ε-Saddle point solution for a nonlinear robot coordination game

Abstract This paper presents an approximated or -saddle point solution for a nonlinear game proposed to solve the coordination of a set of planar robots. The dynamic equation of each individual robot is given by the polynomial approximation of the nonlinear model, this introduces interesting challenges in the coordination control problem. Due to the difficulties in finding an exact solution, we explore the possibilities of the so-called state-dependent Riccati equations to find a near or -saddle point solution that effectively drives of the robots to a particular coordinated movement. A pre-designed trajectory is given to one of the robots in order to achieve the coordination by the group of robots. The proposed solution is given as a polynomial Riccati-like state-dependent differential equation which utilizes a -linear form tensor representation for its polynomial part. A numerical example is presented to illustrate the effectiveness of the approach.