# Real-Time Motion Planning of Legged Robots: A Model Predictive Control Approach

arXiv: https://arxiv.org/abs/1710.04029 · HTML: https://mlsanity.com/paper/1710.04029/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Oct 2017.

## Built on by (most cited first, 10 of 10)

- [Fast and Efficient Locomotion via Learned Gait Transitions](https://mlsanity.com/paper/2104.04644/) (2021)
- [Articulated Object Interaction in Unknown Scenes with Whole-Body Mobile Manipulation](https://mlsanity.com/paper/2103.10534/) (2021)
- [ViNL: Visual Navigation and Locomotion Over Obstacles](https://mlsanity.com/paper/2210.14791/) (2022)
- [High-Performance Reinforcement Learning on Spot: Optimizing Simulation Parameters with Distributional Measures](https://mlsanity.com/paper/2504.17857/) (2025)
- [Agile Maneuvers in Legged Robots: a Predictive Control Approach](https://mlsanity.com/paper/2203.07554/) (2022)
- [Predicting Motion Plans for Articulating Everyday Objects](https://mlsanity.com/paper/2303.01484/) (2023)
- [Benchmarking Model Predictive Control and Reinforcement Learning Based Control for Legged Robot Locomotion in MuJoCo Simulation](https://mlsanity.com/paper/2501.16590/) (2025)
- [Expanding Versatility of Agile Locomotion through Policy Transitions Using Latent State Representation](https://mlsanity.com/paper/2306.08224/) (2023)
- [Opening Articulated Structures in the Real World](https://mlsanity.com/paper/2402.17767/) (2024)
- [Learning to enhance multi-legged robot on rugged landscapes](https://mlsanity.com/paper/2409.09473/) (2024)

## Abstract (arXiv)

We introduce a real-time, constrained, nonlinear Model Predictive Control for the motion planning of legged robots. The proposed approach uses a constrained optimal control algorithm known as SLQ. We improve the efficiency of this algorithm by introducing a multi-processing scheme for estimating value function in its backward pass. This pass has been often calculated as a single process. This parallel SLQ algorithm can optimize longer time horizons without proportional increase in its computation time. Thus, our MPC algorithm can generate optimized trajectories for the next few phases of the motion within only a few milliseconds. This outperforms the state of the art by at least one order of magnitude. The performance of the approach is validated on a quadruped robot for generating dynamic gaits such as trotting.