Balanced Standing on One Foot of Biped Robot Based on Three-Particle Model Predictive Control

Balancing is a fundamental task in the motion control of bipedal robots. Compared to two-foot balancing, one-foot balancing introduces new challenges, such as a smaller supporting polygon and control difficulty coming from the kinematic coupling between the center of mass (CoM) and the swinging leg. Although nonlinear model predictive control (NMPC) may solve this problem, it is not feasible to implement it on the actual robot because of its large amount of calculation. This paper proposes the three-particle model predictive control (TP-MPC) approach. It combines with the hierarchical whole-body control (WBC) to solve the one-leg balancing problem in real time. The bipedal robot's torso and two legs are modeled as three separate particles without inertia. The TP-MPC generates feasible swing leg trajectories, followed by the WBC to adjust the robot's center of mass. Since the three-particle model is linear, the TP-MPC requires less computational cost, which implies real-time execution on an actual robot. The proposed method is verified in simulation. Simulation results show that our method can resist much larger external disturbance than the WBC-only control scheme.