Adaptive control for robot manipulators under ellipsoidal task space constraints

Motivated by applications in robot-assisted physical rehabilitation, this paper presents an adaptive control design for robot manipulators operating in an ellipsoidal constrained region. The ellipsoidal constraint problem is more challenging than the box constraint problem tackled in previous works, since the nonlinear constraint boundary cannot be handled in a decoupled manner along the dimensions of the task space. We introduce a novel Barrier Lyapunov Function (BLF) which contains a quotient of the squared norm of the tracking error over the ellipsoidal task space constraint. This function allows the task space constraint to be handled directly without requiring an intermediate mapping to the error space. We show that, under the proposed BLF-based adaptive control, the end-effector always remains in the constrained region despite the perturbing effects of online parameter adaptation and also the presence of bounded external disturbances. A simulation example illustrates the performance of the proposed control.