# Learning Provably Robust Motion Planners Using Funnel Libraries

arXiv: https://arxiv.org/abs/2111.08733 · HTML: https://mlsanity.com/paper/2111.08733/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 56 references that are in the map.
- First posted on arXiv 16 Nov 2021.

## Builds on (most cited first, 30 of 32)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Domain Randomization for Transferring Deep Neural Networks from Simulation to the Real World](https://mlsanity.com/paper/1703.06907/) (2017)
- [Solving Rubik's Cube with a Robot Hand](https://mlsanity.com/paper/1910.07113/) (2019)
- [Computing Nonvacuous Generalization Bounds for Deep (Stochastic) Neural Networks with Many More Parameters than Training Data](https://mlsanity.com/paper/1703.11008/) (2017)
- [Learning Invariant Representations for Reinforcement Learning without Reconstruction](https://mlsanity.com/paper/2006.10742/) (2020)
- [Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learning](https://mlsanity.com/paper/2108.06266/) (2021)
- [Quantifying Generalization in Reinforcement Learning](https://mlsanity.com/paper/1812.02341/) (2018)
- [Certifying Some Distributional Robustness with Principled Adversarial Training](https://mlsanity.com/paper/1710.10571/) (2017)
- [Emergent Tool Use From Multi-Agent Autocurricula](https://mlsanity.com/paper/1909.07528/) (2019)
- [Multi-Goal Reinforcement Learning: Challenging Robotics Environments and Request for Research](https://mlsanity.com/paper/1802.09464/) (2018)
- [A Study on Overfitting in Deep Reinforcement Learning](https://mlsanity.com/paper/1804.06893/) (2018)
- [Sim-to-Real via Sim-to-Sim: Data-efficient Robotic Grasping via Randomized-to-Canonical Adaptation Networks](https://mlsanity.com/paper/1812.07252/) (2018)
- [DARLA: Improving Zero-Shot Transfer in Reinforcement Learning](https://mlsanity.com/paper/1707.08475/) (2017)
- [Contrastive Behavioral Similarity Embeddings for Generalization in Reinforcement Learning](https://mlsanity.com/paper/2101.05265/) (2021)
- [CausalWorld: A Robotic Manipulation Benchmark for Causal Structure and Transfer Learning](https://mlsanity.com/paper/2010.04296/) (2020)
- [The Limits and Potentials of Deep Learning for Robotics](https://mlsanity.com/paper/1804.06557/) (2018)
- [Evolved Policy Gradients](https://mlsanity.com/paper/1802.04821/) (2018)
- [Improving Generalization in Meta Reinforcement Learning using Learned Objectives](https://mlsanity.com/paper/1910.04098/) (2019)
- [Q-Learning for Robust Satisfaction of Signal Temporal Logic Specifications](https://mlsanity.com/paper/1609.07409/) (2016)
- [Backpropagation through Signal Temporal Logic Specifications: Infusing Logical Structure into Gradient-Based Methods](https://mlsanity.com/paper/2008.00097/) (2020)
- [Distributionally Robust Reinforcement Learning](https://mlsanity.com/paper/1902.08708/) (2019)
- [Distributional Robustness and Regularization in Reinforcement Learning](https://mlsanity.com/paper/2003.02894/) (2020)
- [Control Contraction Metrics: Convex and Intrinsic Criteria for Nonlinear Feedback Design](https://mlsanity.com/paper/1503.03144/) (2015)
- [Invariant Policy Optimization: Towards Stronger Generalization in Reinforcement Learning](https://mlsanity.com/paper/2006.01096/) (2020)
- [PAC-Bayes with Backprop](https://mlsanity.com/paper/1908.07380/) (2019)
- [Funnel Libraries for Real-Time Robust Feedback Motion Planning](https://mlsanity.com/paper/1601.04037/) (2016)
- [JuliaReach: a Toolbox for Set-Based Reachability](https://mlsanity.com/paper/1901.10736/) (2019)
- [PAC-Bayes Control: Learning Policies that Provably Generalize to Novel Environments](https://mlsanity.com/paper/1806.04225/) (2018)
- [Distributionally Robust Policy Learning via Adversarial Environment Generation](https://mlsanity.com/paper/2107.06353/) (2021)
- [Probably Approximately Correct Vision-Based Planning using Motion Primitives](https://mlsanity.com/paper/2002.12852/) (2020)

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

- [Sim-to-Lab-to-Real: Safe Reinforcement Learning with Shielding and Generalization Guarantees](https://mlsanity.com/paper/2201.08355/) (2022)

## Abstract (arXiv)

This paper presents an approach for learning motion planners that are accompanied with probabilistic guarantees of success on new environments that hold uniformly for any disturbance to the robot's dynamics within an admissible set. We achieve this by bringing together tools from generalization theory and robust control. First, we curate a library of motion primitives where the robustness of each primitive is characterized by an over-approximation of the forward reachable set, i.e., a "funnel". Then, we optimize probably approximately correct (PAC)-Bayes generalization bounds for training our planner to compose these primitives such that the entire funnels respect the problem specification. We demonstrate the ability of our approach to provide strong guarantees on two simulated examples: (i) navigation of an autonomous vehicle under external disturbances on a five-lane highway with multiple vehicles, and (ii) navigation of a drone across an obstacle field in the presence of wind disturbances.