User Manual
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1. adj2 adjacency adj2 1 3 0 remove link 0 gt 2 adj2 2 3 1 add link 1 gt 2 changeData 1 struct type commTopology t_change 100 time step of change adjacency adj2 Change topology adj3 adj2 adj3 2 end 2 end ones N make all communications for i 2 N 1 adj3 i i 0 set the diagonal of the adj to 0 end changeData 2 struct type gt commTopology gt t_change 200 step at which the change should occur adjacency adj3 Chenge formation shape changeData 3 struct type constellation t_change 250 absRefInput o 1 1 agent 1 x y z coordinates 0 1 5 1 agent 2 o 2 1 O 2 5 1 0 3 1195 Add agents load copter_models PK plant P and controller K 18 TUHH RTS Andrey Popov new_agents new_agents 1 LinearModel P K zeros 12 1 5 0 0 new_agents 2 LinearModel P K zeros 12 1 6 0 0 agents 3 amp 4 receive from the new agent adj4 adj3 0 0 0 0 0 0 1 0 1 0 0 O 0100000 0 the first new agent receives form agent 1 00000100 the second new agent recevies from agent 5 h 01234567 agent number changeData 4 struct Remove agents changeData 5 struct Save everything to Janes_all_sim mat save Janes_all_sim mat type addAgent t_change 300 ne2. o o o Removing Agents For example to remove agents 2 and 3 in the 700th step time one would need the following code changeData 5 struct type deleteAgent t_change 700 deletelds 2 3 Quite happy with her simulations Jane shows them to her colleague Marta Marta is im pressed when she sees the simulation but is not quite happy with all those definitions and MAT files Jane explains that one could write the definition of the group of agents and the changes more efficiently using loops or and another toolbox named Formation Analysis and Control Toolbox FACT that provides many useful functions Marta agrees that this would be useful but she actually would prefer to by able to make manual changes so to say on the fly to the formation After a lengthy discussion they both agree that the current functionality is useful if one wants to define complicated scenarios that can be reproduced but also some easy changes by hand would be nice Since as they learn this is not on the to do list of the authors of FAST they think about contributing to the project themselves FormAtion Simulation Tool FAST user manual 15 4 7 Non linear agents As Marta is herself interested in non linear systems she wants to try out the original non linear model of the quad rotor In general she would have needed to construct her own non linear model as a child of the object Model using the ob
3. obstacle is intuitive to define and as Jane is not primarily interested in great graphics she sets the number of faces visualizing the ball obstacle to 6 The wall obstacle gives her a bit of a trouble at first until she realizes that by wall is meant just a parallelogram defined by one corner and two offsets i e with corners corner corner di corner d1 d2 and corner d2 Ball shaped obstacle where faces is used for visualization obstacles 1 struct type ball center 0 1 1 radius 0 5 faces 6 Wall shaped obstacle obstacles 2 struct type wall corner 4 0 1 ad 0 0 21 12 0 1 0173 Save the obstacles to a MAT file save Janes_obstacles mat obstacles Then after starting FAST she ticks the check box by Communication obstacles and selects Janes_obstacles mat after which she starts the simulation Later she understands that the advantage of specifying the multi agent system and the obstacles separately is that one can load a new set of obstacles during the simulation Using the manual Reference Input Jane tries driving the formation through and around the obstacles and finds that it works as expected Her only complaint is that the whole simulation seems to take longer but as she later learns that is due to the fact that FAST needs to check for intersection of each communication link with each obstacle and there seems not to be much one could do to
4. TUHH Technische Universitat Hamburg Harburg User Manual Andrey Popov FormAtion Simulation Tool FAST February 2010 Report 2010 03 Contact data Andrey P Popov Institute of Control Systems Hamburg University of Technology Eissendorfer str 40 21073 Hamburg Germany andrey popov tu harburg de http www tu harburg de rts FormAtion Simulation Tool FAST user manual 3 Contents 1 Introduction 2 Toolbox Structure 1 1 Features 2 0 0 0 ew aa a e A e e ee a 172 License a8 a 80 a 8 ee AN 1 3 Download and Development 2 2 2 2 En nn nn 1 4 Inst llationl ias ra e a Gok he a en ea era al 3 Graphical User Interface 6 4 Tutorial on Defining and Simulating Formations 7 ee ee ee a ge ee 7 bit endings O Gon ede ar ee 10 eg SiS a See ee Oe ee en ee E 10 4 4 Communication Obstacles 2 2 2 on nn nn 11 pa ea a ar e 12 yd et Got aot Ek ee eS RP ESE ES EKA GA S 12 ae hhh ha eyo a es ee 12 Formation Shape Change 2 2 En En nn 13 Be er ee ee ee en 14 A ee en es 14 ae ee a ge e ta ee 15 id ote ds ee re See 16 4 TUHH RTS Andrey Popov 1 Introduction The FormAtion Simulation Tool FAST is a tool for Matlab developed in for the pur pose of performing realistic simulations of multi agent systems MAS FAST allows simulating linear and non linear discrete time agents that communicate with each other The communica tion links can be additionally subject to time del
5. at again Next she selects the drop down box under Communication Time Delay on the right side of the GUI and is somewhat disappointed to find out that the only two options are none and fixed and equal She writes to the authors of FAST and asks why no distance dependent or different delays are supported By the reply she learns that actually on their to do list As Jane knows when the own check box is marked the own outputs of the agents are also delayed when computing the error e So she sets upon trying different time delays both with own and without own delay and discovers that whereas even several second delay can make the formation with own delays unstable this was not possible in the absence of own delays even for a big ones Somewhat puzzled she contacts the people who developed the controller she is using who inform her that this is a special feature of their controller and is due to a small gain condition they have employed PW09 This makes Jane wonder if she could use that same approach for her own simulations later on 4 3 Communication Range Jane decides to make the agents communicate only if the distance between them is shorter than 4 units and easily achieves this by ticking the check box by Limited Communication Range and entering 4 in the box But then she faces a new problem she cannot give a reference point far away since than the communication brakes down and agents 1 and 2 do not receive the reference signal She di
6. avoid the slow down 12 TUHH RTS Andrey Popov 4 5 Reference Input from File During the last simulations it was tiring for Jane to adjust the reference signal to the virtual reference agent manually so she decides to define a reference trajectory through a file She decides to make the formation move with a constant speed in y direction and perform sinusoidal oscillations in x direction while keeping the z axis the vertical one at 1 unit This she defines through the following code and saves the reference signal in Janes_reference mat where again the important part is the name of the variable formationRef Input t 0 1000 time steps x 2 sin 0 01x t x axis y 0 002 t y movement with speed of 0 002 units per time step z ones 1 length t constant z position formationRefInput t_step t formationRefInput refPos x y zl save Janes_reference mat formationRefInput If Jane has left formationRefInput t_step empty then the reference signal will considered as one starting from the current time moment Alternatively Jane could have defined only few key points like that hh Specify reference key points formationRefInput t_step 0 200 500 1000 ref pos at time steps formationRefInput refPos 000 at 0 020 at 200 05 1 at 500 0 6 2 at 1000 note the transpose To change the distance between the agents and not only the position fo the reference poin
7. ays range restrictions and obstacles FAST is developed and tested under Matlab 2009a 1 1 Features As by now Feb 2010 FAST provides the following functionality e Simulation of MAS with discrete time dynamics e Linear and non linear agent dynamics the non linear will require manually specifying the dynamics e Adding Removing agents during the simulation requires pre specifying the time of change and the agents to be added removed e Changing the communication topology during the simulation requires pre specifying the time of change and the new topology e Defining communication obstacles with ball or parallelogram shape e Fixed communication delays with or without delayed own outputs of the agents Specifying communication range i e distance dependent communication Graphical User Interface GUI for easy control and visualization Export of the simulation data 1 2 License FAST and this user manual are distributed under GNU v 3 license http www gnu org licenses 1 3 Download and Development FAST can be downloaded by the development repository at http bitbucket org femas fast The latest significant release can be directly downloaded as from the following link http bitbucket org femas fast downloads FAST zip If you are interested in providing additional functionality to FAST improving the code or modifying the GUI you are welcomed to do so Please send a short note to the authors using t
8. controlling the simulation and the switches under that window are for adjusting what and how is visualized As most of the buttons and switches are self explanatory they will not be covered here The style of the animation i e with what symbols and colors are the agents trails and arrows visualized can be adjusted manually via the settings structure in the object Animator FormAtion Simulation Tool FAST user manual 7 4 Tutorial on Defining and Simulating Formations This tutorial is intended for new users of FAST and aims at giving an overview of the main steps in defining and performing a simulation of a multi agent system The tutorial is written in a story like fashion in the hope that this will make it easier to read The code to this tutorial can be found subfolder demo of FAST 4 1 A simple simulation Our story starts with Jane who is a researcher in the area of cooperative control of agents One day Jane discovers a rather interesting example of a formation flight of quad rotor helicopters quadrocopters and decides to perform some simulations While reading the details she is at first taken aback when she learns that the quadrocopters have non linear and unstable dynamics Luckily she discovers a linearized discrete time model P z with 12 states 4 inputs and 15 outputs and a corresponding controller A z and decides to set up a simple simulation in FAST As Jane understands it from the closed loop of agent and contr
9. e does not plan on using at the moment Formation Shape Change For example the following code changes the reference to the agents in the 250th time step such that the agents should arrange themselves at a distance of 0 5 from each other along the y axis and at an altitude of 1 changeData 3 struct type constellation t_change 250 AbsRefInput o 1 1 agent 1 x y z coordinates 0 1 5 1 agent 2 0 2 1 0 2 5 1 0 3 11 14 TUHH RTS Andrey Popov Adding Agents If Jane wanted to add 2 further quad rotor agents at time step 300 the first one of which appears at coordinates 5 0 0 and receives information from agent 1 and sends information to agents 3 and 4 and the second appears at coordinates 6 0 0 one receives information only from agent 5 she should use a code like the following load copter_models PK plant P and controller K new_agents new_agents 1 LinearModel P K zeros 12 1 new_agents 2 LinearModel P K zeros 12 1 2 2 5 0 0 6 0 0 changeData 4 struct type addAgent t_change 300 newAbsRef Input 2 4 1 2 4 1 with respect to ref point adjacency L 000000 gt d we we RRERPRPRPO ORhkROR Orrore Ooo0Perereoo Oo o0o0o0o0ooooOoOo 00 models new_agents note the brackets oOO00o0 oor oo FR FF FOOrRFRFR FE
10. he contact on the second page of this document so that you can obtain Writer rights to the repository FormAtion Simulation Tool FAST user manual 5 1 4 Installation To install FAST add the main folder where you have decompressed the tool to the Matlab path e Use addpath D mytoolboxes FAST for a single use of the tool where you need to change D mytoolboxes FAST to the correct path on your computer e File gt Set Path if you plan to use the tool often 2 Toolbox Structure The toolbox is created using the object oriented capabilities of Matlab version 2008a and later The main objects in the toolbox are e Agents each object agent represents a physical agent and hence includes both a model of the agent and the local controller Key properties of the agent are its states and a key method is a function that computes the outputs and the states for the next time step e Formation this agent comprises all agents and serves as a mediator between the simula tion environment and the agents This object takes care of updating the communication topology when agents get out of range or an obstacle interrupts a communication channel e Simulation environment that is an object that takes care of the progress of the simulation i e main simulation loop and performing any necessary animations e Animator objects used with the graphical user interface GUI of the toolbox to allow easier control of the simulation and vi
11. in mind that the adjacency matrix has to be N 1x N 1 since for FAST agent with number 0 specifies a direct reference input virtual agent without dynamics she defines the topology in Figure 3 by the following 6 x 6 matrix FormAtion Simulation Tool FAST user manual 9 Figure 3 Graph representation of the communication topology with N 5 agents and reference input 0 4 Adjacency matrix agent 012345 adjacency 0 00000 this is the Reference point 101100 agent 1 receives from ref point agents 2 3 100010 agent 2 receives from ref point agent 4 010010 agent 3 receives from agents 1 4 001100 agent 4 receives from agents 2 3 00101 0 agent 5 receives from agents 2 amp 4 Finally Jane defines the reference inputs to the 5 agents compared to the virtual reference agent 0 For now Jane does not want to define a reference sequence for the virtual reference point but will rather use the manual control available in the GUI of FAST She knows that there will be some more information about that subject in Section 4 5 5 Absolute reference input for all agents absRefInput 0 1 0 agent 1 1 2 0 agent 2 1 2 0 1 3 0 1 3 0 agent 5 Finally she saves all the necessary data in a MAT file named Janes_init mat Jane knows what actually matters is not the name of the MAT file but rather the name of the variables She always pays attenti
12. ject oriented principle of inheritance However this time she is lucky as the authors of FAST have already implemented the non linear model of the quad rotor helicopters This turns out to be really helpful weeks later when she implements a non linear model of a walking robot by using the non linear model of the quad rotor as a template However for the moment all that she needs to do to change from the linear to the non linear model is to replace the first code fragment with this one 1 Load the agent and controller models load copter_models K load only controller 2 Specify the agents init state init position models 1 QuadrocopterModel K zeros 12 1 1 0 0 models 2 QuadrocopterModel K zeros 12 1 2 0 0 models 3 QuadrocopterModel K zeros 12 1 3 0 0 models 4 QuadrocopterModel K zeros 12 1 4 0 0 models 5 QuadrocopterModel K zeros 12 1 5 0 0 16 TUHH RTS Andrey Popov 4 8 A complete scenario Together Marta and Jane shorten up the definition of the scenario Jane has been working on to the following one can be found under demo FAST_demo_complete m in the folder of FAST hh Specify Agents and References de Le 3 Spatial Coordinates absRefInput O 1 0 agent 1 1 2 0 agent 2 1 2 OS 1 3 0 1 3 0 agent 5 hh Specify obstacles Wall shaped obstacle d1 0 O 2 d2 0 2 0 Load the agent and co
13. ntroller models load copter_models P K plant P and controller K models 2 Specify the agents init state init position QuadrocopterModel K zeros 12 1 Init_Pos ind N 5 num of agents Init_Pos 1 N zeros N 1 zeros N 1 for ind 1 2 linear models models ind LinearModel P end for ind 3 N non linear models models ind end output2Coordinates eye 3 h X y Z 4 Adjacency matrix agent 012345 adjacency 0 00000 this is the Reference point 101100 agent 1 receives from ref point agents 2 amp 3 100010 agent 2 receives from ref point agent 4 010010 agent 3 receives from agents 1 A 001100 agent 4 receives from agents 2 amp 3 00101 0 agent 5 receives from agents 2 amp 4 5 Absolute reference input for all agents Ball shaped obstacle where faces is used for visualization obstacles 1 struct type ball center 0 1 1 radius 0 5 faces 6 obstacles 2 struct type wall corner 3 0 1 K zeros 12 1 Init_Pos ind FormAtion Simulation Tool FAST user manual 17 hh Specify reference key points formationRefInput t_step 0 200 500 1000 ref pos at time steps formationRefInput refPos 000 at 0 020 at 200 05 1 at 500 0 6 2 at 1000 note the transpose hh Specify topology changes changeData Change topology
14. oller has the form as shown in Figure 2 the first 3 outputs of each quadrocopters y are simply the coordinates of the agent and the next 12 outputs are the states The controller uses the state information to locally stabilize the quad rotor and the other 3 outputs are send to other agents aka y E Fo Figure 2 Local feedback of single agent and its controller Jane is further delighted to understand that the additional input e of the controller is the average error of that particular agent in the multi agent system which corresponds to what she has been using previously e y Y rm J dl keJ where J is the set of agents from which agent 7 receives information and r are commanded positions At this place Jane makes a mental note that if she doesn t include a leader or an absolute reference to the formation later the whole multi agent system will attain the shape specified by r but not necessary on the positions r Having understood all that Jane sets upon defining a formation of N 5 agents in FAST First she loads the system model and the controller and defines the dynamics of the agents As she is not a big fan of loops she decides to do it by hand for now so that it is easier to make simple changes She sets the initial states of all quad rotors to zero and positions them on a distance of 1 unit from each other on the x axis 8 TUHH RTS Andrey Popov 1 Load the agent and cont
15. on when saving her data so that she avoids errors and problems later on save Janes_init mat models output2Coordinates adjacency absRefInput Next she evokes FAST clicks on New Simulation and selects the file Janes_init mat From now on it is all quite easy Jane starts the simulation by Start Simulation and lets it run for several seconds Then because she doesn t want to see the fine details but the overall behavior 10 TUHH RTS Andrey Popov she types 20 in the Animate every time steps box which forces FAST to visualize the position only after every 20 steps Further Jane un checks the Show trails box in the bottom right corner and uses the small button in the upper left corner to rotate the view and see the formation from different points At about 19th second she pauses the simulation with Interrupt Simulation and defines O 2 1 as a new reference point for the formation by typing the tree numbers in the Reference Input box After some more time Jane decides that she has seen enough for the time and ends the simulation Because she is not yet sure whether she will use the data later she decides to saves them by clicking on Save Data and typing in an appropriate name 4 2 Communication Delays Having succeeded with her first simulation of a quad rotor formation flight Jane decides to explore the effect of communication delays For the purpose she selects New Simulation and loads Janes_init m
16. roller models load copter_models P K plant P and controller K 2 Specify the agents init state init pos models 4X y z coordinate models 1 LinearModel P K zeros 12 1 1 0 0 models 2 LinearModel P K zeros 12 1 2 0 0 models 3 LinearModel P K zeros 12 1 3 0 0 models 4 LinearModel P K zeros 12 1 4 0 0 models 5 LinearModel P K zeros 12 1 5 0 0 Jane knows that by specifying the initial position as a 3 dimensional vector she is actually specifying the dimension of y from which the function LinearModel automatically deduces the dimension of to be the number of outputs of P z minus 3 i e 12 Next Jane specifies which of the signals in y should be plotted along which coordinate As she wants to obtain a 3 dimensional plot and as the signals in y are already in the correct sequence x y z she just defines 3 Spatial Coordinates output2Coordinates 100 010 00 1 Had she wanted to make a 2 d visualization in the x y plane she could have defined it as follows 3 Spatial Coordinates output2Coordinates 100 o 1 01 In both cases Jane knows that all three elements of y will be saved from FAST for later analysis In the next step Jane sets upon defining how the agents communicate with one another Late she will want to try some changing topologies but at first she decides to keep it simple Keeping
17. scusses this with a colleague of hers who has more experience with FAST who tells her that there is a simple solution to this she simply needs to define the entries in the adjacency matrix that shouldn t be distance dependent with a negative sign Jane gives it a thought an decides that only the communications between the reference signal and agents 1 and 2 need to be unbreakable for her purposes so she redefines the adjacency matrix as follows FormAtion Simulation Tool FAST user manual 11 4 Adjacency matrix agent 012345 adjacency 000000 this is the Reference point 101100 agent 1 receives from ref point agents 2 amp 3 100010 agent 2 receives from ref point agent 4 010010 agent 3 receives from agents 1 amp 4 001100 agent 4 receives from agents 2 amp 3 00101 0 agent 5 receives from agents 2 amp 4 and does not forget to export the whole settings as a MAT file save Janes_init mat models output2Coordinates adjacency absRefInput 4 4 Communication Obstacles Already having some experience with FAST Jane decides to try and add some communication obstacles As she had learned from Ros09 in FAST the agents do not collide yet but the communication connections can be broken due to obstacles Jane decides to try out both of the currently supported obstacles by FAST balls and walls She defines them and saves them to a file named Janes_obstacles mat The ball
18. sualization of the data For more information on programs please refer to Ros09 6 TUHH RTS Andrey Popov 3 Graphical User Interface The easiest way to perform a simulation of a multi agent system is by using the graphical user interface of FAST It is possible to perform a simulation of a MAS from a command line in Matlab but is not discussed here as it requires manually constructing all objects Agents Formation Simulation Manager etc in the correct order To start the GUI of FAST just evoke FAST in Matlab A snap shot of the GUI is shown in Figure I Formation Simulation 5 xi 9 XY KZ YZ 3D 6 9 sec steps New Simulation Resume Simulation End Simulation Plot Save Data Reference Input manual bd 000 Formation Specification directed Vectors Communication Time Delay frone z 2 steps 7 own Limited Communication Range 5 units m Communication Obstacles Vv Janes_all_sim mat Formation Changes u Animation Settings Axes Dimensions IV Show Communication Links IV Show Agent IDs J Show Trails Trail Length 10 Animate every J 10 time steps jauto Figure 1 Snap shot of the GUI of FAST The GUI is split on 3 main parts The big window in the upper left part is where the formation is visualized The buttons to the right of it are for
19. t Jane moves on to the next section 4 6 Formation Changes Communication Topology Change One last thing that Jane wants to simulate is the behavior of the above quad rotor formation when the communication topology is changing She decides that she wants to perform only two changes to the topology at time steps 100 and 200 correspondingly At the first change she wants to remove the link from the reference to agent 2 and add a link from agent 1 to agent 2 At the second change time she wants to switch to complete communication topology but leave agent 1 as the only one receiving information from the leader All this she defines via the following changeData cell array FormAtion Simulation Tool FAST user manual 13 changeData changeData 1 struct type commTopology t_change 100 change occurs at this time step adjacency 000000 101100 010010 010010 001100 001010 changeData 2 struct type gt commTopology t_change 200 step at which the change should occur adjacency 000000 101111 010111 011011 011101 011110 save Janes_changes mat changeData She starts FAST marks the check box under Formation Changes and chooses Janes_changes mat from the menu and waits until steps 100 and 200 to see the desired changes in the topology There are 3 other possibilities for types of changes that Jan
20. wAbsRef Input 2 4 1 2 4 1 with respect to virtual ref adjacency adj4 models new_agents note the brackets type deleteAgent t_change 700 deletelds 2 3 Note that now Janes_all_sim mat contains all above discussed features of FAST However if she just starts FAST and uses New Simulation then the obstacles reference signal and changes will not be loaded For example to load the changes she needs as before to check the box under Formation Changes and select Janes_all_sim mat References PPW09 U Pilz A Popov and H Werner Robust controller design for formation flight of quad rotor helicopters In Proc 48th IEEE Conference on Decision and Control pages 8322 8327 2009 PW09 A Popov and H Werner A robust control approach to formation control In Proc of the European Control Conference pages 4428 4433 2009 Ros09 H Rose Design and implementation of a simulation environment for multi agent system formation control Diplomarbeit Technische Universit t Hamburg Harburg 2009
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