Tactical Game-theoretic Decision-making with Homotopy Class Constraints

TL;DR

This paper introduces a homotopy-aware decision-making framework for urban game-theoretic motion planning that efficiently finds globally optimal Nash equilibria by partitioning the solution space into tactical homotopy classes, significantly reducing computation time.

Contribution

It presents a novel homotopy class-based approach for urban motion planning that improves computational efficiency and solution optimality in game-theoretic scenarios.

Findings

Achieves 78% average reduction in computational time.

On average 5-times faster than non-homotopic methods.

Successfully validated on urban driving scenarios from the rounD dataset.

Abstract

We propose a tactical homotopy-aware decision-making framework for game-theoretic motion planning in urban environments. We model urban driving as a generalized Nash equilibrium problem and employ a mixed-integer approach to tame the combinatorial aspect of motion planning. More specifically, by utilizing homotopy classes, we partition the high-dimensional solution space into finite, well-defined subregions. Each subregion (homotopy) corresponds to a high-level tactical decision, such as the passing order between pairs of players. The proposed formulation allows to find global optimal Nash equilibria in a computationally tractable manner by solving a mixed-integer quadratic program. Each homotopy decision is represented by a binary variable that activates different sets of linear collision avoidance constraints. This extra homotopic constraint allows to find solutions in a more efficient way (on a roundabout scenario on average 5-times faster). We experimentally validate the proposed approach on scenarios taken from the rounD dataset. Simulation-based testing in receding horizon fashion demonstrates the capability of the framework in achieving globally optimal solutions while yielding a 78% average decrease in the computational time with respect to an implementation without the homotopic constraints.