A Nonsmooth Newton Method for Linear Model-Predictive Control in Tracking Tasks for a Mobile Robot With Obstacle Avoidance

We investigate tracking tasks for an automatic mobile robot with obstacle avoidance. To this end we apply a linear model-predictive control (LMPC) method to the nonlinear robot model. The LMPC uses a linearized robot model around the reference track and takes into account (fixed or moving) obstacles, which the robot has to avoid. The resulting discretized linear-quadratic optimal control problems are solved numerically by a semismooth Newton method, which turns out to be fast and robust. Furthermore, we propose a structure exploitation strategy to reduce the computational effort of the semismooth Newton method. Simulation results for a two-wheeled robot are presented to validate the control algorithm.