Contingency Model Predictive Control for Bipedal Locomotion on Moving Surfaces with a Linear Inverted Pendulum Model

Gait control of legged robotic walkers on dynamically moving surfaces (e.g., ships and vehicles) is challenging due to the limited balance control actuation and unknown surface motion. We present a contingent model predictive control (CMPC) for bipedal walker locomotion on moving surfaces with a linear inverted pendulum (LIP) model. The CMPC is a robust design that is built on regular model predictive control (MPC) to incorporate the "worst case" predictive motion of the moving surface. Integrated with an LIP model and walking stability constraints, the CMPC framework generates a set of consistent control inputs considering to anticipated uncertainties of the surface motions. Simulation results and comparison with the regular MPC for bipedal walking are conducted and presented. The results confirm the feasibility and superior performance of the proposed CMPC design over the regular MPC under various motion profiles of moving surfaces.