Cooperative tracking control and obstacles avoidance for single-integrator dynamics

In this paper, we present a unified cooperative tracking control with obstacle avoidance of multiple autonomous robots modeled by single integrator dynamics. The construction of the control law relies on a combination of optimal control theory and graph theory, and mainly based on the minimization of a Hamiltonian function in which the quadratic function consists of a consensus tracking cost function and an effort cost function and the Lyapunov function associated with the Hamiltonian contains an optimal cost to go function and an obstacle avoidance potential function. The control law proposed is simulated for four robots in two scenarios, in the first one, they should track a time-varying circular reference and in the second one, they should maintain a diamante formation while tracking a diamante virtual structure moving in a circular shape, in the two scenarios the robots are required to avoid obstacles which my appear in their detection regions, these simulations demonstrate the effectiveness of our control law.