Zero-Sum Nonlinear Polynomial Game for Planar Robots Coordination

This paper proposes a scheme for the coordination of planar mobile robots based on Zero-Sum differential game model. The robots' dynamic are given in the polynomial approximation of the nonlinear model, we explore the so-called state-dependent Riccati equations to find a set of strategies that guarantee the effectively drive the robots to a particular formation. One of the robots acts as the leader following a free designed trayectory meanwhile the rest of the robots just follow him. The proposed solution is given as a polynomial Riccati-like state-dependent differential equation which utilizes a p-linear form tensor representation for its polynomial part. A numerical example is presented to illustrate effectiveness of the approach.