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

TL;DR

QuasiNav is introduced, a novel reinforcement learning framework that integrates quasimetric embeddings to explicitly model asymmetric costs and guide efficient, safe navigation and demonstrates its effectiveness in both simulated and real-world environments.

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, 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.

Figures (4)

• Figure 1: An illustration of asymmetric traversal costs during navigation. The green path ($15^\circ$ slope) represents a gentler, more energy-efficient route, while the red path ($10^\circ$ slope) is steeper and potentially riskier. This scenario demonstrates how QuasiNav's quasimetric embedding can capture the directional dependence of terrain traversability, favoring the longer but safer and more efficient green path over the shorter but more challenging red path.
• Figure 2: A sample state transition diagram with associated costs.
• Figure 3: Overview of QuasiNav System Architecture.
• Figure 4: Real-world navigation experiments using QuasiNav on a Clearpath Jackal robot, demonstrating its ability to optimize navigation in complex outdoor environments with asymmetric traversal costs: (a) Undulating Terrain Navigation: The robot selects a longer, gentler path (blue) over a steeper alternative (red), prioritizing energy efficiency. (b) Hill Traversal with Asymmetric Costs: QuasiNav chooses a winding, lower-gradient route (blue) instead of a direct steep climb (red), reflecting its understanding of asymmetric elevation costs. (c) Directionally Dependent Terrain Traversal: The robot opts for a longer but less challenging path (blue), avoiding a direct but energy-intensive route (red) through difficult terrain. These experiments validate QuasiNav's effectiveness in real-world scenarios, successfully translating learned policies from simulation to complex, unstructured outdoor settings.

Theorems & Definitions (1)

• proof