Inferring Occluded Agent Behavior in Dynamic Games from Noise Corrupted Observations

TL;DR

An occlusion-aware game-theoretic inference method to estimate the locations of potentially occluded agents, and simultaneously infer the intentions of both visible and occluded agents, which best accounts for the observations of visible agents is presented.

Abstract

In mobile robotics and autonomous driving, it is natural to model agent interactions as the Nash equilibrium of a noncooperative, dynamic game. These methods inherently rely on observations from sensors such as lidars and cameras to identify agents participating in the game and, therefore, have difficulty when some agents are occluded. To address this limitation, this paper presents an occlusion-aware game-theoretic inference method to estimate the locations of potentially occluded agents, and simultaneously infer the intentions of both visible and occluded agents, which best accounts for the observations of visible agents. Additionally, we propose a receding horizon planning strategy based on an occlusion-aware contingency game designed to navigate in scenarios with potentially occluded agents. Monte Carlo simulations validate our approach, demonstrating that it accurately estimates the game model and trajectories for both visible and occluded agents using noisy observations of visible agents. Our planning pipeline significantly enhances navigation safety when compared to occlusion-ignorant baseline as well.

Figures (7)

• Figure 1: Occlusion-aware contingency game planner in an intersection scenario. The green vehicle can only see the red vehicle in the adjacent lane and is uncertain about the existence of occluded vehicles in the horizontal lanes. The green vehicles makes two assumptions: either 1) occluded vehicles exist. It can then use our proposed approach to estimate their trajectories by observing the red vehicle’s deceleration and plans the dark green trajectory; or 2) there are no occluded vehicles. It then only interacts with the red vehicle and plans the light green trajectory. Our contingency planning approach blends these two alternative strategies, while accounting for the fact that any occluded agents will be visible in the near future as the green vehicle approaches the intersection.
• Figure 2: 4-agent occlusion-aware contingency game. When $k<\ $$t_b$, agent $i$ considers two possibilities: $\theta_1$ (occluded agents are present) and $\theta_2$ (there are no occluded agents). It chooses a single control input $u_k^i=\ $$u_{k;\theta_1,i}^i$$=\ $$u_{k;\theta_2,i}^i$ balancing its uncertainty between both hypotheses $($$\theta_1$, $\theta_2$$)$. When $k\geq\ $$t_b$, any occluded agents are visible, and the $i^\text{th}$ agent will pick either $u_{k;\theta_1,i}^i$ or $u_{k;\theta_2,i}^i$ based on the ground truth value of $\theta$, i.e. the (non)existence of the occluded agents, which is assumed to be revealed at $t_b$.
• Figure 3: Demonstration for the 3-agent interaction scenario in Section \ref{['sec:three_player_interaction']}, with observation noise standard devioveration $\sigma=0.07$m across 20 different observation sequences, in which all agents apply open-loop Nash strategies. (a) Ground truth trajectory of each agent. (b) Observations, where the trajectories of the blue agents are corrupted by noise and the green agent is occluded. (c) Estimated trajectories by the occlusion-aware game estimator (ours). (d) Estimated trajectories by the occlusion-ignorant estimator (baseline). Our method 1) enables estimation of the occluded agent, and 2) provides more accurate estimation of observed agents than the baseline.
• Figure 4: Estimation performance for occlusion-aware game estimator (ours) and the occlusion-ignorant game estimator (baseline). (a) Parameter estimation performance. (b) Trajectory estimation performance. Our method estimates the weighting parameters and state trajectories of both visible and occluded agents more accurately than the baseline.
• Figure 5: Bootstrapped confidence intervals of the median for $d_\mathrm{min}$\ref{['eqn:minimumdist']} in 4, 6, and 8-agent planning scenarios. Left: Minimum distance between all pairs of agents. Right: Minimum distance between agents that are initially occluded to each other. Our method enables the agents to keep a larger distance from both visible and occluded agents than the occlusion-ignorant baseline, and this pattern persists across multiple values of $b(\theta_1)$ and $t_b$.