# Force-and-moment-based Model Predictive Control for Achieving Highly Dynamic Locomotion on Bipedal Robots

arXiv: https://arxiv.org/abs/2104.00065 · HTML: https://mlsanity.com/paper/2104.00065/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Mar 2021.

## Built on by (most cited first, 4 of 4)

- [OGMP: Oracle Guided Multi-mode Policies for Agile and Versatile Robot Control](https://mlsanity.com/paper/2403.04205/) (2024)
- [BarlowWalk: Self-supervised Representation Learning for Legged Robot Terrain-adaptive Locomotion](https://mlsanity.com/paper/2508.00939/) (2025)
- [Autotuning Bipedal Locomotion MPC with GRFM-Net for Efficient Sim-to-Real Transfer](https://mlsanity.com/paper/2409.15710/) (2024)
- [PTRL: Prior Transfer Deep Reinforcement Learning for Legged Robots Locomotion](https://mlsanity.com/paper/2504.05629/) (2025)

## Abstract (arXiv)

In this paper, we propose a novel framework on force-and-moment-based Model Predictive Control (MPC) for dynamic legged robots. Specifically, we present a formulation of MPC designed for 10 degree-of-freedom (DoF) bipedal robots using simplified rigid body dynamics with input forces and moments. This MPC controller will calculate the optimal inputs applied to the robot, including 3-D forces and 2-D moments at each foot. These desired inputs will then be generated by mapping these forces and moments to motor torques of 5 actuators on each leg. We evaluate our proposed control design on physical simulation of a 10 degree-of-freedom (DoF) bipedal robot. The robot can achieve fast walking speed up to 1.6 m/s on rough terrain, with accurate velocity tracking. With the same control framework, our proposed approach can achieve a wide range of dynamic motions including walking, hopping, and running using the same set of control parameters.