# Representation-Free Model Predictive Control for Dynamic Motions in Quadrupeds

arXiv: https://arxiv.org/abs/2012.10002 · HTML: https://mlsanity.com/paper/2012.10002/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Dec 2020.

## Built on by (most cited first, 13 of 13)

- [Concurrent Training of a Control Policy and a State Estimator for Dynamic and Robust Legged Locomotion](https://mlsanity.com/paper/2202.05481/) (2022)
- [Grow Your Limits: Continuous Improvement with Real-World RL for Robotic Locomotion](https://mlsanity.com/paper/2310.17634/) (2023)
- [Learning Visual Quadrupedal Loco-Manipulation from Demonstrations](https://mlsanity.com/paper/2403.20328/) (2024)
- [Text2Robot: Evolutionary Robot Design from Text Descriptions](https://mlsanity.com/paper/2406.19963/) (2024)
- [DecAP: Decaying Action Priors for Accelerated Imitation Learning of Torque-Based Legged Locomotion Policies](https://mlsanity.com/paper/2310.05714/) (2023)
- [PIP-Loco: A Proprioceptive Infinite Horizon Planning Framework for Quadrupedal Robot Locomotion](https://mlsanity.com/paper/2409.09441/) (2024)
- [SLR: Learning Quadruped Locomotion without Privileged Information](https://mlsanity.com/paper/2406.04835/) (2024)
- [Residual MPC: Blending Reinforcement Learning with GPU-Parallelized Model Predictive Control](https://mlsanity.com/paper/2510.12717/) (2025)
- [Whole-Brain Connectomic Graph Model Enables Whole-Body Locomotion Control in Fruit Fly](https://mlsanity.com/paper/2602.17997/) (2026)
- [Agile perceptive multi-skill locomotion for quadrupedal robots in the wild](https://mlsanity.com/paper/2607.13579/) (2026)
- [Autonomous Reality Modelling for Cultural Heritage Sites employing cooperative quadrupedal robots and unmanned aerial vehicles](https://mlsanity.com/paper/2402.12794/) (2024)
- [Ask1: Development and Reinforcement Learning-Based Control of a Custom Quadruped Robot](https://mlsanity.com/paper/2412.08019/) (2024)
- [Quadrupedal Robot Skateboard Mounting via Reverse Curriculum Learning](https://mlsanity.com/paper/2505.06561/) (2025)

## Abstract (arXiv)

This paper presents a novel Representation-Free Model Predictive Control (RF-MPC) framework for controlling various dynamic motions of a quadrupedal robot in three dimensional (3D) space. Our formulation directly represents the rotational dynamics using the rotation matrix, which liberates us from the issues associated with the use of Euler angles and quaternion as the orientation representations. With a variation-based linearization scheme and a carefully constructed cost function, the MPC control law is transcribed to the standard Quadratic Program (QP) form. The MPC controller can operate at real-time rates of 250 Hz on a quadruped robot. Experimental results including periodic quadrupedal gaits and a controlled backflip validate that our control strategy could stabilize dynamic motions that involve singularity in 3D maneuvers.