Finite-gain L2 stability for position/force control of robot manipulators with constraint uncertainties

The present paper considers a position and force control method for robot manipulators under holonomic constraints. The constraint surface type is assumed to be known, whereas the parameters of the surface are not known. The parameters of the constraint surface are estimated using the least squares method, and the incorrect target position is modified optimally to be on the true constraint surface. In the proportional-integral-derivative (PID) controller, finite-gain L₂ stability is achieved based on passivity. The proposed method is verified through numerical simulations on a two-link robot arm with a planar constraint surface with parameter uncertainties.