# A Generalized Continuous Collision Detection Framework of Polynomial Trajectory for Mobile Robots in Cluttered Environments

arXiv: https://arxiv.org/abs/2206.13175 · HTML: https://mlsanity.com/paper/2206.13175/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jun 2022.

## Built on by (most cited first, 4 of 4)

- [NeuPAN: Direct Point Robot Navigation with End-to-End Model-based Learning](https://mlsanity.com/paper/2403.06828/) (2024)
- [Neural Potential Field for Obstacle-Aware Local Motion Planning](https://mlsanity.com/paper/2310.16362/) (2023)
- [A self-learning framework for adaptive free-form pipe routing in aeroengines](https://mlsanity.com/paper/2504.03669/) (2025)
- [LLM-Driven Scenario-Aware Planning for Autonomous Driving](https://mlsanity.com/paper/2601.21876/) (2026)

## Abstract (arXiv)

In this paper, we introduce a generalized continuous collision detection (CCD) framework for the mobile robot along the polynomial trajectory in cluttered environments including various static obstacle models. Specifically, we find that the collision conditions between robots and obstacles could be transformed into a set of polynomial inequalities, whose roots can be efficiently solved by the proposed solver. In addition, we test different types of mobile robots with various kinematic and dynamic constraints in our generalized CCD framework and validate that it allows the provable collision checking and can compute the exact time of impact. Furthermore, we combine our architecture with the path planner in the navigation system. Benefiting from our CCD method, the mobile robot is able to work safely in some challenging scenarios.