Game-Theoretic Planning for Risk-Aware Interactive Agents

Modeling the stochastic behavior of interacting agents is key for safe motion planning. In this paper, we study the interaction of risk-aware agents in a game-theoretical framework. Under the entropic risk measure, we derive an iterative algorithm for approximating the intractable feedback Nash equilibria of a risk-sensitive dynamic game. We use an iteratively linearized approximation of the system dynamics and a quadratic approximation of the cost function in solving a backward recursion for finding feedback Nash equilibria. In this respect, the algorithm shares a similar structure with DDP and iLQR methods. We conduct experiments in a set of challenging scenarios such as roundabouts. Compared to ignoring the game interaction or the risk sensitivity, we show that our risk-sensitive game-theoretic framework leads to more timeefficient, intuitive, and safe behaviors when facing underlying risks and uncertainty.

Authors

• Mingyu Wang 0002
• Negar Mehr
• Adrien Gaidon
• Mac Schwager

Keywords

• Uncertainty
• Sensitivity
• System dynamics
• Heuristic algorithms
• Stochastic processes
• Games
• Planning
• Cost Function
• Risk Measures
• Nash Equilibrium
• Roundabout
• Agent Interactions
• Dynamic Game
• Game-theoretic Framework
• Optimal Control
• Minimum Distance
• Quadratic Function
• Nonlinear Systems
• Control Input
• Risk Aversion
• Nonlinear Dynamics
• Intelligence Agencies
• State Trajectories
• Trajectory Optimization
• Autonomous Agents
• Linear Dynamics
• Linear Quadratic Gaussian
• Nonlinear Cost
• Conditional Value At Risk
• Nominal Trajectory
• Matrices Of Appropriate Dimensions
• Inverse Reinforcement Learning
• Quadratic Cost
• Certainty Equivalent
• General Case
• Optimal Control Policy