Formation control and vision based localization of system of mobile robots

In this presentation we give an overview of different control algorithms designed for both set point and trajectory tracking problems for a set of mobile robots moving in environment with static obstacles. An arbitrary number of robots and obstacles can be used. Two new control algorithms are proposed. One is designed at the kinematic level and the second one at the dynamic level. It is assumed that we know all kinematical and dynamical parameters of robots. They can be different for all units which are used to build formation. Control scheme proposed at the kinematical level is based on a novel Vector Field Orientation (VFO) feedback control method developed in the Chair of Control and Systems Engineering with applications to a differentially-driven vehicle. We describe the control concept and control design methodology which originates from simple geometrical interpretations connected with the vehicle model structure. Novelty of the VFO method allows treating two considered control tasks - trajectory tracking and point stabilization - in a unified manner. Control system with VFO controllers reveal several practically desirable features like fast and non-oscillatory error convergence, simple interpretation of control inputs effect and, as a consequence, particular simplicity of the controller parametric synthesis. A new Lyapunov function candidate is proposed which takes into account control objectives and obstacle avoidance. It is shown that the proposed control algorithm is globally asymptotically stable to a small ball with radius which can be made arbitrary small. Next this result is extended to the case when dynamics of robots is taken into account using standard back-stepping technique. Numerical stability and robustness to potential functions high values near robots and obstacles are very important issues which are widely discussed along with computational complexity of all algorithms and their comparison with existing computational schemes. It is shown that increasing number of robots does not change computational burden significantly. Robots avoid obstacles both static and dynamic, in the case moving robots. It is shown how to avoid saddle points which are associated with obstacles in a set point control problem. Theoretical considerations are supported by simulation results which are widely discussed. Next experimental work is presented and it clearly illustrates theoretical considerations. The multi-robot test-bed that was designed and implemented in the Chair of Control and Systems Engineering at Poznan University of Technology and uses vision-based localization. The camera is located above the task space and active LED markers are mounted on the top of differentially driven mobile robots. The image form the camera is transmitted to the vision server that identifies markers and stores their positions and orientations in the array. Then the resulting array is broadcasted to the robots with UDP packets. The data can be used to control the multi-robot system. Unsolved problems of control of multi agent systems are outlined at the end of presentation.