Inferring Occluded Agent Behavior in Dynamic Games with Noise-Corrupted Observations

Robots and autonomous vehicles must rely on sensor observations, e.g., from lidars and cameras, to comprehend their environment and provide safe, efficient services. In multi-agent scenarios, they must additionally account for other agents' intrinsic motivations, which ultimately determine the observed and future behaviors. Dynamic game theory provides a theoretical framework for modeling the behavior of agents with different objectives who interact with each other over time. Previous works employing dynamic game theory often overlook occluded agents, which can lead to risky navigation decisions. To tackle this issue, this paper presents an inverse dynamic game technique which optimizes the game model itself to infer unobserved, occluded agents' behavior that best explains the observations of visible agents. Our framework concurrently predicts agents' future behavior based on the reconstructed game model. Furthermore, we introduce and apply a novel receding horizon planning pipeline in several simulated scenarios. Results demonstrate that our approach offers 1) robust estimation of agents' objectives and 2) precise trajectory predictions for both visible and occluded agents from observations of only visible agents. Experimental findings also indicate that our planning pipeline leads to safer navigation decisions compared to existing baseline methods

Leadership Inference for Multi-Agent Interactions

Effectively predicting intent and behavior requires inferring leadership in multi-agent interactions. Dynamic games provide an expressive theoretical framework for modeling these interactions. Employing this framework, we propose a novel method to infer the leader in a two-agent game by observing the agents' behavior in complex, long-horizon interactions. We make two contributions. First, we introduce an iterative algorithm that solves dynamic two-agent Stackelberg games with nonlinear dynamics and nonquadratic costs, and demonstrate that it consistently converges. Second, we propose the Stackelberg Leadership Filter (SLF), an online method for identifying the leading agent in interactive scenarios based on observations of the game interactions. We validate the leadership filter's efficacy on simulated driving scenarios to demonstrate that the SLF can draw conclusions about leadership that match right-of-way expectations.Comment: 8 pages, 5 figures, submitted for publication to IEEE Robotics and Automation Letter

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

We present a novel algorithm for motion planning in complex, multi-agent scenarios in which occlusions prevent all agents from seeing one another. In this setting, the fundamental information that each agent has, i.e., the information structure of the interaction, is determined by the precise configurations in which agents come into view of one another. Occlusions prevent the use of existing pure feedback solutions, which assume availability of the state information of all agents at every time step. On the other hand, existing open-loop solutions only assume availability of the initial agent states. Thus, they do not fully utilize the information available to agents during periods of unhampered visibility. Here, we first introduce an algorithm for solving an occluded, linear-quadratic (LQ) dynamic game, which computes Nash equilibrium by using hybrid information and switching between feedback and open-loop information structures. We then design an efficient iterative algorithm for decision-making which exploits this hybrid information structure. Our method is demonstrated in overtaking and intersection traffic scenarios. Results confirm that our method outputs trajectories with favorable running times, converging much faster than recent methods employing reachability analysis

Robust Forecasting for Robotic Control: A Game-Theoretic Approach

Modern robots require accurate forecasts to make optimal decisions in the real world. For example, self-driving cars need an accurate forecast of other agents' future actions to plan safe trajectories. Current methods rely heavily on historical time series to accurately predict the future. However, relying entirely on the observed history is problematic since it could be corrupted by noise, have outliers, or not completely represent all possible outcomes. To solve this problem, we propose a novel framework for generating robust forecasts for robotic control. In order to model real-world factors affecting future forecasts, we introduce the notion of an adversary, which perturbs observed historical time series to increase a robot's ultimate control cost. Specifically, we model this interaction as a zero-sum two-player game between a robot's forecaster and this hypothetical adversary. We show that our proposed game may be solved to a local Nash equilibrium using gradient-based optimization techniques. Furthermore, we show that a forecaster trained with our method performs 30.14% better on out-of-distribution real-world lane change data than baselines

Alternating Direction Method of Multipliers for Decomposable Saddle-Point Problems

Saddle-point problems appear in various settings including machine learning, zero-sum stochastic games, and regression problems. We consider decomposable saddle-point problems and study an extension of the alternating direction method of multipliers to such saddle-point problems. Instead of solving the original saddle-point problem directly, this algorithm solves smaller saddle-point problems by exploiting the decomposable structure. We show the convergence of this algorithm for convex-concave saddle-point problems under a mild assumption. We also provide a sufficient condition for which the assumption holds. We demonstrate the convergence properties of the saddle-point alternating direction method of multipliers with numerical examples on a power allocation problem in communication channels and a network routing problem with adversarial costs.Comment: Accepted to 58th Annual Allerton Conference on Communication, Control, and Computin