Abstract not found

We consider the problem of finding optimal gaits for a quadruped robot. Paths are sought which minimize the actuation energy required for walking in an attempt to approximate natural motion. The number of possible gaits for a quadruped is quite large when one considers varied orders of leg motion, different liftoff times, and various ground contact combinations for the legs. The problem is treated as a fully nonlinear optimal hybrid path planning problem on a 22dimensional state space. Modeling aspects, our numerical approach, and experimental results are discussed in this paper.

A large class of optimal control problems for hybrid dynamic systems can be formulated as mixed-integer optimal control problems (MIOCPs). It is the intrinsic combinatorial complexity, in addition to the nonlinearity of the continuous, multi-phase optimal control problems that is largely responsible for the challenges in the theoretical and numerical solution of MIOCPs. We present a new decomposition approach to numerically solving fairly general MICOPs with binary control variables. A Branch and Bound (B&B) technique is applied to efficiently search the entire discrete solution space performing a truncated binary tree search for the discrete variables maintaining upper and lower bounds on the performance index. The partially relaxed binary variables at an inner node define an optimal control problem with dynamic equations defined in multiple phases. Its global solution provides a lower bound on the performance index for all nodes of the subtree. If the lower bound for a given subtree is greater than the current global upper bound then that entire subtree need no longer be searched. The many optimal control problems with nonlinear, continuous state dynamics defined in multiple phases subject to nonlinear constraints are solved most efficiently by a sparse direct collocation transcription. Hereby, the multi-phase optimal control problem is transcribed to a sparse, large-scale nonlinear programming problem being solved efficiently by a tailored SQP method. Despite the high efficiency of the sparse direct collocation method, the efficiency of the decomposition technique for MIOCPs strongly depends on

Abstract not found