Considering Uncertainty in Optimal Robot Control Through High-Order Cost Statistics

As the application of probabilistic models in robotic applications increases, a systematic robot control approach considering the effects of uncertainty becomes indispensable. Inspired by human sensorimotor findings, in this paper, we study the stochastic optimal control problem with high-order cost statistics in order to synthesize uncertainty-dependent actions in robotic scenarios with multiple uncertainty sources. We present locally optimal risk-sensitive and cost-cumulant solutions for settings with nonlinear dynamics, multiple additive uncertainty sources, and nonquadratic costs. The influence of each uncertainty source on the cost can be individually parameterized offering additional flexibility in the control design. We further analyze the case in which the static uncertain parameters are involved. The simulations of several linear and nonlinear settings with nonquadratic costs and an experiment on a real robotic platform validate our approach and illustrate its peculiarities.