# Bridging the Gap Between Safety and Real-Time Performance in Receding-Horizon Trajectory Design for Mobile Robots

arXiv: https://arxiv.org/abs/1809.06746 · HTML: https://mlsanity.com/paper/1809.06746/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Sep 2018.

## Built on by (most cited first, 11 of 11)

- [The Safety Filter: A Unified View of Safety-Critical Control in Autonomous Systems](https://mlsanity.com/paper/2309.05837/) (2023)
- [Safe Reinforcement Learning Using Black-Box Reachability Analysis](https://mlsanity.com/paper/2204.07417/) (2022)
- [Safe Autonomous Racing via Approximate Reachability on Ego-vision](https://mlsanity.com/paper/2110.07699/) (2021)
- [CIMRL: Combining IMitation and Reinforcement Learning for Safe Autonomous Driving](https://mlsanity.com/paper/2406.08878/) (2024)
- [Deception Game: Closing the Safety-Learning Loop in Interactive Robot Autonomy](https://mlsanity.com/paper/2309.01267/) (2023)
- [Safe LLM-Controlled Robots with Formal Guarantees via Reachability Analysis](https://mlsanity.com/paper/2503.03911/) (2025)
- [Safe Large-Scale Robust Nonlinear MPC in Milliseconds via Reachability-Constrained System Level Synthesis on the GPU](https://mlsanity.com/paper/2604.07644/) (2026)
- [Safe Reinforcement Learning using Data-Driven Predictive Control](https://mlsanity.com/paper/2211.11027/) (2022)
- [Case Studies for Computing Density of Reachable States for Safe Autonomous Motion Planning](https://mlsanity.com/paper/2209.08073/) (2022)
- [No Free Checker: A Survey of Verifiers for Robot Policies](https://mlsanity.com/paper/2609.09250/) (2026)
- [Safe Multi-Robot Coordination via VLM-LLM Reasoning and Reachability Analysis](https://mlsanity.com/paper/2609.27816/) (2026)

## Abstract (arXiv)

To operate with limited sensor horizons in unpredictable environments, autonomous robots use a receding-horizon strategy to plan trajectories, wherein they execute a short plan while creating the next plan. However, creating safe, dynamically-feasible trajectories in real time is challenging; and, planners must ensure persistent feasibility, meaning a new trajectory is always available before the previous one has finished executing. Existing approaches make a tradeoff between model complexity and planning speed, which can require sacrificing guarantees of safety and dynamic feasibility. This work presents the Reachability-based Trajectory Design (RTD) method for trajectory planning. RTD begins with an offline Forward Reachable Set (FRS) computation of a robot's motion when tracking parameterized trajectories; the FRS provably bounds tracking error. At runtime, the FRS is used to map obstacles to parameterized trajectories, allowing RTD to select a safe trajectory at every planning iteration. RTD prescribes an obstacle representation to ensure that obstacle constraints can be created and evaluated in real time while maintaining safety. Persistent feasibility is achieved by prescribing a minimum sensor horizon and a minimum duration for the planned trajectories. A system decomposition approach is used to improve the tractability of computing the FRS, allowing RTD to create more complex plans at runtime. RTD is compared in simulation with Rapidly-Exploring Random Trees and Nonlinear Model-Predictive Control. RTD is also demonstrated in randomly-crafted environments on two hardware platforms: a differential-drive Segway, and a car-like Rover. The proposed method is safe and persistently feasible across thousands of simulations and dozens of real-world hardware demos.