Cafe-Mpc: A Cascaded-Fidelity Model Predictive Control Framework with Tuning-Free Whole-Body Control (2403.03995v3)

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.

• The paper proposes a cascaded-fidelity MPC that dynamically adjusts model precision along the prediction horizon to balance accuracy and computational load.
• It introduces a value-function-based whole-body controller (VWBC) that eliminates heuristic tuning by integrating control within a quadratic programming framework.
• The framework demonstrated robust real-world performance on the MIT Mini Cheetah, enabling advanced maneuvers like mid-air barrel rolls.

Analysis of {\sc Cafe-Mpc}: A Cascaded-Fidelity Model Predictive Control Framework

The framework presented, dubbed {\sc Cafe-Mpc}, represents an advancement in the optimization-based locomotion control of legged robots. The integration of cascaded-fidelity model predictive control (MPC) with a tuning-free whole-body controller (WBC) emphasizes both computational efficiency and performance improvement, key challenges inherent to real-time robotic applications.

The core of the paper is the proposal of a cascaded-fidelity MPC, a concept that builds upon and generalizes past efforts centered around Model Hierarchy Predictive Control (MHPC). By introducing an MPC scheme that dynamically reduces fidelity along the prediction horizon, the authors cleverly trade off model precision in the interest of computational efficiency. The framework incorporates a short horizon, high-fidelity plan governed by whole-body (WB) dynamics, while the distant term utilizes reduced-fidelity, Single-Rigid-Body (SRB) dynamics. Leveraging this approach allows for longer prediction horizons without a proportional increase in computational burden. Notably, the strategy of varying integration steps and relaxing constraints for long-term predictions further bolsters computational tractability.

The authors develop a modified multiple-shooting iteratively Linear Quadratic Regulator (MS-iLQR) solver tailored to solve the TO problems imbued in such a hybrid MPC setup. The framework handles all hybrid system intricacies by extending MS-DDP concepts to perform robustly on these mixed-fidelity objectives by meticulously managing state transitions across dynamics phases.

A standout aspect of this work is the value-function-based whole-body controller (VWBC). While traditional WBCs necessitate intricate and heuristic-dependent tuning, the VWBC circumvents this by employing the action-value function derived from the cascaded MPC. By embedding this in a quadratic programming (QP) problem, the VWBC establishes itself as a rigorous connector between high-level planning and low-level execution. It balances optimal performance derived from the value function with the physical constraints of the quadrupedal system, eliminating the need for additional control signal tuning.

Quantitative analysis reveals the robust performance of this framework across several locomotive tasks. Specifically, their evaluations strongly suggest that incorporating long-term predictions with coarse-model fidelity tangibly benefits state tracking over increased prediction horizons without drastically increasing computation costs. The deployment of the proposed control scheme on the quintessentially agile MIT Mini Cheetah underscores the practical capability of their control architecture. Importantly, the authors demonstrate an unprecedented running barrel roll with mid-air rotations on quadrupedal hardware, signaling a capacity to perform maneuvers beyond the current operational envelope.

Furthermore, the paper validates the accuracy and efficiency of the VWBC against traditional implementations. Through simulations and hardware experiments, the VWBC maintains constraints such as those imposed by friction cones, which are crucial for realistic robotic motion in dynamic environments.

This research offers compelling advancements for roboticists dedicated to enhancing the agility and dynamism of legged robots. The theoretical rigour in constraint handling, the innovative MPC formulation, and the seamless integration into whole-body control yield a framework ripe for further exploration. Potential future directions might involve extending this control structure to humanoids or deploying advanced dynamic maneuvers necessitating non-planar joint representations, enhancing versatility against diverse terrains, and possibly integrating adaptive complexity considerations to tackle scenarios with unforeseen environmental interactions or errors in contact timings.