On the structure of time-optimal trajectories for manipulators: the two d.o.f. case

The author considers the structure of solutions in time-optimal point to point motion for rigid manipulators. An analytic approach is presented based on the specific structure of two-link rigid manipulators. Partial results on regularity and the reduction of the number of types of solutions in comparison with the general affine problem are discussed. First, the Hamiltonian form of the dynamic model of manipulators is briefly recalled. The three kinds of candidate controls for general affine systems are presented. Generic properties of n-link manipulators related to their nice Lie-algebraic structure are considered. An original approach based on the existence of a cyclic generalized coordinate is shown to be fruitful and leads to a deeper analysis in the case of two degree-of-freedom (DOF) manipulators.<
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