Relative Position Matters: Trajectory Prediction and Planning with Polar Representation

2025-08-15

AI Summary

A key challenge in autonomous vehicle trajectory prediction and planning lies in modeling dynamic interactions between the ego-vehicle and surrounding traffic agents, which exhibit distance- and direction-dependent geometric relationships. Conventional Cartesian-coordinate-based methods struggle to naturally encode such relative spatial dependencies. This paper introduces, for the first time, a full polar-coordinate framework for trajectory prediction and planning, explicitly representing relative positions via radius and angle. We design a dedicated polar encoder and a relation refinement module to enhance spatial awareness and structured reasoning. The approach supports multi-agent interaction modeling and long-horizon forecasting. Evaluated on Argoverse 2 and nuPlan benchmarks, our method achieves state-of-the-art performance, significantly outperforming leading Cartesian-based approaches. Results demonstrate the effectiveness and generalizability of polar-coordinate representations for traffic scene modeling.

Technology Category

• Planning, Routing, and Scheduling: Planning with Language Models
• Humans and AI: Human-Aware Planning and Behavior Prediction
• Multiagent Systems: Multiagent Planning

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Search and Retrieval-Augmented AI: Agentic search

Abstract

Trajectory prediction and planning in autonomous driving are highly challenging due to the complexity of predicting surrounding agents' movements and planning the ego agent's actions in dynamic environments. Existing methods encode map and agent positions and decode future trajectories in Cartesian coordinates. However, modeling the relationships between the ego vehicle and surrounding traffic elements in Cartesian space can be suboptimal, as it does not naturally capture the varying influence of different elements based on their relative distances and directions. To address this limitation, we adopt the Polar coordinate system, where positions are represented by radius and angle. This representation provides a more intuitive and effective way to model spatial changes and relative relationships, especially in terms of distance and directional influence. Based on this insight, we propose Polaris, a novel method that operates entirely in Polar coordinates, distinguishing itself from conventional Cartesian-based approaches. By leveraging the Polar representation, this method explicitly models distance and direction variations and captures relative relationships through dedicated encoding and refinement modules, enabling more structured and spatially aware trajectory prediction and planning. Extensive experiments on the challenging prediction (Argoverse 2) and planning benchmarks (nuPlan) demonstrate that Polaris achieves state-of-the-art performance.

Problem

• Modeling ego-surrounding vehicle relationships in Cartesian coordinates is suboptimal
• Polar coordinates better capture relative distance and directional influences
• Autonomous driving needs improved trajectory prediction and planning methods

Innovation

• Polar coordinate system representation
• Dedicated encoding and refinement modules
• State-of-the-art trajectory prediction and planning