1、A Practical Approach to Robotic Swarms,IASTED Conference on Control and Applications May 2008Howard M. Schwartz and Sidney N. Givigi Jr.,Objectives,Develop a practical approach to robotic swarms. Must be easy to implement and tractable. Must appeal to the control engineers sense of performance.,Lite
2、rature Review,Olfati-Saber, R., “Flocking for Multi-Agent Dynamic Systems: Algorithms and Theory”, IEEE Trans. Auto. Contr. 2006. Tanner, H.G., Jadbabaie, A., and Pappas G.J., “Stable Flocking of Mobile Agents, Part I: Fixed Topology”, Proc. of CDC, 2003. These methods require one design an attracti
3、on and repulsive function. Designing this function is not clear. Loss of control engineers intuition. Is the system working correctly?,Our Method,We use an inertial model,Define Connected and Unconnected Sets,Connected,Unconnected,The Forces on the Robots,The force on unconnected robots is a type of
4、 gravity force.,The force on the connected robots is a type of spring damper force,The total force on a given robot is,Where, is the unit vector from i to j And rij is the distance from i to j,Simulation Results,20 Robots, 100x100 grid, kp=4, kv=4, d0=10, kg=100, and r=12.,Swarming with obstacle avo
5、idance,Define a potential field.,Forces act along negative gradient of field,Then the complete force acting on each robot is,Simulation of robots swarming with obstacle avoidance,kf = 200 all other terms are the same as before.,Swarm robots with constant motion and obstacle avoidance.,Define specifi
6、ed velocity vxd = 1.0, then the force becomes,Stability Analysis,Why does this work.,Substituting for kv = 4 and kp = 4, we get the eigenvalues, 1= -1.17, 2 = -6.82, 3 = 0.,Stability of 3 Connected Robots,Linearize for small motions about the equilibrium point.,The force on robot 1 due to robot 3 du
7、e to small motions is,The force in the x direction then becomes,Stability of 3 robots,The acceleration of robot i in the x direction is,In the case of 3 connected robots we have 12 states and we can write the linearized equations in the form,Stability of 20 Robots,Using a computer to evaluate the co
8、nfiguration and recognizing only 3 distinct relationships between robots, we get the following maximum and minimum eigenvalues for the linearized system, max = -19.86, min = -0.120.47j Therefore the origin is asymptotically stable.,Experimental Results,The robots are given positions over bluetooth l
9、ink. The robots are controlled by a HC11 Handyboard. Web cameras installed in the ceiling track the robots.,Robots Following each other and doing obstacle avoidance,Conclusion,Practical approach to swarm robots Connected and unconnected sets, gravity and spring/damper forces,Potential fields define obstaclesThe swarm is locally stableExperimental results validate the method.,
