Recoverability-Based Optimal Control for a Bipedal Walking Model with Foot Slip

Walking on slippery surfaces presents a challenge for bipedal walkers. A moving contact point between a biped foot and the ground introduces nonlinearities, which are usually not explicitly captured in the existing biped dynamics models. This work uses a two-mass linear inverted pendulum (LIP) model to describe the dynamics of walking gait in both the presence and absence of a foot slip. A single optimization-based controller is presented for control of both the normal walking and slip gait. The appropriate control strategy is determined by recoverability analysis. Based on the current state of the walker that lies within the recoverable or the fall-prone set, the proposed algorithm determines single and multiple step targets that lead the walker to recover to either the stationary configuration or to the periodic gait, respectively. An optimal control is designed within every swing phase to track the target states. When the within-step control is not sufficient, the algorithm searches for the optimal foot placement location and commands a recovery step to regain stability. The performance of the proposed control algorithm is validated by simulation, and results demonstrate successful recovery for within step and multi-step recovery of a walker.