Obstacle-Sensitive Trajectory Regulation via Gain Scheduling and Semidefinite Programming

The regulation of vehicle trajectories in the vicinity of obstacles must focus on “critical outputs,” which vary as a function of the vehicle's position relative to obstacles as exemplified by the task of parking a car. We present an application of linear parameter-varying techniques to address this problem. We design closed-loop stable, parameter-dependent controllers, whose strategy changes depending on the position of the vehicle in the obstacle environment. We also provide a fast and easy-to-implement algorithm for online controller construction. Last, the proposed approach is demonstrated on a three degrees-of-freedom helicopter.