# Tailoring Solution Accuracy for Fast Whole-body Model Predictive Control of Legged Robots

arXiv: https://arxiv.org/abs/2407.10789 · HTML: https://mlsanity.com/paper/2407.10789/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jul 2024.

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

- [Distillation-PPO: A Novel Two-Stage Reinforcement Learning Framework for Humanoid Robot Perceptive Locomotion](https://mlsanity.com/paper/2503.08299/) (2025)
- [SkillBlender: Towards Versatile Humanoid Whole-Body Loco-Manipulation via Skill Blending](https://mlsanity.com/paper/2506.09366/) (2025)
- [CusADi: A GPU Parallelization Framework for Symbolic Expressions and Optimal Control](https://mlsanity.com/paper/2408.09662/) (2024)
- [Enhancing Model-Based Step Adaptation for Push Recovery through Reinforcement Learning of Step Timing and Region](https://mlsanity.com/paper/2411.01000/) (2024)
- [Booster Gym: An End-to-End Reinforcement Learning Framework for Humanoid Robot Locomotion](https://mlsanity.com/paper/2506.15132/) (2025)
- [Residual MPC: Blending Reinforcement Learning with GPU-Parallelized Model Predictive Control](https://mlsanity.com/paper/2510.12717/) (2025)
- [Accelerating and Scaling MPC-Guided Reinforcement Learning for Humanoid Locomotion and Manipulation](https://mlsanity.com/paper/2606.05687/) (2026)
- [REFINE-DP: Diffusion Policy Fine-tuning for Humanoid Loco-manipulation via Reinforcement Learning](https://mlsanity.com/paper/2603.13707/) (2026)
- [AdaptManip: Learning Adaptive Whole-Body Object Lifting and Delivery with Online Recurrent State Estimation](https://mlsanity.com/paper/2602.14363/) (2026)
- [Autotuning Bipedal Locomotion MPC with GRFM-Net for Efficient Sim-to-Real Transfer](https://mlsanity.com/paper/2409.15710/) (2024)
- [Switch-JustDance: Benchmarking Whole Body Motion Tracking Controllers Using a Commercial Console Game](https://mlsanity.com/paper/2511.17925/) (2025)
- [GaitSpan: Growing Humanoid Locomotion from Walking to Running](https://mlsanity.com/paper/2607.12114/) (2026)
- [Opt2VLA: Force-Aware Vision-Language-Action for Contact-Rich Humanoid Whole-Body Manipulation](https://mlsanity.com/paper/2609.23968/) (2026)

## Abstract (arXiv)

Thanks to recent advancements in accelerating non-linear model predictive control (NMPC), it is now feasible to deploy whole-body NMPC at real-time rates for humanoid robots. However, enforcing inequality constraints in real time for such high-dimensional systems remains challenging due to the need for additional iterations. This paper presents an implementation of whole-body NMPC for legged robots that provides low-accuracy solutions to NMPC with general equality and inequality constraints. Instead of aiming for highly accurate optimal solutions, we leverage the alternating direction method of multipliers to rapidly provide low-accuracy solutions to quadratic programming subproblems. Our extensive simulation results indicate that real robots often cannot benefit from highly accurate solutions due to dynamics discretization errors, inertial modeling errors and delays. We incorporate control barrier functions (CBFs) at the initial timestep of the NMPC for the self-collision constraints, resulting in up to a 26-fold reduction in the number of self-collisions without adding computational burden. The controller is reliably deployed on hardware at 90 Hz for a problem involving 32 timesteps, 2004 variables, and 3768 constraints. The NMPC delivers sufficiently accurate solutions, enabling the MIT Humanoid to plan complex crossed-leg and arm motions that enhance stability when walking and recovering from significant disturbances.