Trajectory Tracking Control of Planar Underactuated Vehicles

Abstract

This work presents a novel nonlinear trajectory tracking control framework for general planar models of underactuated vehicles with six states and two control inputs. In this framework, feasible state trajectories are derived through utilization of nonholonomic constraints and a transitional trajectory is introduced that reduces the sixth order system into a fourth order error dynamic stabilization problem. A nonlinear sliding mode control law is employed to stabilize the error dynamics. It is shown that the control law is uniformly asymptotically stable if unknown disturbances and modeling uncertainties are bounded. The framework is applied to differential drive mobile robots, air vehicles operating in the vertical plane, and marine vehicles. Simulations are presented for models of in-house mobile robots and surface vessels subject to unknown disturbances.