A Sum of Squares Approach for Trajectory Tracking Control of a Differential Drive Mobile Robot

Abstract

This paper tackles the trajectory tracking problem of a mobile robot with differential drive by presenting the sum-of-squares (SOS) framework to reformulate the Lyapunov stability theorem as SOS decompositions, thus enabling state feedback controller synthesis algorithmically. This is realized by implementing a SOS optimization program, as its solution will comprise the controller gains and the Lyapunov function coefficients. The controller should asymptotically stabilize the tracking error for different initial conditions and reference trajectories. Herein, a circle and a lemniscate are tested. Also, since only polynomials have a SOS decomposition, the nonlinear robot tracking model is recasted as a polynomial input-affine system to enable the program implementation.