Model-based adaptive hybrid control for manipulators with geometric endpoint constraint

A model-based adaptive controller for robot manipulators under geometric endpoint constraint is proposed on the basis of joint-space orthogonalization of feedback signals. The adaptive law is devised by referring to the basic properties of robot dynamics, which are (1) passivity of robot dynamics, (2) use of feedback of residual error velocity and position signals that are projected to the tangent plane in joint space and orthogonal to the joint force vector caused by the contact (this is called 'joint-space orthogonalization'), and (3) use of the fact that important but uncertain physical parameters enter linearly in the equation of motion of robots. The convergence of tracking errors on the surface is proved under an appropriate initial condition and the smoothness of the surface. In addition, the convergence of force error is proved provided that the endpoint is kept to in contact with the surface.