# An Error-State Model Predictive Control on Connected Matrix Lie Groups for Legged Robot Control

arXiv: https://arxiv.org/abs/2203.08728 · HTML: https://mlsanity.com/paper/2203.08728/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Mar 2022.

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

- [Energy-based Legged Robots Terrain Traversability Modeling via Deep Inverse Reinforcement Learning](https://mlsanity.com/paper/2207.03034/) (2022)
- [Equivariant Action Sampling for Reinforcement Learning and Planning](https://mlsanity.com/paper/2412.12237/) (2024)
- [SoLo T-DIRL: Socially-Aware Dynamic Local Planner based on Trajectory-Ranked Deep Inverse Reinforcement Learning](https://mlsanity.com/paper/2209.07996/) (2022)
- [Leveraging Symmetry to Accelerate Learning of Trajectory Tracking Controllers for Free-Flying Robotic Systems](https://mlsanity.com/paper/2409.11238/) (2024)
- [Can Euclidean Symmetry be Leveraged in Reinforcement Learning and Planning?](https://mlsanity.com/paper/2307.08226/) (2023)

## Abstract (arXiv)

This paper reports on a new error-state Model Predictive Control (MPC) approach to connected matrix Lie groups for robot control. The linearized tracking error dynamics and the linearized equations of motion are derived in the Lie algebra. Moreover, given an initial condition, the linearized tracking error dynamics and equations of motion are globally valid and evolve independently of the system trajectory. By exploiting the symmetry of the problem, the proposed approach shows faster convergence of rotation and position simultaneously than the state-of-the-art geometric variational MPC based on variational-based linearization. Numerical simulation on tracking control of a fully-actuated 3D rigid body dynamics confirms the benefits of the proposed approach compared to the baselines. Furthermore, the proposed MPC is also verified in pose control and locomotion experiments on a quadrupedal robot MIT Mini Cheetah.