Deformable Multibody Modeling for Model Predictive Control in Legged Locomotion with Embodied Compliance

The paper presents a method to stabilize dynamic gait for a legged robot with embodied compliance. Our approach introduces a unified description for rigid and compliant bodies to approximate their deformation and a formulation for deformable multibody systems. We develop the centroidal composite predictive deformed inertia (CCPDI) tensor of a deformable multibody system and show how to integrate it with the standard-of-practice model predictive controller (MPC). Simulation shows that the resultant control framework can stabilize trot stepping on a quadrupedal robot with both rigid and compliant spines under the same MPC configurations. Compared to standard MPC, the developed CCPDI-enabled MPC distributes the ground reactive forces closer to the heuristics for body balance, and it is thus more likely to stabilize the gaits of the compliant robot. A parametric study shows that our method preserves some level of robustness within a suitable envelope of key parameter values.