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Uncertainty-dependent optimal control for robot control considering high-order cost statistics

As the application of probabilistic models in robotic applications increases, the necessity of a systematic robot-control method that considers the effects of multiple uncertainty sources becomes more evident. Motivated by human sensorimotor findings, in this work we study the stochastic locally optimal feedback control problem with high-order cost statistics where dynamics have multiple additive noise sources and cost variability produced by each uncertainty source is evaluated marginally. We present risk-sensitive and cost-cumulant solutions for this problem for non-linear dynamics and non-quadratic costs. Locally optimal solutions are found by iteratively performing a linear quadratic approximation around a nominal trajectory, solving the local problem and updating the trajectory until convergence. Simulation results of a point mass robot and a two-link manipulator validate the applicability of the proposed approach and illustrate its peculiarities.