# Whole-Body Nonlinear Model Predictive Control Through Contacts for Quadrupeds

arXiv: https://arxiv.org/abs/1712.02889 · HTML: https://mlsanity.com/paper/1712.02889/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Dec 2017.

## Built on by (most cited first, 20 of 20)

- [Reaching the Limit in Autonomous Racing: Optimal Control versus Reinforcement Learning](https://mlsanity.com/paper/2310.10943/) (2023)
- [Advanced Skills by Learning Locomotion and Local Navigation End-to-End](https://mlsanity.com/paper/2209.12827/) (2022)
- [Learning Quadruped Locomotion Using Differentiable Simulation](https://mlsanity.com/paper/2403.14864/) (2024)
- [Physics-Driven Data Generation for Contact-Rich Manipulation via Trajectory Optimization](https://mlsanity.com/paper/2502.20382/) (2025)
- [CACTO: Continuous Actor-Critic with Trajectory Optimization -- Towards global optimality](https://mlsanity.com/paper/2211.06625/) (2022)
- [Stability Verification of Neural Network Controllers using Mixed-Integer Programming](https://mlsanity.com/paper/2206.13374/) (2022)
- [Agile Maneuvers in Legged Robots: a Predictive Control Approach](https://mlsanity.com/paper/2203.07554/) (2022)
- [Identifying Important Sensory Feedback for Learning Locomotion Skills](https://mlsanity.com/paper/2306.17101/) (2023)
- [Quadruped Locomotion on Non-Rigid Terrain using Reinforcement Learning](https://mlsanity.com/paper/2107.02955/) (2021)
- [Reinforcement Learning For Quadrupedal Locomotion: Current Advancements And Future Perspectives](https://mlsanity.com/paper/2410.10438/) (2024)
- [Robust Contact State Estimation in Humanoid Walking Gaits](https://mlsanity.com/paper/2208.00278/) (2022)
- [Expanding Versatility of Agile Locomotion through Policy Transitions Using Latent State Representation](https://mlsanity.com/paper/2306.08224/) (2023)
- [SATA: Safe and Adaptive Torque-Based Locomotion Policies Inspired by Animal Learning](https://mlsanity.com/paper/2502.12674/) (2025)
- [Flexible Locomotion Learning with Diffusion Model Predictive Control](https://mlsanity.com/paper/2510.04234/) (2025)
- [GPO: Growing Policy Optimization for Legged Robot Locomotion and Whole-Body Control](https://mlsanity.com/paper/2601.20668/) (2026)
- [Curriculum Reinforcement Learning for Quadrotor Racing with Random Obstacles](https://mlsanity.com/paper/2602.24030/) (2026)
- [Energy-Efficient Arm Reaching for a Humanoid Robot via Deep Reinforcement Learning with Identified Power Models](https://mlsanity.com/paper/2606.15918/) (2026)
- [Adaptive MPC-based quadrupedal robot control under periodic disturbances](https://mlsanity.com/paper/2505.12361/) (2025)
- [RL-Augmented MPC for Non-Gaited Legged and Hybrid Locomotion](https://mlsanity.com/paper/2603.10878/) (2026)
- [Energy-Efficient Quadruped Locomotion with Compliant Feet](https://mlsanity.com/paper/2605.14411/) (2026)

## Abstract (arXiv)

In this work we present a whole-body Nonlinear Model Predictive Control approach for Rigid Body Systems subject to contacts. We use a full dynamic system model which also includes explicit contact dynamics. Therefore, contact locations, sequences and timings are not prespecified but optimized by the solver. Yet, thorough numerical and software engineering allows for running the nonlinear Optimal Control solver at rates up to 190 Hz on a quadruped for a time horizon of half a second. This outperforms the state of the art by at least one order of magnitude. Hardware experiments in form of periodic and non-periodic tasks are applied to two quadrupeds with different actuation systems. The obtained results underline the performance, transferability and robustness of the approach.