Linear acceleration-based redundancy resolution schemes that diverge in finite time

The minimum torque norm control scheme for redundant manipulators has long been known to exhibit instabilities. In the paper an analysis is made of a class of acceleration-level redundancy resolution schemes that includes this and other well-known schemes. It is proved that divergence of the joint velocity norm to infinity in finite time is possible, and in fact does occur for self-motions of mechanisms with one degree of redundancy under almost all such schemes in the class, i.e., generically. The schemes that do not diverge in finite time are associated with conserved quantities and include minimum acceleration norm and dynamically-consistent redundancy resolution schemes. It is also proved that exponential dissipation of space velocity cannot eliminate the divergence.