# Feedback MPC for Torque-Controlled Legged Robots

arXiv: https://arxiv.org/abs/1905.06144 · HTML: https://mlsanity.com/paper/1905.06144/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 May 2019.

## Built on by (most cited first, 21 of 21)

- [BeyondMimic: From Motion Tracking to Versatile Humanoid Control via Guided Diffusion](https://mlsanity.com/paper/2508.08241/) (2025)
- [Fast and Efficient Locomotion via Learned Gait Transitions](https://mlsanity.com/paper/2104.04644/) (2021)
- [VLMPC: Vision-Language Model Predictive Control for Robotic Manipulation](https://mlsanity.com/paper/2407.09829/) (2024)
- [RAYEN: Imposition of Hard Convex Constraints on Neural Networks](https://mlsanity.com/paper/2307.08336/) (2023)
- [Imitation Learning from MPC for Quadrupedal Multi-Gait Control](https://mlsanity.com/paper/2103.14331/) (2021)
- [Evaluating model-based planning and planner amortization for continuous control](https://mlsanity.com/paper/2110.03363/) (2021)
- [Learning Low-Frequency Motion Control for Robust and Dynamic Robot Locomotion](https://mlsanity.com/paper/2209.14887/) (2022)
- [A Learning Framework for Diverse Legged Robot Locomotion Using Barrier-Based Style Rewards](https://mlsanity.com/paper/2409.15780/) (2024)
- [Agile Maneuvers in Legged Robots: a Predictive Control Approach](https://mlsanity.com/paper/2203.07554/) (2022)
- [Continuous Versatile Jumping Using Learned Action Residuals](https://mlsanity.com/paper/2304.08663/) (2023)
- [Vision-Language Model Predictive Control for Manipulation Planning and Trajectory Generation](https://mlsanity.com/paper/2504.05225/) (2025)
- [Benchmarking Model Predictive Control and Reinforcement Learning Based Control for Legged Robot Locomotion in MuJoCo Simulation](https://mlsanity.com/paper/2501.16590/) (2025)
- [ZipMPC: Compressed Context-Dependent MPC Cost via Imitation Learning](https://mlsanity.com/paper/2507.13088/) (2025)
- [LocoMamba: Vision-Driven Locomotion via End-to-End Deep Reinforcement Learning with Mamba](https://mlsanity.com/paper/2508.11849/) (2025)
- [QuadKAN: KAN-Enhanced Quadruped Motion Control via End-to-End Reinforcement Learning](https://mlsanity.com/paper/2508.19153/) (2025)
- [Learning to enhance multi-legged robot on rugged landscapes](https://mlsanity.com/paper/2409.09473/) (2024)
- [WOLF-VLA: Whole-Body Humanoid Optimal Locomotion Framework for Vision-Language-Action Learning](https://mlsanity.com/paper/2606.25591/) (2026)
- [Effective Virtual Reality Teleoperation of an Upper-body Humanoid with Modified Task Jacobians and Relaxed Barrier Functions for Self-Collision Avoidance](https://mlsanity.com/paper/2411.07534/) (2024)
- [Constrained Stein Variational Gradient Descent for Robot Perception, Planning, and Identification](https://mlsanity.com/paper/2506.00589/) (2025)
- [Feedback-MPPI: Fast Sampling-Based MPC via Rollout Differentiation -- Adios low-level controllers](https://mlsanity.com/paper/2506.14855/) (2025)
- [Vision-Proprioception Fusion with Mamba2 in End-to-End Reinforcement Learning for Motion Control](https://mlsanity.com/paper/2509.07593/) (2025)

## Abstract (arXiv)

The computational power of mobile robots is currently insufficient to achieve torque level whole-body Model Predictive Control (MPC) at the update rates required for complex dynamic systems such as legged robots. This problem is commonly circumvented by using a fast tracking controller to compensate for model errors between updates. In this work, we show that the feedback policy from a Differential Dynamic Programming (DDP) based MPC algorithm is a viable alternative to bridge the gap between the low MPC update rate and the actuation command rate. We propose to augment the DDP approach with a relaxed barrier function to address inequality constraints arising from the friction cone. A frequency-dependent cost function is used to reduce the sensitivity to high-frequency model errors and actuator bandwidth limits. We demonstrate that our approach can find stable locomotion policies for the torque-controlled quadruped, ANYmal, both in simulation and on hardware.