The general stochastic optimal control (SOC) problem in robotics scenarios is often too complex to be solved exactly and in near real time. A classical approximate solution is to first compute an optimal (deterministic) trajectory and then solve a local linear-quadratic-gaussian (LQG) perturbation model to handle the system stochasticity. We present a new algorithm for this approach which improves upon previous algorithms like iLQG. We consider a probabilistic model for which the maximum likelihood (ML) trajectory coincides with the optimal trajectory and which, in the LQG case, re-produces the classical SOC solution. The algorithm then utilizes approximate inference methods (similar to expectation propagation) that efficiently generalize to non-LQG systems. We demonstrate the algorithm on a simulated 39-DoF humanoid robot.
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