Formation Control and Tracking for Co-operative Robots with Non-holonomic Constraints

Abstract

This paper mainly addresses formation control problem of non-holonomic systems in an optimized manner. Instead of using linearization to solve this problem approximately, we designed control laws with guaranteed global convergence by leveraging nonlinear transformations. Under this nonlinear transformation, consensus of non-holonomic robots can be converted into a stabilization problem, to which optimal treatment applies. This concept is then extended to the formation control and tracking problem for a team of robots following leader-follower strategy. A trajectory generator prescribes the feasible motion of virtual reference robot, a decentralized control law is used for each robot to track the reference while maintaining the formation. The asymptotic convergence of follower robots to the position and orientation of the reference robot is ensured using the Lyapunov function which is also generated using chained form differential equations. In order to witness the efficacy of the scheme, simulations results are presented for Unicycle and Car-like robots.