MPC for Humanoid Gait Generation: Stability and Feasibility
This work addresses the challenge of real-time, stable gait generation for humanoid robots, representing an incremental improvement by integrating stability constraints into MPC for enhanced feasibility.
The authors tackled the problem of generating stable and feasible gaits for humanoid robots by proposing IS-MPC, an intrinsically stable model predictive control framework that incorporates an explicit stability constraint to ensure bounded CoM trajectories relative to ZMP trajectories, with simulation and experimental validation on NAO and HRP-4 humanoids.
We present IS-MPC, an intrinsically stable MPC framework for humanoid gait generation which incorporates an explicit stability constraint in the formulation. The proposed method uses as prediction model a dynamically extended LIP where ZMP velocities are the control inputs, producing in real time a gait (including footsteps with the associated timing) that realizes omnidirectional motion commands coming from an external source. The stability constraint links the future ZMP velocities to the current system state so as to guarantee the essential requirement that the generated CoM trajectory is bounded with respect to the ZMP trajectory. Since the control horizon of the MPC algorithm is finite, only part of the future ZMP velocities are decision variables of the QP problem; the remaining part, called tail, must be either conjectured or anticipated using preview information on the reference motion. Several possible options for the tail are discussed, and each of them is shown to correspond to a specific terminal constraint. A theoretical analysis of the feasibility of the generic MPC iteration is developed and used to obtain sufficient conditions for recursive feasibility. Finally, it is proved that IS-MPC guarantees stability of the CoM/ZMP dynamics if it is recursively feasible. Simulation and experimental results on the NAO and the HRP-4 humanoids are presented to illustrate the performance of the proposed method.