An Approximate Inference Approach to Temporal Optimization in Optimal Control

Algorithms based on iterative local approximations present a practical approach to optimal control in robotic systems. However, they generally require the temporal parameters (for e.g. the movement duration or the time point of reaching an intermediate goal) to be specified a priori. Here, we present a methodology that is capable of jointly optimizing the temporal parameters in addition to the control command profiles. The presented approach is based on a Bayesian canonical time formulation of the optimal control problem, with the temporal mapping from canonical to real time parametrised by an additional control variable. An approximate EM algorithm is derived that efficiently optimizes both the movement duration and control commands offering, for the first time, a practical approach to tackling generic via point problems in a systematic way under the optimal control framework. The proposed approach, which is applicable to plants with non-linear dynamics as well as arbitrary state dependent and quadratic control costs, is evaluated on realistic simulations of a redundant robotic plant.