# QuasiNav: Asymmetric Cost-Aware Navigation Planning with Constrained Quasimetric Reinforcement Learning

arXiv: https://arxiv.org/abs/2410.16666 · HTML: https://mlsanity.com/paper/2410.16666/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL for robot navigation and UAV control, one of 15 directions in Deep reinforcement learning methods.
- Builds on 21 of its 34 references that are in the map.
- First posted on arXiv 22 Oct 2024.

## Placed in

- Deep reinforcement learning methods / [RL for robot navigation and UAV control](https://mlsanity.com/deeprl/rl-for-robot-navigation-and-uav-control/)

## Builds on (most cited first, 21 of 21)

- [Constrained Policy Optimization](https://mlsanity.com/paper/1705.10528/) (2017)
- [End-to-End Training of Deep Visuomotor Policies](https://mlsanity.com/paper/1504.00702/) (2015)
- [Reinforcement learning](https://mlsanity.com/paper/2405.10369/) (2024)
- [Cognitive Mapping and Planning for Visual Navigation](https://mlsanity.com/paper/1702.03920/) (2017)
- [Weakly- and Semi-Supervised Learning of a DCNN for Semantic Image Segmentation](https://mlsanity.com/paper/1502.02734/) (2015)
- [Optimal Goal-Reaching Reinforcement Learning via Quasimetric Learning](https://mlsanity.com/paper/2304.01203/) (2023)
- [GANav: Efficient Terrain Segmentation for Robot Navigation in Unstructured Outdoor Environments](https://mlsanity.com/paper/2103.04233/) (2021)
- [Learning Goal-Conditioned Policies Offline with Self-Supervised Reward Shaping](https://mlsanity.com/paper/2301.02099/) (2023)
- [An Inductive Bias for Distances: Neural Nets that Respect the Triangle Inequality](https://mlsanity.com/paper/2002.05825/) (2020)
- [Improved Representation of Asymmetrical Distances with Interval Quasimetric Embeddings](https://mlsanity.com/paper/2211.15120/) (2022)
- [On the Learning and Learnability of Quasimetrics](https://mlsanity.com/paper/2206.15478/) (2022)
- [CoverNav: Cover Following Navigation Planning in Unstructured Outdoor Environment with Deep Reinforcement Learning](https://mlsanity.com/paper/2308.06594/) (2023)
- [Learning-based Uncertainty-aware Navigation in 3D Off-Road Terrains](https://mlsanity.com/paper/2209.09177/) (2022)
- [Safe Navigation in Unstructured Environments by Minimizing Uncertainty in Control and Perception](https://mlsanity.com/paper/2306.14601/) (2023)
- [TopoNav: Topological Navigation for Efficient Exploration in Sparse Reward Environments](https://mlsanity.com/paper/2402.04061/) (2024)
- [Sensor-Based Distributionally Robust Control for Safe Robot Navigation in Dynamic Environments](https://mlsanity.com/paper/2405.18251/) (2024)
- [Quasimetric embeddings and their applications](https://mlsanity.com/paper/1608.01396/) (2016)
- [Predicting Energy Consumption of Ground Robots On Uneven Terrains](https://mlsanity.com/paper/2212.06393/) (2022)
- [Goal-Conditioned Reinforcement Learning from Sub-Optimal Data on Metric Spaces](https://mlsanity.com/paper/2402.10820/) (2024)
- [Predicting Energy Consumption and Traversal Time of Ground Robots for Outdoor Navigation on Multiple Types of Terrain](https://mlsanity.com/paper/2308.15978/) (2023)
- [EnCoMP: Enhanced Covert Maneuver Planning with Adaptive Threat-Aware Visibility Estimation using Offline Reinforcement Learning](https://mlsanity.com/paper/2403.20016/) (2024)

## Abstract (arXiv)

Autonomous navigation in unstructured outdoor environments is inherently challenging due to the presence of asymmetric traversal costs, such as varying energy expenditures for uphill versus downhill movement. Traditional reinforcement learning methods often assume symmetric costs, which can lead to suboptimal navigation paths and increased safety risks in real-world scenarios. In this paper, we introduce QuasiNav, a novel reinforcement learning framework that integrates quasimetric embeddings to explicitly model asymmetric costs and guide efficient, safe navigation. QuasiNav formulates the navigation problem as a constrained Markov decision process (CMDP) and employs quasimetric embeddings to capture directionally dependent costs, allowing for a more accurate representation of the terrain. This approach is combined with adaptive constraint tightening within a constrained policy optimization framework to dynamically enforce safety constraints during learning. We validate QuasiNav across three challenging navigation scenarios-undulating terrains, asymmetric hill traversal, and directionally dependent terrain traversal-demonstrating its effectiveness in both simulated and real-world environments. Experimental results show that QuasiNav significantly outperforms conventional methods, achieving higher success rates, improved energy efficiency, and better adherence to safety constraints.