First Order Approximation of Model Predictive Control Solutions for High Frequency Feedback

The lack of computational power on mobile robots is a well-known challenge when it comes to implementing a real-time MPC scheme to perform complex motions. Currently the best solvers are barely able to reach 100 Hz for computing the control of a whole-body legged model, while modern robots are expecting new torque references in less than 1 ms. This problem is usually tackled by using a handcrafted low-level tracking control whose inputs are the low-frequency trajectory computed by the MPC. We show that a linear state feedback controller naturally arises from the optimal control formulation and can be used directly in the low-level control loop along with other sensitivities of relevant time-varying parameters of the problem. When the optimal control problem is solved by DDP, this linear controller can be computed for cheap as a by-product of the backward pass, and corresponds in part to the classical Riccati gains. A side effect of our proposition is to show that Riccati gains are valuable assets that must be used to achieve an efficient control and that they are not stiffer than the optimal control scheme itself. We propose a complete implementation of this idea on a full-scale humanoid robot and demonstrate its importance with real experiments on the robot Talos.