# Reachable Sets for Safe, Real-Time Manipulator Trajectory Design

arXiv: https://arxiv.org/abs/2002.01591 · HTML: https://mlsanity.com/paper/2002.01591/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Feb 2020.

## Built on by (most cited first, 6 of 6)

- [Safe Value Functions](https://mlsanity.com/paper/2105.12204/) (2021)
- [Efficient Motion Planning for Manipulators with Control Barrier Function-Induced Neural Controller](https://mlsanity.com/paper/2404.01184/) (2024)
- [RAIL: Reachability-Aided Imitation Learning for Safe Policy Execution](https://mlsanity.com/paper/2409.19190/) (2024)
- [An Empirical Analysis of the Use of Real-Time Reachability for the Safety Assurance of Autonomous Vehicles](https://mlsanity.com/paper/2205.01419/) (2022)
- [Robustness of Robotic Manipulation: Foundations and Frontiers](https://mlsanity.com/paper/2606.31494/) (2026)
- [Zero-Shot Reactive Obstacle Avoidance for Generative Robot Policies](https://mlsanity.com/paper/2609.35231/) (2026)

## Abstract (arXiv)

For robotic arms to operate in arbitrary environments, especially near people, it is critical to certify the safety of their motion planning algorithms. However, there is often a trade-off between safety and real-time performance; one can either carefully design safe plans, or rapidly generate potentially-unsafe plans. This work presents a receding-horizon, real-time trajectory planner with safety guarantees, called ARMTD (Autonomous Reachability-based Manipulator Trajectory Design). The method first computes (offline) a reachable set of parameterized trajectories for each joint of an arm. Each trajectory includes a fail-safe maneuver (braking to a stop). At runtime, in each receding-horizon planning iteration, ARMTD constructs a parameterized reachable set of the full arm in workspace and intersects it with obstacles to generate sub-differentiable, provably-conservative collision-avoidance constraints on the trajectory parameters. ARMTD then performs trajectory optimization over the parameters, subject to these constraints. On a 6 degree-of-freedom arm, ARMTD outperforms CHOMP in simulation, never crashes, and completes a variety of real-time planning tasks on hardware.