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.
Some researchers have utilized the information about the game environment to create partition regions where the pursuers and evaders might traverse to. One such method @cite_5 converts an occupancy grid map to a graph with restrictions by partitioning the workspace. They decompose the occupancy grid using Generalized Voronoi Diagrams to obtain a reduced graph representation of the environment with reduced action space which makes it easy for the pursuer to traverse in the environment.
@cite_5
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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. In a pursuit-evasion game, a team of pursuers attempt to capture an evader. The players alternate turns, move with equal speed, and have full information about the state of the game. We consider the most restrictive capture condition: a pursuer must become colocated with the evader to win the game. We prove two general results about this adversarial motion planning problem in geometric spaces. First, we show that one pursuer has a winning strategy in any compact CAT(0) space. This complements a result of Alexander, Bishop and Ghrist, who provide a winning strategy for a game with positive capture radius. Second, we consider the game played in a compact domain in Euclidean two-space with piecewise analytic boundary and arbitrary Euler characteristic. We show that three pursuers always have a winning strategy by extending recent work of Bhadauria, Klein, Isler and Suri from polygonal environments to our more general setting. This paper presents an extension of the standard occupancy grid for 3D environment mapping. The presented approach adds a fusion process after the occupancy update which modifies the resolution of the grid cells in an incremental manner. Consequently, the proposed approach requires fewer grid cells for 3D representation in comparison to a standard occupancy grid. The resolution adaptation process is based on the occupancy probabilities of the grid cells and leads to the relaxation of the cubic grid cell assumption common to most 3D occupancy grids. The aim of this paper is to show the advantage of the proposed incremental fusion process which leads to the approximation of the 3D environment using rectangular cuboids. Evaluation on a large scale dataset and comparison to the state of the art shows that the proposed approach has faster access time for all occupied grid cells and requires a smaller number of cells for 3D environment representation. Occupancy grid mapping approaches, especially those that additionally estimate the dynamics, enable a robust and consistent modeling of the local environment in a cell-level representation. But a scene understanding of surrounding traffic participants requires a generalized object-level representation. This work presents an object tracking approach based on dynamic occupancy grids. The association of occupied grid cells with existing object tracks is solved individually on the cell-level without clustering or forming object hypotheses. New object tracks are extracted using a clustering strategy and a velocity variance analysis of neighboring occupied cells to reduce false positives. In order to improve the estimates of the position and size, an object boundary extraction is presented that takes the surrounding free space of the selected box representation into account. Experimental results with real sensor data show the effectiveness of the proposed object tracking approach in challenging urban scenarios with dense traffic.