Using different Models of Computation for distributed control the Robot Diffusion Problem Sarah Bergbreiter Mentors Bruno Sinopoli Alessandro Pinto Thanks Outline What is a good Model of Computation for distributed control Robot Diffusion as an example of distributed control Modeling and Simulation using Esterel Discussion and Future Work Platform Based Design Concepts We have already completed the bottom triangle Robot Platform internal workings of sensors and actuators are isolated from the robot application an API including functionality of motors speed direction turning and sensors distance etc presented to control programs Now we would like a method of completing the top triangle FUNCTIONAL DESCRIPTION PLATFORM API HARDWARE ARCHITECTURE Why should we use a specific Model of Computation Distributed control problems involve complex timing many interconnected components that may need to communicate Classical control does not deal effectively with these issues MoC is a formal framework that allows Verification Code Synthesis Abstraction Abstraction Abstraction Synchronous v Asynchronous Models Synchronous Models shared global clock often easier to model and verify more difficult to apply to distributed systems Asynchronous Models no shared notion of time more difficult to model natural for distributed systems So what s the question SYNCHRONOUS FUNCTIONAL DESC For a distributed system it is easier to model and verify properties of the system using a synchronous MoC However the distributed system is naturally asynchronous Solution is to add another layer If I model my system with a synchronous MoC how do important control properties such as stability hold up under the transition to an asynchronous MoC What happens here GALS PLATFORM HARDWARE ARCHITECTURE What is Robot Diffusion and Why do we care Given n robots in a bounded area A the robots should try to maximize their distances between each other Lots of extensions to this definition maintain communication network maximize sensor coverage etc Useful for distributing sensors to maximize coverage mapping applications etc Robot Diffusion Distributed Controller 30 K FEEDBACK AND CONTROL LOOP T z 1 K ROBOT MOTOR T z 1 DISTANCE SENSOR Robot Diffusion Distributed Controller Assuming a stable system the steady state positions for each robot are robot1 0 robot2 1 robot3 2 robotN N 1 Stability Analysis for a 3 car Synchronous System zero delay Sampling Time System Gain K T Find the eigenvalues of the closed loop equation y k 1 A y k B u k Stability region decreases as number of robots or delay in feedback path increases by simulation STABLE REGION Feedback Gain Modeling in Esterel Functional Model robot1 robot2 getDistance Distance robotN setSpeed setDir Note As expected the functional model includes no details of implementation We are not constrained on how each robot finds the distance to its neighbor or on what kind of robot platform we use module robot1 input frontDistance1 double rearDistance1 double output setSpeed1 double setDir1 integer output getDistance constant GAIN 0 2 double var speed 0 0 double dir 1 integer in loop emit getDistance1 emit setSpeed1 speed emit setDir1 dir await frontDistance1 await rearDistance1 speed GAIN frontDistance1 rearDistance1 if speed 0 0 then dir 1 else dir 1 end if end loop end var end module Simulation of System in Esterel Master Code ROBOT1 DISTANCE COMM performs integration and senses distance information ROBOT2 ROBOTN functional Master code is used to provide the environment for the C code obtained from Esterel esterel A modulenames strl VIRTUAL MOTOR architecture Asynchrony is simulated by including a random delay between when a message should be sent to when it is actually sent Simulation Results of Unstable Attempts STABLE UNSTABLE Increasing Asynchrony msgs delayed Discussion and Future Work MoCs provide a new method of approaching distributed control problems We would prefer to model our systems in the synchronous domain to allow for easier modeling and verifiability but distributed systems are naturally asynchronous This project has shown that while the synchronously modeled system may hold key control properties stability these properties may no longer hold as the hardware platform becomes more asynchronous For future work theoretical results on the stability of the system with varying degrees of asynchrony code generation for the CotsBots platform from Esterel based on TinyOS
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