  The problem of optimal motion planing and control is fundamental in robotics.
However, this problem is intractable for continuous-time stochastic systems in
general and the solution is difficult to approximate if non-instantaneous
nonlinear performance indices are present. In this work, we provide an
efficient algorithm, PIPC (Probabilistic Inference for Planning and Control),
that yields approximately optimal policies with arbitrary higher-order
nonlinear performance indices. Using probabilistic inference and a Gaussian
process representation of trajectories, PIPC exploits the underlying sparsity
of the problem such that its complexity scales linearly in the number of
nonlinear factors. We demonstrate the capabilities of our algorithm in a
receding horizon setting with multiple systems in simulation.
