# Reachability-based Trajectory Safeguard (RTS): A Safe and Fast Reinforcement Learning Safety Layer for Continuous Control

arXiv: https://arxiv.org/abs/2011.08421 · HTML: https://mlsanity.com/paper/2011.08421/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Nov 2020.

## Built on by (most cited first, 28 of 28)

- [Enforcing Hard Constraints with Soft Barriers: Safe Reinforcement Learning in Unknown Stochastic Environments](https://mlsanity.com/paper/2209.15090/) (2022)
- [State-wise Safe Reinforcement Learning: A Survey](https://mlsanity.com/paper/2302.03122/) (2023)
- [Provably Safe Reinforcement Learning: Conceptual Analysis, Survey, and Benchmarking](https://mlsanity.com/paper/2205.06750/) (2022)
- [HardNet: Hard-Constrained Neural Networks with Universal Approximation Guarantees](https://mlsanity.com/paper/2410.10807/) (2024)
- [Safe Reinforcement Learning Using Black-Box Reachability Analysis](https://mlsanity.com/paper/2204.07417/) (2022)
- [Provably Safe Reinforcement Learning via Action Projection using Reachability Analysis and Polynomial Zonotopes](https://mlsanity.com/paper/2210.10691/) (2022)
- [Provably Safe Deep Reinforcement Learning for Robotic Manipulation in Human Environments](https://mlsanity.com/paper/2205.06311/) (2022)
- [Safe Reinforcement Learning of Dynamic High-Dimensional Robotic Tasks: Navigation, Manipulation, Interaction](https://mlsanity.com/paper/2209.13308/) (2022)
- [Safe Reinforcement Learning on the Constraint Manifold: Theory and Applications](https://mlsanity.com/paper/2404.09080/) (2024)
- [A Simple and Efficient Sampling-based Algorithm for General Reachability Analysis](https://mlsanity.com/paper/2112.05745/) (2021)
- [Safe Reinforcement Learning using Data-Driven Predictive Control](https://mlsanity.com/paper/2211.11027/) (2022)
- [Safe Reinforcement Learning with Dead-Ends Avoidance and Recovery](https://mlsanity.com/paper/2306.13944/) (2023)
- [RAIL: Reachability-Aided Imitation Learning for Safe Policy Execution](https://mlsanity.com/paper/2409.19190/) (2024)
- [From Demonstrations to Safe Deployment: Path-Consistent Safety Filtering for Diffusion Policies](https://mlsanity.com/paper/2511.06385/) (2025)
- [Bridging the gap between Learning-to-plan, Motion Primitives and Safe Reinforcement Learning](https://mlsanity.com/paper/2408.14063/) (2024)
- [Risk Conditioned Neural Motion Planning](https://mlsanity.com/paper/2108.01851/) (2021)
- [Safety-Driven Deep Reinforcement Learning Framework for Cobots: A Sim2Real Approach](https://mlsanity.com/paper/2407.02231/) (2024)
- [Traffic-Rule-Compliant Trajectory Repair via Satisfiability Modulo Theories and Reachability Analysis](https://mlsanity.com/paper/2412.15837/) (2024)
- [Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces](https://mlsanity.com/paper/2507.20853/) (2025)
- [Do No Harm: A Counterfactual Approach to Safe Reinforcement Learning](https://mlsanity.com/paper/2405.11669/) (2024)
- [X-Safe: Embodiment-Agnostic Safeguarding for Robot Arm Manipulation Policies via Action Masking](https://mlsanity.com/paper/2606.22278/) (2026)
- [Predictive Safety Shield for Dyna-Q Reinforcement Learning](https://mlsanity.com/paper/2511.21531/) (2025)
- [Dyna-Style Safety Augmented Reinforcement Learning: Staying Safe in the Face of Uncertainty](https://mlsanity.com/paper/2604.25508/) (2026)
- [Safe Deep RL for Intraoperative Planning of Pedicle Screw Placement](https://mlsanity.com/paper/2305.05354/) (2023)
- [Adaptive Policy Learning to Additional Tasks](https://mlsanity.com/paper/2305.15193/) (2023)
- [Absolute State-wise Constrained Policy Optimization: High-Probability State-wise Constraints Satisfaction](https://mlsanity.com/paper/2410.01212/) (2024)
- [Directional Constraints for Efficient Exploration in Safe Reinforcement Learning](https://mlsanity.com/paper/2607.12784/) (2026)
- [No Free Checker: A Survey of Verifiers for Robot Policies](https://mlsanity.com/paper/2609.09250/) (2026)

## Abstract (arXiv)

Reinforcement Learning (RL) algorithms have achieved remarkable performance in decision making and control tasks due to their ability to reason about long-term, cumulative reward using trial and error. However, during RL training, applying this trial-and-error approach to real-world robots operating in safety critical environment may lead to collisions. To address this challenge, this paper proposes a Reachability-based Trajectory Safeguard (RTS), which leverages reachability analysis to ensure safety during training and operation. Given a known (but uncertain) model of a robot, RTS precomputes a Forward Reachable Set of the robot tracking a continuum of parameterized trajectories. At runtime, the RL agent selects from this continuum in a receding-horizon way to control the robot; the FRS is used to identify if the agent's choice is safe or not, and to adjust unsafe choices. The efficacy of this method is illustrated on three nonlinear robot models, including a 12-D quadrotor drone, in simulation and in comparison with state-of-the-art safe motion planning methods.