Desensitization and Deception in Differential Games with Asymmetric Information

TL;DR

The paper tackles pursuit-evasion-style differential games under asymmetric information by pairing deception (from the more informed agent) with desensitized planning (for the less informed agent). It introduces a sensitivity-function framework to quantify how parametric uncertainty in the environment affects trajectory constraints, and embeds a risk-averse regularizer into the pursuer's payoff to reduce constraint violations. A deceptive strategy for the evader and a receding-horizon, risk-aware planning method for the pursuer are developed and tested in scenarios with an uncertain dynamic obstacle. Results show that desensitized planning can mitigate constraint violations and that deception can significantly influence game outcomes, offering a framework for robust, safe decision-making in adversarial, uncertain environments. The approach has potential impact for cyber-physical systems and aviation applications where information asymmetry and uncertain dynamics are prevalent.

Abstract

Desensitization addresses safe optimal planning under parametric uncertainties by providing sensitivity function-based risk estimates. This paper expands upon the existing work on desensitization in optimal control to address safe planning for a class of two-player differential games. In the proposed game, parametric uncertainties correspond to variations of the model parameters for each player about their nominal values. The two players in the proposed formulation are assumed to have perfect information about these nominal parameter values. However, it is assumed that only one of the players has complete knowledge of the actual parameter value, resulting in information asymmetry in the proposed game. This lack of knowledge regarding the parameter variations is expected to result in state constraint violations for the player with an information disadvantage. In this regard, a desensitized feedback strategy that provides safe trajectories is proposed for the player with incomplete information. The proposed feedback strategy is evaluated for instances involving a single pursuer and a single evader with an uncertain moving obstacle, where the pursuer is assumed to only know the nominal value of the obstacle's speed. At the same time, the evader knows the obstacle's true speed, and also the fact that the pursuer knows only the nominal value of the obstacle's speed. Subsequently, deceptive strategies are proposed for the evader, who has an information advantage, and these strategies are assessed against the pursuer's desensitized strategy.

Figures (9)

• Figure 1: Norm of the proposed RCS ($S_\gamma$) matrix around the evader at $t=10$ for two different instances of uncertainty in obstacle' velocity
• Figure 2: An instance where the pursuer does not penalize the proposed risk estimate that leads to collision (pursuer solves $\mathcal{P}_o$). Black dotted circle - initial position of the obstacle; Blue solid circle - Nominal Obstacle; Red solid circle - True Obstacle; Green line - RHC-based look-ahead of the player.
• Figure 3: Simulation results for an instance where the pursuer penalizes the proposed risk estimate with $Q=1$, and successfully captures the evader while avoiding the obstacle. The uncertain parameter is the obstacle's speed along $x_2$-axis.
• Figure 4: Simulation results for an instance where the pursuer employs the proposed desensitized strategy with $Q=1$ while the evader interacts with the obstacle. The uncertain parameter is the obstacle's speed along $x_1$-axis.
• Figure 5: Simulation results for the instance where the pursuer initially moves towards the local minimum that is dominated by the RCS cost-map before capturing the evader ($Q=1$).