Learning Control for Motions under Geometric Endpoint Constraint

Practices-based "learning control" is discussed for a class of robotic tasks under geometric endpoint constraints. A simple algorithm for updating the control input is proposed, which makes the next input be composed of the previous input plus modified terms of previous velocity and force errors at the robot endpoint constrained on a surface. Simulations are presented to demonstrate the convergence of both position and force trackings to a desired path and force specified on the surface. The problem and difficulty of theoretical proof of the convergence are then discussed and a few of partial results are presented with a rough sketch of their proofs.