A stopping algorithm for mechanical systems underactuated by one control

Analysis and control of underactuated mechanical systems in the nonzero velocity setting remains a challenging problem. In this paper, we demonstrate the utility of a recently developed alternative representation of the equations of motion for this large class of nonlinear control systems. The alternative representation gives rise to an intrinisic symmetric form. The generalized eigenvalues and eigenvectors associated with the symmetric form are used to determine control inputs that will drive a class of mechanical systems underactuated by one control to rest from an arbitrary initial configuration and velocity. We focus on systems whose symmetric form is indefinite for almost all configurations. Finally, we illustrate the stopping algorithm by presenting numerical simulation results for the planar rigid body, snakeboard and planar rollerblader.