Contributions to tracking control for mechanical systems on SE(2)

Compared to rich achievements for fully-actuated systems, intrinsic tracking control of underactuated systems is certainly a big challenge. In this paper, the problem is formulated by considering the natural configuration space for planar rigid bodies, the Special Euclidean group SE(2). First, we formulate the problem and implement a trajectory tracking control, which is well developed for fully-actuated systems on Lie groups based on navigation or error functions. Our new contribution is to propose error functions in some new variables compatible with the underactuation properties of the system and to design position tracking control according to the gradient vector field of these functions. To accomplish this task the gradient vector field is also weighted with some adaptable gains. We present some stability analyses and simulation results to support the approach.