# Frequency-Aware Model Predictive Control

arXiv: https://arxiv.org/abs/1809.04539 · HTML: https://mlsanity.com/paper/1809.04539/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Sep 2018.

## Built on by (most cited first, 5 of 5)

- [Learning Vision-Guided Quadrupedal Locomotion End-to-End with Cross-Modal Transformers](https://mlsanity.com/paper/2107.03996/) (2021)
- [Agile But Safe: Learning Collision-Free High-Speed Legged Locomotion](https://mlsanity.com/paper/2401.17583/) (2024)
- [Neural Volumetric Memory for Visual Locomotion Control](https://mlsanity.com/paper/2304.01201/) (2023)
- [GLiDE: Generalizable Quadrupedal Locomotion in Diverse Environments with a Centroidal Model](https://mlsanity.com/paper/2104.09771/) (2021)
- [Generalized Animal Imitator: Agile Locomotion with Versatile Motion Prior](https://mlsanity.com/paper/2310.01408/) (2023)

## Abstract (arXiv)

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.