postmaster 3 1 2 Socket data transmission Once the initialization has been completed the data transfer can be established The size of the data transmitted is determined based on the type The socket class supports the following types of data transfers short int long float double char short int long float double In the case of pointers the number of elements being transmitted or received must be specified For char pointers a character string ending in zero may also be provided In all cases the synchronization between the client and server in terms of the type of data being transmitted must be respected Exemple 4 Transmission between client and server Server Include OSDL socket h short sl 2 s2 double d 1 4 static int 15151 1 2 3 Es Pis char str salut Socket S test server Initialization with the Postmaster send s1 send d recv amp s2 send i5 5 Send str nana an 10 Microb
67. t to provide their own inverse kinematics develop a new controller or spread out the calculations on different platforms It is therefore important to properly understand Microb s general structure and the tools it contains These tools are grouped in nine libraries which are interrelated as shown in Figure 1 gt L V NI V control Mer re core d nfig ura ti DA ae v AN V e V Figure 1 Microb s structure Microb User s Manual 5 Chapter 2 Microb s General Structure 2 1 OSDL The Operating System Dependent Library OSDL allows Microb to run under different operating systems In fact this library provides an interface for all functionalities which can vary from one operating system to another The following classes are found Sandglass clock Socket inter process and inter CPU communication Thread parallel execution threads Engine execution loop Semaphore synchronization and certain functions related to the operating system random number generator task management etc When Microb is migrated to a new operating system this is the only library that must be modified Users are strongly urged to use OSDL classes so that their code can be reused more easily To date OSDL supports SunOS Solaris 2 6 Linux QNX Irix VxWorks and WindowsNT 2 2 Utilities The Utilities libr
68. thms for serial robots as well as the inverse kinematic algorithms for serial six DOF wrist partitioned robots For other robots the inverse kinematics must be rewritten by overloading the default kinematics As for the actual controller Microb already has several and new ones can be quickly defined using the available tools One of Microb s advantages in relation to other products on the market is the large number of operating systems that it supports The code developed using Microb can be tested on one platform and used on another one This facilitates such aspects as team work and favours the use of algorithms over the long term This document describes each module in the library in detail The applications manual can be consulted for examples on how to use the modules Microb User s Manual 3 Microb s General Structure Microb is made up of a group of modules that allow users to quickly develop robot controllers that can operate on different platforms A controller s level of complexity can vary greatly based on the type of robot to be controlled and the tasks to be carried out In the typical case of a serial six DOF wrist partitioned robot presented in the applications manual the use of Microb is greatly simplified since its inverse kinematic methods already support this type of robot In addition in the example shown the controller is also one of Microb s generic controllers However in many cases Microb users will wan
69. tion P1 1 2 3 Position P2 5 1 2 3 4 Euler angle E 0 1 57 1 57 Transform Tl E Pl Create T2 made up of the rotation part of T1 and Pi Transform T2 Rotation T1 P2 Microb User s Manual 53 Signal_processing The Signal_processing library has classes that process data This is especially useful when the robot is equipped with sensors with noisy input e g potentiometer force sensor or for control algorithms e g integrators differentiators etc The available classes are Mean Median Butterworth Derivative Integration and Lagrange der The classes can process one signal at a time or a group of signals as will be shown further on As the classes process temporal data they will introduce a time lag that is proportional to the size of the operation used 6 1 Mean filter The Mean class implements a filter that returns the mean value among the last N values provided In the example that follows we will be using the mean filter to attenuate noise on a sinusoidal signal The signal contains 128 data while the filter has a width of 5 The constructor is used to specify the width of the filter while the process method is used for the actual filtering Exemple 13 include Signal processing mean h include Vectmath vectmath h const int nb data 128 const int filter width 5 Mean mean filter width Vector data in nb data Vector data out ob data int 1 for i 0 i lt nb
70. uption between two instructions in a task to continue executing the control loop This method thus does not ensure periodicity However it minimizes the risk of data becoming corrupted These systems are of course not recommended for robot force and velocity control If non periodicity is detected the mc_overrun_warning function is called up by default This function prints out in the following sequence a warning message the desired period the duration of the last period and the time required by the CPU to execute the periodic function If this time exceeds the desired period the latter value has to be increased However if the last period is greater 16 Microb User s Manual Chapitre 3 OSDL than the desired period the user must decrease the tolerance and or increase the number of clock overrun permits nb_overrun_max attribute in the Engine class The Engine set_overrun_function method is used to specify that another function is to be called up if non periodicity is detected This is especially useful when the robot needs to be stopped immediately 3 6 3 Recording synchronous data The Engine class is used to record data synchronously i e at each iteration The record method is used to specify an input function a data pointer and the size of the table that is to be recorded Data recording begins when this method is called or if the engine is not running when the start method is called The get_record method is used
71. vector Z P x y zl row position vector 5 5 2 Creating position vectors Since a position vector always has a length of 3 its dimensions do not need to be specified when it is being created 5 5 2 1 Creating a position vector without specifying the dimensions Position Pl Column position vector Position P2 mc _transpose 3 Row position vector 5 5 3 Initializing a position A position can be initialized in several ways 5 5 3 1 By specifying one term at a time Position VD 23 Aye When being created Position V1 Create a column position v1 0 Le Initialize element 0 v1 1 Ze v1 2 EF Position V2 mc_transpose 3 Row position v2 0 4 v2 1 Ds v2 2 6 5 5 3 2 By calling up a function that returns a position Position P P functionx functionx returns a position 5 5 3 3 By copying a position into another position Position Vl V2 v1 0 1 KS Ze v1 2 3 V2 V1 V1 will be copied into V2 5 5 3 4 By copying the result of an operation Position Vl V2 double d 3 0 Microb User s Manual 37 Chapter 5 Vectmath v1 0 1 v1 1 2 v1 2 3 V2 V1 d The product of Vi d will be inserted into V2 5 5 3 5 Using the constructor Position V1 1 2 34 45 Position V2 1 5 All the elements will be 1 5 5 5 4 Vector functions 5 6 Quaternion and Quaternion_xyz 5 6 1 Introduction The Quaternion class is derived from the Vector class It supports
72. vectors and row Angle axis vectors The referencing of the nth element of an angle axis row or column P is notated P x 1 since indexing starts at 0 A 0 A REI A A 3 column vector A 4 A 5 AL6 A 4 07 A0 42 413 A4 A5 A 6 row vector 42 Microb User s Manual Chapitre 5 Vectmath 5 8 2 Creating angle _axis vectors The angle axis vector is always of length 6 or 7 and its dimensions may be specified when it is being created it has a length of 6 by default 5 8 2 1 Creating an angle _axis vector Angle axis Angle axis Angle axis Angle axis Angle axis Al A2 A2 A3 A4 Column vector 6 Colum vector 7 Column vector mc_transpose 6 Row vector of mc_transpose 7 Row vector of 5 8 3 Initializing an angle_axis vector An angle axis vector can be initialized in several ways 5 8 3 1 By specifying each term one at a time of length 6 of length 6 of length 7 length 6 length 7 Angle_axis Al 7 Create an angle axis column A1 0 1 Initialize the element 0 Al 0 A1 2 0 A1 3 0 A1 4 A1 5 A1 6 0 Angle axis A2 mc transpose 7 Angle axis row A2 0 0 68825 A2 0 555325 A2 2 0 215254 A2 3 0 414239 A1 4 A1 5 A1 6 1 5 8 3 2 By calling up a function that returns an angle_axis vector Angle_axis A A functionx 5 8 3 3 By copying one angle_axis vector into another Angle_

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