Real-time Model Predictive Control with two-step optimization based on singularly perturbed system

In this paper, we propose a computationally efficient Model Predictive Control (MPC) towards development of a policy optimization method for realtime humanoid robot control. MPC is one of the useful approaches to effectively derive a feedback controller for nonlinear dynamical systems. However, realtime MPC for a robot system which has fast dynamics has been considered as impractical since MPC is computationally intensive. But due to the recent rapid improvements in computer performance, MPC with considering an approximated robot model which has less number of dimensionality than the original system is becoming a popular approach to design a humanoid controller for specific purposes such as balancing or walking. On the other hand, considering the full dynamics of the original humanoid model in MPC framework for realtime control is still a challenging problem. To cope with this problem, in our study, we propose a MPC method which has two-step optimization procedure based on the results of the transformation into a singularly perturbed system to reduce the computation time of optimization. We evaluate our proposed MPC in a simple toy problem and a simulated biped model. We show that the proposed method successfully reduces the computation time without significantly degrading the control performance.