  This paper presents a stochastic/robust nonlinear model predictive control
(NMPC) to enhance the robustness of legged locomotion against contact
uncertainties. We integrate the contact uncertainties into the covariance
propagation of stochastic/robust NMPC framework by leveraging the guard
saltation matrix and an extended Kalman filter-like covariance update. We
achieve fast stochastic/robust NMPC computation by utilizing the zero-order
stochastic/robust NMPC algorithm with additional improvements in computational
efficiency concerning the feedback gains. We conducted numerical experiments
and demonstrate that the proposed method can accurately forecast future state
covariance and generate trajectories that satisfies constraints even in the
presence of the contact uncertainties. Hardware experiments on the perceptive
locomotion of a wheeled-legged robot were also carried out, validating the
feasibility of the proposed method in a real-world system with limited on-board
computation.
