# Optimization-Based Control for Dynamic Legged Robots

arXiv: https://arxiv.org/abs/2211.11644 · HTML: https://mlsanity.com/paper/2211.11644/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Nov 2022.

## Built on by (most cited first, 30 of 35)

- [Reinforcement Learning for Versatile, Dynamic, and Robust Bipedal Locomotion Control](https://mlsanity.com/paper/2401.16889/) (2024)
- [HOMIE: Humanoid Loco-Manipulation with Isomorphic Exoskeleton Cockpit](https://mlsanity.com/paper/2502.13013/) (2025)
- [RL + Model-based Control: Using On-demand Optimal Control to Learn Versatile Legged Locomotion](https://mlsanity.com/paper/2305.17842/) (2023)
- [CTS: Concurrent Teacher-Student Reinforcement Learning for Legged Locomotion](https://mlsanity.com/paper/2405.10830/) (2024)
- [Being-0: A Humanoid Robotic Agent with Vision-Language Models and Modular Skills](https://mlsanity.com/paper/2503.12533/) (2025)
- [A Survey of Optimization-based Task and Motion Planning: From Classical To Learning Approaches](https://mlsanity.com/paper/2404.02817/) (2024)
- [Design and Control of a Bipedal Robotic Character](https://mlsanity.com/paper/2501.05204/) (2025)
- [A Learning Framework for Diverse Legged Robot Locomotion Using Barrier-Based Style Rewards](https://mlsanity.com/paper/2409.15780/) (2024)
- [Reinforcement Learning for Blind Stair Climbing with Legged and Wheeled-Legged Robots](https://mlsanity.com/paper/2402.06143/) (2024)
- [Control-oriented Clustering of Visual Latent Representation](https://mlsanity.com/paper/2410.05063/) (2024)
- [Generative Predictive Control: Flow Matching Policies for Dynamic and Difficult-to-Demonstrate Tasks](https://mlsanity.com/paper/2502.13406/) (2025)
- [Chasing Stability: Humanoid Running via Control Lyapunov Function Guided Reinforcement Learning](https://mlsanity.com/paper/2509.19573/) (2025)
- [Robot Crash Course: Learning Soft and Stylized Falling](https://mlsanity.com/paper/2511.10635/) (2025)
- [Accelerating and Scaling MPC-Guided Reinforcement Learning for Humanoid Locomotion and Manipulation](https://mlsanity.com/paper/2606.05687/) (2026)
- [Is Linear Feedback on Smoothed Dynamics Sufficient for Stabilizing Contact-Rich Plans?](https://mlsanity.com/paper/2411.06542/) (2024)
- [CrossTracker: Robust Multi-modal 3D Multi-Object Tracking via Cross Correction](https://mlsanity.com/paper/2411.18850/) (2024)
- [Vision-Language-Policy Model for Dynamic Robot Task Planning](https://mlsanity.com/paper/2512.19178/) (2025)
- [CACTO-BIC: Scalable Actor-Critic Learning via Biased Sampling and GPU-Accelerated Trajectory Optimization](https://mlsanity.com/paper/2602.19699/) (2026)
- [TurboMPC: Fast, Scalable, and Differentiable Model Predictive Control on the GPU](https://mlsanity.com/paper/2606.24039/) (2026)
- [Constrained Reinforcement Learning for Unstable Point-Feet Bipedal Locomotion Applied to the Bolt Robot](https://mlsanity.com/paper/2508.02194/) (2025)
- [INTENTION: Inferring Tendencies of Humanoid Robot Motion Through Interactive Intuition and Grounded VLM](https://mlsanity.com/paper/2508.04931/) (2025)
- [MASH: Cooperative-Heterogeneous Multi-Agent Reinforcement Learning for Single Humanoid Robot Locomotion](https://mlsanity.com/paper/2508.10423/) (2025)
- [Primitive Agentic First-Order Optimization](https://mlsanity.com/paper/2406.04841/) (2024)
- [Principles of frugal inference and control](https://mlsanity.com/paper/2406.14427/) (2024)
- [Autotuning Bipedal Locomotion MPC with GRFM-Net for Efficient Sim-to-Real Transfer](https://mlsanity.com/paper/2409.15710/) (2024)
- [Learning Impact-Rich Rotational Maneuvers via Centroidal Velocity Rewards and Sim-to-Real Techniques: A One-Leg Hopper Flip Case Study](https://mlsanity.com/paper/2505.12222/) (2025)
- [Whole-Body Constrained Learning for Legged Locomotion via Hierarchical Optimization](https://mlsanity.com/paper/2506.05115/) (2025)
- [Feedback-MPPI: Fast Sampling-Based MPC via Rollout Differentiation -- Adios low-level controllers](https://mlsanity.com/paper/2506.14855/) (2025)
- [One-shot Adaptation of Humanoid Whole-body Motion with Walking Priors](https://mlsanity.com/paper/2510.25241/) (2025)
- [Kinematics-Aware Multi-Policy Reinforcement Learning for Force-Capable Humanoid Loco-Manipulation](https://mlsanity.com/paper/2511.21169/) (2025)

## Abstract (arXiv)

In a world designed for legs, quadrupeds, bipeds, and humanoids have the opportunity to impact emerging robotics applications from logistics, to agriculture, to home assistance. The goal of this survey is to cover the recent progress toward these applications that has been driven by model-based optimization for the real-time generation and control of movement. The majority of the research community has converged on the idea of generating locomotion control laws by solving an optimal control problem (OCP) in either a model-based or data-driven manner. However, solving the most general of these problems online remains intractable due to complexities from intermittent unidirectional contacts with the environment, and from the many degrees of freedom of legged robots. This survey covers methods that have been pursued to make these OCPs computationally tractable, with specific focus on how environmental contacts are treated, how the model can be simplified, and how these choices affect the numerical solution methods employed. The survey focuses on model-based optimization, covering its recent use in a stand alone fashion, and suggesting avenues for combination with learning-based formulations to further accelerate progress in this growing field.