Given a mapped environment, we formulate the problem of visually tracking and following an evader using a probabilistic framework. In this work, we consider a non-holonomic robot with a limited visibility depth sensor in an indoor environment with obstacles. The mobile robot that follows the target is considered a pursuer and the agent being followed is considered an evader. We propose a probabilistic framework for both the pursuer and evader to achieve their conflicting goals. We introduce a smart evader that has information about the location of the pursuer. The goal of this variant of the evader is to avoid being tracked by the pursuer by using the visibility region information obtained from the pursuer, to further challenge the proposed smart pursuer. To validate the efficiency of the framework, we conduct several experiments in simulation by using Gazebo and evaluate the success rate of tracking an evader in various environments with different pursuer to evader speed ratios. Through our experiments we validate our hypothesis that a smart pursuer tracks an evader more effectively than a pursuer that just navigates in the environment randomly. We also validate that an evader that is aware of the actions of the pursuer is more successful at avoiding getting tracked by a smart pursuer than a random evader. Finally, we empirically show that while a smart pursuer does increase it's average success rate of tracking compared to a random pursuer, there is an increased variance in its success rate distribution when the evader becomes aware of its actions.
Using game theory, @cite_9 formulated the pursuit-evasion problem as a partial information Markov game, and proposed a Nash solution to the resulting one-step non-zero sum game, provided the evader has access to the pursuer's information. For the visibility based variant, where both pursuer and evader are holonomic with bounded speeds and both have complete knowledge of the map, @cite_4 presented strategies for players that are in Nash equilibrium.
@cite_9 @cite_4
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This paper addresses the control of a team of autonomous agents pursuing a smart evader in a non-accurately mapped terrain. By describing the problem as a partial information Markov game, we are able to integrate map-learning and pursuit. We propose receding horizon control policies, in which the pursuers and the evader try to respectively maximize and minimize the probability of capture at the next time instant. Since this probability is conditioned to distinct observations for each team, the resulting game is nonzero-sum. When the evader has access to the pursuers' information, we show that a Nash solution to the one-step nonzero-sum game always exists. Moreover, we propose a method to compute the Nash equilibrium policies by solving an equivalent zero-sum matrix game. A simulation example shows the feasibility of the proposed approach. In this paper, we present a game-theoretic analysis of a visibility-based pursuit-evasion game in a planar environment containing obstacles. The pursuer and the evader are holonomic having bounded speeds. Both players have a complete map of the environment. Both players have omnidirectional vision and have knowledge about each other's current position as long as they are visible to each other. The pursuer wants to maintain visibility of the evader for the maximum possible time and the evader wants to escape the pursuer's sight as soon as possible. Under this information structure, we present necessary and sufficient conditions for surveillance and escape. We present strategies for the players that are in Nash equilibrium. The strategies are a function of the value of the game. Using these strategies, we construct a value function by integrating the adjoint equations backward in time from the termination situations provided by the corners in the environment. From these value functions we recompute the control strategies for the players to obtain optimal trajectories for the players near the termination situation. This is the first work that presents the necessary and sufficient conditions for tracking for a visibility based pursuit-evasion game and presents the equilibrium strategies for the players.