Control of redundant robots on cyclic trajectories

The authors investigate the problem of how to achieve a cyclic joint behavior in redundant robots performing cyclic tasks, motivated by the fact that most singularity-free local resolution methods produce nonrepeatable joint motions. A controllability analysis of the inverse kinematic system makes it possible to recover the well-known repeatability conditions of T. Shamir and Y. Yomdin (1988), and to further conclude that no null space velocity can be specified if a repeatable scheme is sought, unless it is chosen as a linear term in the end-effector velocity. The problem of achieving asymptotic cyclicity for a given inversion strategy has been solved via suitable kinematic controls, which guarantee convergence to cyclic joint trajectories along the desired end-effector path. Depending on the structure of the feedforward and feedback terms in the control law, a number of different schemes are proposed, yielding exact or asymptotic end-effector tracking. The stability proofs and the satisfactory simulation results confirm the advantage of using these simple control strategies