Backstepping Control of Underactuated Planar Vehicles With Nonholonomic Constraints

This paper documents the development of a backstepping controller to track a generic underactuated planar vehicle along a trajectory, the implementation of the controller for a surface vessel model in simulation, and its performance validation in experiments. The tracking controller design is made possible by taking the six position / orientation and velocity states and transforming them into four error states. Designing the controller for a generic vehicle means that several different vehicle types can track a trajectory as long as they each satisfy the vehicle’s nonholonomic constraints. The backstepping controller derived herein can be applied to mobile robots, aircraft in the vertical plane, and surface vessels, with the last being implemented in this paper.