Real-Time Whole-Body Model Predictive Control for Versatile 3D Bipedal Locomotion via Novel Kino-Dynamic Model

Achieving versatile 3D bipedal locomotion in real-time is essential for humanoid robots navigating complex terrains such as stairs and uneven terrains. This paper extends our previous research on real-time WB-MPC by proposing a novel whole-body model predictive control (WB-MPC) framework that enables real-time 3D locomotion through an innovative kino-dynamic model integrating the virtual-mass-ellipsoid inverted pendulum model (VIPM) with the full kinematic model (FKM). Thanks to the dynamic properties of VIPM, the proposed kino-dynamic model accounts for the vertical center of mass motion, enabling stable locomotion on stair-like terrains. Furthermore, it also ensures real-time performance by maintaining continuity in the dynamics of the optimization problem. The modularized multi-layer perceptron based warm-start strategy and the ZMP-based whole-body controller, which were used in previous work to enhance the real-time performance and control effectiveness of the WB-MPC framework, have been modified and adapted in this study to suit the proposed model. Validated through simulations and real robot experiments on the humanoid TOCABI, our framework demonstrates stable stair ascent and descent with a WB-MPC latency below $18.25~ms$ and convergence in an average of 3.14 iterations. Moreover, the real-time capability of our proposed WB-MPC framework significantly improves balance recovery performance under external perturbations compared to existing algorithms.