# Navigation without localisation: reliable teach and repeat based on the convergence theorem

arXiv: https://arxiv.org/abs/1711.05348 · HTML: https://mlsanity.com/paper/1711.05348/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Nov 2017.

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

- [RoboHop: Segment-based Topological Map Representation for Open-World Visual Navigation](https://mlsanity.com/paper/2405.05792/) (2024)
- [TANGO: Traversability-Aware Navigation with Local Metric Control for Topological Goals](https://mlsanity.com/paper/2509.08699/) (2025)
- [ObjectReact: Learning Object-Relative Control for Visual Navigation](https://mlsanity.com/paper/2509.09594/) (2025)
- [Multi-Platform Teach-and-Repeat Navigation by Visual Place Recognition Based on Deep-Learned Local Features](https://mlsanity.com/paper/2503.13090/) (2025)
- [Event-Based Visual Teach-and-Repeat via Fast Fourier-Domain Cross-Correlation](https://mlsanity.com/paper/2509.17287/) (2025)

## Abstract (arXiv)

We present a novel concept for teach-and-repeat visual navigation. The proposed concept is based on a mathematical model, which indicates that in teach-and-repeat navigation scenarios, mobile robots do not need to perform explicit localisation. Rather than that, a mobile robot which repeats a previously taught path can simply `replay' the learned velocities, while using its camera information only to correct its heading relative to the intended path. To support our claim, we establish a position error model of a robot, which traverses a taught path by only correcting its heading. Then, we outline a mathematical proof which shows that this position error does not diverge over time. Based on the insights from the model, we present a simple monocular teach-and-repeat navigation method. The method is computationally efficient, it does not require camera calibration, and it can learn and autonomously traverse arbitrarily-shaped paths. In a series of experiments, we demonstrate that the method can reliably guide mobile robots in realistic indoor and outdoor conditions, and can cope with imperfect odometry, landmark deficiency, illumination variations and naturally-occurring environment changes. Furthermore, we provide the navigation system and the datasets gathered at http://www.github.com/gestom/stroll_bearnav.