Strong recursive feasibility in model predictive control of biped walking

Abstract

Realizing a stable walking motion requires satisfying a set of constraints. Model Predictive Control (MPC) is one of few suitable methods to handle such constraints. The capacity to satisfy constraints, which is usually called feasibility, is classically guaranteed recursively. In our applications, an important aspect is that the MPC scheme has to adapt continuously to the dynamic environment of the robot (e.g. collision avoidance, physical interaction). We aim therefore at guaranteeing recursive feasibility for all possible scenarios, which is called strong recursive feasibility. Recursive feasibility is classically obtained by introducing a terminal constraint at the end of the prediction horizon. Between two standard approaches for legged robot, in our applications we favor a capturable terminal constraint. When the robot is not really planning to stop and considers actually making a new step, recursive feasibility is not guaranteed anymore. We demonstrate numerically that recursive feasibility is actually guaranteed, even when a new step is added in the prediction horizon.