# Reachability-based Trajectory Design with Neural Implicit Safety Constraints

arXiv: https://arxiv.org/abs/2302.07352 · HTML: https://mlsanity.com/paper/2302.07352/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Feb 2023.

## Built on by (most cited first, 5 of 5)

- [RAIL: Reachability-Aided Imitation Learning for Safe Policy Execution](https://mlsanity.com/paper/2409.19190/) (2024)
- [Transport of Algebraic Structure to Latent Embeddings](https://mlsanity.com/paper/2405.16763/) (2024)
- [Neural Implicit Swept Volume Models for Fast Collision Detection](https://mlsanity.com/paper/2402.15281/) (2024)
- [Toward Generalist Neural Motion Planners for Robotic Manipulators: Challenges and Opportunities](https://mlsanity.com/paper/2603.24318/) (2026)
- [Safe Multi-Robot Coordination via VLM-LLM Reasoning and Reachability Analysis](https://mlsanity.com/paper/2609.27816/) (2026)

## Abstract (arXiv)

Generating safe motion plans in real-time is a key requirement for deploying robot manipulators to assist humans in collaborative settings. In particular, robots must satisfy strict safety requirements to avoid self-damage or harming nearby humans. Satisfying these requirements is particularly challenging if the robot must also operate in real-time to adjust to changes in its environment.This paper addresses these challenges by proposing Reachability-based Signed Distance Functions (RDFs) as a neural implicit representation for robot safety. RDF, which can be constructed using supervised learning in a tractable fashion, accurately predicts the distance between the swept volume of a robot arm and an obstacle. RDF's inference and gradient computations are fast and scale linearly with the dimension of the system; these features enable its use within a novel real-time trajectory planning framework as a continuous-time collision-avoidance constraint. The planning method using RDF is compared to a variety of state-of-the-art techniques and is demonstrated to successfully solve challenging motion planning tasks for high-dimensional systems faster and more reliably than all tested methods.