  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 unrealisable jerks and even infeasible
solutions. This paper proposes the mixed control, which blends the single-axis
model predictive control (MPC) and proportional derivate (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 optimisation 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.
