# Proofs of Technical Results Justifying an Algorithm of Reactive 3D Navigation of a Mobile Robot through an Unknown Tunnel

arXiv: https://arxiv.org/abs/1803.00803 · HTML: https://mlsanity.com/paper/1803.00803/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Mar 2018.

## Built on by (most cited first, 1 of 1)

- [Advanced Algorithms of Collision Free Navigation and Flocking for Autonomous UAVs](https://mlsanity.com/paper/2111.00166/) (2021)

## Abstract (arXiv)

A nonholonomic under-actuated robot with a bounded control range travels inside an unknown and unstructured 3D tunnel bounded by a generic 2D surface. The robot has access to the nearest point of the surface and measures the distance to the surface along any ray from a narrow beam emitted from the robot around the direction to the nearest point. The paper presents some mathematical facts underlying justification of the convergence and performance of a new navigation law that ensures constant advancement of the robot through the tunnel, along with respecting a given safety margin to its surface, driving the robot to the desired distance to it, and subsequently maintaining this distance.