Hyp2Nav: Hyperbolic Planning and Curiosity for Crowd Navigation

TL;DR

Hyp$^2$Nav tackles crowd navigation by embedding MDP states in a hyperbolic space, enabling compact, hierarchical representations with only $2$-dimensional latent vectors. It introduces a hyperbolic policy network (HyperPlanner) and a hyperbolic curiosity module (HyperCuriosity) that operate entirely in hyperbolic space, yielding high success rates and rewards with markedly fewer parameters than Euclidean counterparts. The approach demonstrates strong performance in simple and complex CrowdNav scenarios, with interpretable signals such as the hyperbolic radius that correlate with uncertainty and interaction difficulty. Overall, HyperPlanner and HyperCuriosity together enable efficient, interpretable, and robust crowd navigation suitable for real-time embedded deployment and potentially broader hierarchical decision-making tasks.

Abstract

Autonomous robots are increasingly becoming a strong fixture in social environments. Effective crowd navigation requires not only safe yet fast planning, but should also enable interpretability and computational efficiency for working in real-time on embedded devices. In this work, we advocate for hyperbolic learning to enable crowd navigation and we introduce Hyp2Nav. Different from conventional reinforcement learning-based crowd navigation methods, Hyp2Nav leverages the intrinsic properties of hyperbolic geometry to better encode the hierarchical nature of decision-making processes in navigation tasks. We propose a hyperbolic policy model and a hyperbolic curiosity module that results in effective social navigation, best success rates, and returns across multiple simulation settings, using up to 6 times fewer parameters than competitor state-of-the-art models. With our approach, it becomes even possible to obtain policies that work in 2-dimensional embedding spaces, opening up new possibilities for low-resource crowd navigation and model interpretability. Insightfully, the internal hyperbolic representation of Hyp2Nav correlates with how much attention the robot pays to the surrounding crowds, e.g. due to multiple people occluding its pathway or to a few of them showing colliding plans, rather than to its own planned route. The code is available at https://github.com/GDam90/hyp2nav.

Figures (5)

• Figure 1: Visualizing the hyperbolic radius, the magnitude of the hyperbolic embeddings. Optimizing policies for crowd navigation in hyperbolic space results in embeddings that correlate with the robot's uncertainty in navigating within the obstacles in the scene. In the bottom left plot, the value of the hyperbolic radius (y-axis) is depicted over time (x-axis) in a typical rollout. The radius decreases when encountering obstacles directed towards the robot (top-left box), indicating reduced confidence in the robot's decisions. Notice that people are color-coded circle, the red-er, the larger is the robot attention to them (instead of self). Conversely, as the robot successfully navigates through challenging scenarios (bottom-right), the hyperbolic radius increases (top center), reflecting improved confidence and more straightforward decision-making toward the final goal (top right).
• Figure 2: Overview of Hyp$^2$Nav. We propose a hyperbolic policy network and a curiosity module to enable effective crowd navigation using only a few embedding dimensions. Modules in purple denote hyperbolic networks, which are composed of several concatenated h-MLP layers.
• Figure 3: Learning curves during training of the navigation time and success rate of Hyp$^2$Nav, SGDQ3N martinez2023, and SafeCrowdNav xu2023. The smoothing factor is 0.99.
• Figure 4: Comparison of the proposed Hyp$^2$Nav and SGDQ3N martinez2023 with different embedding dimensions. For both navigation time (left) and success rate (right), Hyp$^2$Nav achieves better performance across all the dimensionalities. In the case of 2 and 8, SGDQ3N martinez2023 fails to converge, whereas our proposed model shows the best performance with 2 dimensions.
• Figure 5: Correlation analysis between hyperbolic radius and robot uncertainty. Our hyperbolic embedding spaces inherently encode various navigation scenarios, ranging from simple to complex. Complex scenarios often require altering a planned trajectory or adjusting steering to avoid potential collisions. When dealing with many close obstacles and possible collisions, our policy obtains embeddings closer to the origin (purple and red frames in the Figure) . At the same time, easier and more certain cases (green and yellow frames) yield embeddings near the boundary of hyperbolic space. Hence, our approach comes with a simple way to measure how certain a robot is at any given time.