Mixed Control for Whole-Body Compliance of a Humanoid Robot

The hierarchical quadratic programming (HQP) is commonly applied to consider strict hierarchies of multi-tasks and robot's physical inequality constraints during whole-body compliance. However, for the one-step HQP, the solution can oscillate when it is close to the boundary of constraints. It is because the abrupt hit of the bounds gives rise to unrealizable jerks and even infeasible solutions. This paper proposes the mixed control, which blends the single-axis model predictive control (MPC) and proportional derivative (PD) control for the whole-body compliance to overcome these deficiencies. The MPC predicts the distances between the bounds and the control target of the critical tasks, and it provides smooth and feasible solutions by prediction and optimization in advance. However, applying MPC will inevitably increase the computation time. Therefore, to achieve a 500 Hz servo rate, the PD controllers still regulate other tasks to save computation resources. Also, we use a more efficient null space projection (NSP) whole-body controller instead of the HQP and distribute the single-axis MPCs into four CPU cores for parallel computation. Finally, we validate the desired capabilities of the proposed strategy via simulations and the experiment on the humanoid robot Walker X.