Cafe-Mpc: A Cascaded-Fidelity Model Predictive Control Framework with Tuning-Free Whole-Body Control

TL;DR

The proposed framework enables accomplishing a gymnastic-style running barrel roll for the first time on quadruped hardware, where Cafe-Mpc runs at 50 Hz, and the solver spends on average 5.3 ms per iteration.

Abstract

This work introduces an optimization-based locomotion control framework for on-the-fly synthesis of complex dynamic maneuvers. At the core of the proposed framework is a cascaded-fidelity model predictive controller (Cafe-Mpc). Cafe-Mpc strategically relaxes the planning problem along the prediction horizon (i.e., with descending model fidelity, increasingly coarse time steps, and relaxed constraints) for computational and performance gains. This problem is numerically solved with an efficient customized multiple-shooting iLQR (MS-iLQR) solver that is tailored for hybrid systems. The action-value function from Cafe-Mpc is then used as the basis for a new value-function-based whole-body control (VWBC) technique that avoids additional tuning for the WBC. In this respect, the proposed framework unifies whole-body MPC and more conventional whole-body quadratic programming (QP), which have been treated as separate components in previous works. We study the effects of the cascaded relaxations in Cafe-Mpc on the tracking performance and required computation time. We also show that the Cafe-Mpc, if configured appropriately, advances the performance of whole-body MPC without necessarily increasing computational cost. Further, we show the superior performance of the proposed VWBC over the Riccati feedback controller in terms of constraint handling. The proposed framework enables accomplishing for the first time gymnastic-style running barrel rolls on the MIT Mini Cheetah. Video: https://youtu.be/YiNqrgj9mb8.

Figures (18)

• Figure 1: In-place barrel roll on the MIT Mini Cheetah accomplished with the proposed control framework. The robot performs an in-place barrel roll, followed by a hopping step, and a pacing gait. All motions and transitions are fully synthesized online. The results section includes more challenging tasks where the robot performs a barrel roll in the middle of running.
• Figure 2: An overview of the system architecture. The proposed control framework takes a reference trajectory as input, and outputs commands that are directly executable on the robot. The motion compiler consists of the Cafe-Mpc, the customized MS-iLQR solver for numerical optimization, and the VWBC. The MS-iLQR solver is used for offline TO as well. The MPC shares the same cost function for all tasks, and the VWBC is tuning-free.
• Figure 3: Illustration of forward sweep and backward sweep of MS-DDP for hybrid systems TO.
• Figure 4: Illustration of the sequentially cascaded-fidelity plans along the prediction horizon.
• Figure 5: Illustration of large defect when a new phase involving state jumps is added to the current MPC problem. In warm-starting the current MPC problem, the previous MPC is shifted forward by one step. The last state of the previous MPC solution is duplicated to initialize the newly created state, which produces a large defect due to the state jump. The illustration example shows when the MPC moves out of a flight phase, and adds in a new stance phase.

Theorems & Definitions (3)

• Remark 1
• Remark 2
• Remark 3