Optimal control theory and complexity of the time-optimal problem for rigid manipulators

This paper addresses the time-optimal point to point motion problem for rigid manipulators. The goal is to clarify analytical results provided by optimal control theory and the reduction of complexity they induce in a numerical search. The nature of exact and approximate solutions is discussed in the general n-link case. Then, extending results obtained previously, it is shown that a class of two-link rigid manipulators has many properties that are false for generic multi-input affine systems of the same dimensions. Particularly, a great improvement is realized from the complexity viewpoint. The results are of interest for both designing and verifying a numerical method