Frequency-Aware Model Predictive Control

TL;DR

This paper introduces frequency-shaped cost functions in model predictive control to enhance robustness of legged robot motions against unmodeled dynamics and actuator bandwidth limitations, validated through simulations and hardware experiments.

Contribution

It proposes a novel frequency-aware cost function for trajectory optimization that improves robustness and feasibility in real-world robotic applications.

Findings

Enhanced motion tracking on quadrupedal robot ANYmal

Robust walking on terrain with unmodeled compliance

Improved torque and force trajectory accuracy

Abstract

Transferring solutions found by trajectory optimization to robotic hardware remains a challenging task. When the optimization fully exploits the provided model to perform dynamic tasks, the presence of unmodeled dynamics renders the motion infeasible on the real system. Model errors can be a result of model simplifications, but also naturally arise when deploying the robot in unstructured and nondeterministic environments. Predominantly, compliant contacts and actuator dynamics lead to bandwidth limitations. While classical control methods provide tools to synthesize controllers that are robust to a class of model errors, such a notion is missing in modern trajectory optimization, which is solved in the time domain. We propose frequency-shaped cost functions to achieve robust solutions in the context of optimal control for legged robots. Through simulation and hardware experiments we show that motion plans can be made compatible with bandwidth limits set by actuators and contact dynamics. The smoothness of the model predictive solutions can be continuously tuned without compromising the feasibility of the problem. Experiments with the quadrupedal robot ANYmal, which is driven by highly-compliant series elastic actuators, showed significantly improved tracking performance of the planned motion, torque, and force trajectories and enabled the machine to walk robustly on terrain with unmodeled compliance.