# Dynamic Tube MPC: Learning Tube Dynamics with Massively Parallel Simulation for Robust Safety in Practice

arXiv: https://arxiv.org/abs/2411.15350 · HTML: https://mlsanity.com/paper/2411.15350/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 43 references that are in the map.
- First posted on arXiv 22 Nov 2024.

## Builds on (most cited first, 25 of 25)

- [Isaac Gym: High Performance GPU-Based Physics Simulation For Robot Learning](https://mlsanity.com/paper/2108.10470/) (2021)
- [Learning to Walk in Minutes Using Massively Parallel Deep Reinforcement Learning](https://mlsanity.com/paper/2109.11978/) (2021)
- [Neural Lyapunov Control](https://mlsanity.com/paper/2005.00611/) (2020)
- [Reinforcement Learning for Versatile, Dynamic, and Robust Bipedal Locomotion Control](https://mlsanity.com/paper/2401.16889/) (2024)
- [Safe Nonlinear Control Using Robust Neural Lyapunov-Barrier Functions](https://mlsanity.com/paper/2109.06697/) (2021)
- [DeepReach: A Deep Learning Approach to High-Dimensional Reachability](https://mlsanity.com/paper/2011.02082/) (2020)
- [Real-time Neural-MPC: Deep Learning Model Predictive Control for Quadrotors and Agile Robotic Platforms](https://mlsanity.com/paper/2203.07747/) (2022)
- [Berkeley Humanoid: A Research Platform for Learning-based Control](https://mlsanity.com/paper/2407.21781/) (2024)
- [Safety Certification for Stochastic Systems via Neural Barrier Functions](https://mlsanity.com/paper/2206.01463/) (2022)
- [FaSTrack: a Modular Framework for Real-Time Motion Planning and Guaranteed Safe Tracking](https://mlsanity.com/paper/2102.07039/) (2021)
- [Learning for CasADi: Data-driven Models in Numerical Optimization](https://mlsanity.com/paper/2312.05873/) (2023)
- [Deep Learning Tubes for Tube MPC](https://mlsanity.com/paper/2002.01587/) (2020)
- [Dynamic Tube MPC for Nonlinear Systems](https://mlsanity.com/paper/1907.06553/) (2019)
- [Model-Free Safety-Critical Control for Robotic Systems](https://mlsanity.com/paper/2109.09047/) (2021)
- [Safety-Critical Control for Autonomous Systems: Control Barrier Functions via Reduced-Order Models](https://mlsanity.com/paper/2403.09865/) (2024)
- [Planning, Fast and Slow: A Framework for Adaptive Real-Time Safe Trajectory Planning](https://mlsanity.com/paper/1710.04731/) (2017)
- [Adaptive MPC under Time Varying Uncertainty: Robust and Stochastic](https://mlsanity.com/paper/1909.13473/) (2019)
- [A System Level Approach to Tube-based Model Predictive Control](https://mlsanity.com/paper/2103.02460/) (2021)
- [Generative Modeling of Residuals for Real-Time Risk-Sensitive Safety with Discrete-Time Control Barrier Functions](https://mlsanity.com/paper/2311.05802/) (2023)
- [Tube-Certified Trajectory Tracking for Nonlinear Systems With Robust Control Contraction Metrics](https://mlsanity.com/paper/2109.04453/) (2021)
- [Multi-Rate Planning and Control of Uncertain Nonlinear Systems: Model Predictive Control and Control Lyapunov Functions](https://mlsanity.com/paper/2204.00152/) (2022)
- [Robust Agility via Learned Zero Dynamics Policies](https://mlsanity.com/paper/2409.06125/) (2024)
- [Robust Approximate Simulation for Hierarchical Control of Linear Systems under Disturbances](https://mlsanity.com/paper/2003.04136/) (2020)
- [Nonlinear Model Predictive Control of a 3D Hopping Robot: Leveraging Lie Group Integrators for Dynamically Stable Behaviors](https://mlsanity.com/paper/2209.11808/) (2022)
- [Constructive Nonlinear Control of Underactuated Systems via Zero Dynamics Policies](https://mlsanity.com/paper/2408.14749/) (2024)

## Built on by (most cited first, 1 of 1)

- [Learning for Layered Safety-Critical Control with Predictive Control Barrier Functions](https://mlsanity.com/paper/2412.04658/) (2024)

## Abstract (arXiv)

Safe navigation of cluttered environments is a critical challenge in robotics. It is typically approached by separating the planning and tracking problems, with planning executed on a reduced order model to generate reference trajectories, and control techniques used to track these trajectories on the full order dynamics. Inevitable tracking error necessitates robustification of the nominal plan to ensure safety; in many cases, this is accomplished via worst-case bounding, which ignores the fact that some trajectories of the planning model may be easier to track than others. In this work, we present a novel method leveraging massively parallel simulation to learn a dynamic tube representation, which characterizes tracking performance as a function of actions taken by the planning model. Planning model trajectories are then optimized such that the dynamic tube lies in the free space, allowing a balance between performance and safety to be traded off in real time. The resulting Dynamic Tube MPC is applied to the 3D hopping robot ARCHER, enabling agile and performant navigation of cluttered environments, and safe collision-free traversal of narrow corridors.