A Unified Approach to Stabilization, Trajectory Tracking, and Formation Control of Planar Underactuated Vehicles

This paper develops a procedure to design passivity-based controllers for stabilization, trajectory tracking, and formation control of a class of underactuated planar vehicles. The proposed approach uses generalized canonical transformations and energy shaping techniques and offers a framework to design stabilization and trajectory tracking controllers with the same structure. This approach is further applied to multi-agent formation stabilization and tracking problems. The proposed method can be used to solve motion control problems for a class of underactuated planar vehicles with a unified controller structure. As an example, the method is then applied to design controllers for planar mobile robots. Numerical simulations are presented for each case.