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

Jumman Hossain1, Abu-Zaher Faridee1,2, Derrik Asher3, Jade Freeman3, Theron Trout4, Timothy Gregory3, Nirmalya Roy1
1Department of Information Systems, University of Maryland, Baltimore County, USA 2Amazon Inc., USA 3DEVCOM Army Research Lab, USA 4Stormfish Scientific Corporation, USA
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Asymmetric Traversal Costs in Outdoor Navigation

Asymmetric Traversal Costs
Fig. 1: An illustration of asymmetric traversal costs during navigation. The green path (10° slope) is gentler and more energy-efficient, while the red path (15° slope) is steeper and potentially riskier. This scenario demonstrates how QuasiNav’s quasimetric embedding captures the directional dependence of terrain traversability, favoring the longer but safer green path over the shorter, more challenging red path.

QuasiNav: Asymmetric Cost-Aware Navigation

Abstract

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,
  • Directionally dependent terrain traversal.

Experimental results show that QuasiNav significantly outperforms conventional methods, achieving higher success rates, improved energy efficiency, and better adherence to safety constraints.

BibTeX

@inproceedings{hossain2025quasinav,
  author       = {Hossain, Jumman and Faridee, Abu-Zaher and Asher, Derrik and Freeman, Jade and Trout, Theron and Gregory, Timothy and Roy, Nirmalya},
  title        = {QuasiNav: Learning Optimal Policies with Quasi-Potential Functions for Asymmetric Traversal},
  booktitle    = {Proceedings of the IEEE International Conference on Robotics and Automation (ICRA)},
  year         = {2025},
  pages        = {TBD},
  publisher    = {IEEE}
}