PD-like Regulation of Mechanical Systems with Prescribed Bounds of Exponential Stability: The Point-to-Point Case

This letter discusses an extension of the famous PD regulator implementing point to point motions with prescribed exponential rates of convergence. This is achieved by deriving a novel global exponential stability result, dealing with mechanical systems evolving on uni-dimensional invariant manifolds of the configuration space. The construction of closed loop controllers enforcing the existence of such manifolds is then discussed. Explicit upper and lower bounds of convergence are provided, and connected to the gains of the closed loop controller. Simulations are carried out, assessing the effectiveness of the controller and the tightness of the exponential bounds.