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

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 realworld 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. We combine this approach with adaptive constraint tightening. This ensures that safety constraints are dynamically enforced during learning. We validate QuasiNav on a Clearpath Jackal robot in 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 (13.6 % reduction in energy consumption compared to baseline methods), and better adherence to safety constraints.