Game-theoretic Occlusion-Aware Motion Planning: an Efficient Hybrid-Information Approach

TL;DR

The paper tackles multi-agent motion planning under occlusions by modeling it as a hybrid-information dynamic game that alternates between open-loop and feedback information. It introduces a Hybrid LQ Nash Game solver for known occlusion patterns and an iterative framework, OGSolve, that reduces nonlinear problems to sequences of hybrid-information LQ games to approximate Nash equilibria. The approach achieves cubic-time complexity for the LQ case and demonstrates reliable convergence in driving scenarios, providing a practical path toward real-time, occlusion-aware planning. The results show improved safety and decision-making compared with pure open-loop strategies while remaining robust to occlusions, highlighting the method's potential for scalable, occlusion-aware robotic navigation.

Abstract

We present a novel algorithm for game-theoretic trajectory planning, tailored for settings in which agents can only observe one another in specific regions of the state space. Such problems arise naturally in the context of multi-robot navigation, where occlusions due to environment geometry naturally mask agents' view of one another. In this paper, we formalize these settings as dynamic games with a hybrid information structure, which interleaves so-called "open-loop" periods (in which agents cannot observe one another) with "feedback" periods (with full state observability). We present two main contributions. First, we study a canonical variant of these hybrid information games in which agents' dynamics are linear, and objectives are convex and quadratic. Here, we build upon classical solution methods for the open-loop and feedback variants of these games to derive an algorithm for the hybrid information case that matches the cubic runtime of the classical settings. Second, we consider a far broader class of problems in which agents' dynamics are nonlinear, and objectives are nonquadratic; we reduce these problems to sequences of hybrid information linear-quadratic games and empirically demonstrate that iteratively solving these simpler problems with the proposed algorithm yields reliable convergence to approximate Nash equilibria through simulation studies of overtaking and intersection traffic scenarios.

Figures (7)

• Figure 1: Example of an occlusion scenario potentially benefiting from a hybrid information dynamic game formulation. The green and brown cars cannot see each other currently, yet each car's current actions will influence the cars’ future visibility and, ultimately, one another’s future strategy.
• Figure 2: Illustration of the novel hybrid information structure which we introduce in Algorithm \ref{['algo: solveLQHybrid']}. By taking terminal costs for each period from the cost-to-go of the next period, successive periods are linked together, which enables periods to reason about future occlusions. This figure represents a trajectory with two periods of occlusions and two periods of visibility $(o=2, v=2)$.
• Figure 3: Traffic Intersection: Player 1 (green car) and Player 2 (orange car) are occluded due to a stationary blue bus at an intersection. Both want to keep going forward on their respective paths.
• Figure 4: Three Player Overtaking Scenario: example of a converged trajectory obtained through OGSolve, with every $25^{th}$ time step marked. Players 1 & 3 were found to be occluded for about 15% of the time horizon.
• Figure 5: Hybrid information leads to better decision-making compared to the open-loop information structure. Comparison of OGSolve with pure feedback and pure open-loop solutions in the three-player overtaking scenario.

Theorems & Definitions (4)

• Remark 1
• Remark 2
• Remark 3
• Remark 4