A model-based adaptive controller for robot manipulators under geometr
ic endpoint constraint is proposed on the basis of joint-space orthogo
nalization of feedback signals. The adaptive law is devised by referri
ng 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 spac
e and orthogonal to the joint force vector caused by the contact (this
is called 'joint-space orthogonalization'), and (3) use of the fact t
hat important but uncertain physical parameters enter linearly in the
equation of motion of robots. The convergence of tracking errors on th
e surface is proved under an appropriate initial condition and the smo
othness of the surface. In addition, the convergence of force error is
proved provided that the endpoint is kept to in contact with the surf
ace.