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

Search and Pursuit-Evasion in Mobile Robotics, A survey

This paper surveys recent results in pursuitevasion and autonomous search relevant to applications in mobile robotics. We provide a taxonomy of search problems that highlights the differences resulting from varying assumptions on the searchers, targets, and the environment. We then list a number of fundamental results in the areas of pursuit-evasion and probabilistic search, and we discuss field implementations on mobile robotic systems. In addition, we highlight current open problems in the area and explore avenues for future work

Randomized Pursuit-Evasion with Local Visibility

We study the following pursuit-evasion game: One or more hunters are seeking to capture an evading rabbit on a graph. At each round, the rabbit tries to gather information about the location of the hunters but it can see them only if they are located on adjacent nodes. We show that two hunters su#ce for catching rabbits with such local visibility with high probability. We distinguish between reactive rabbits who move only when a hunter is visible and general rabbits who can employ more sophisticated strategies. We present polynomial time algorithms that decide whether a graph G is hunter-win, that is, if a single hunter can capture a rabbit of either kind on G

Pursuit-Evasion with Acceleration, Sensing Limitation, and Electronic Counter Measures

Abstract: The use of game theory to analyze the optimal behaviors of both pursuers and evaders originated with Isaac\u27s work at the Rand Corporation in the 1950\u27s. Although many variations of this problem have been considered, published work to date is limited to the case where both players have constant velocities. In this thesis, we extend previous work by allowing players to accelerate. Analysis of this new problem using Newton\u27s laws imposes an additional constraint to the system, which is the relationship between players\u27 velocities and allowed turning radius. We find that analysis of this relationship provides new insight into the evader capture criteria for the constant velocity case. We summarize our results in a flow chart that expresses the parameter values that determine both the games of kind and games of degree associated with this problem. Pursuit-evasion games in the literature typically either assume both players have perfect knowledge of the opponent\u27s position, or use primitive sensing models. These unrealistically skew the problem in favor of the pursuer who need only maintain a faster velocity at all turning radii. In real life, an evader usually escapes when the pursuer no longer knows the evader\u27s position. We analyze the pursuit-evasion problem using a realistic sensor model and information theory to compute game theoretic payoff matrices. Our results show that this problem can be modeled as a two-person bi-matrix game. This game has a saddle point when the evader uses strategies that exploit sensor limitations, while the pursuer relies on strategies that ignore sensing limitations. Later we consider for the first time the effect of many types of electronic counter measures (ECM) on pursuit evasion games. The evader\u27s decision to initiate its ECM is modeled as a function of the distance between the players. Simulations show how to find optimal strategies for ECM use when initial conditions are known. We also discuss the effectiveness of different ECM technologies in pursuit-evasion games

Mobile robotic network deployment for intruder detection and tracking

This thesis investigates the problem of intruder detection and tracking using mobile robotic networks. In the first part of the thesis, we consider the problem of seeking an electromagnetic source using a team of robots that measure the local intensity of the emitted signal. We propose a planner for a team of robots based on Particle Swarm Optimization (PSO) which is a population based stochastic optimization technique. An equivalence is established between particles generated in the traditional PSO technique, and the mobile agents in the swarm. Since the positions of the robots are updated using the PSO algorithm, modifications are required to implement the PSO algorithm on real robots to incorporate collision avoidance strategies. The modifications necessary to implement PSO on mobile robots, and strategies to adapt to real environments are presented in this thesis. Our results are also validated on an experimental testbed. In the second part, we present a game theoretic framework for visibility-based target tracking in multi-robot teams. A team of observers (pursuers) and a team of targets (evaders) are present in an environment with obstacles. The objective of the team of observers is to track the team of targets for the maximum possible time. While the objective of the team of targets is to escape (break line-of-sight) in the minimum time. We decompose the problem into two layers. At the upper level, each pursuer is allocated to an evader through a minimum cost allocation strategy based on the risk of each evader, thereby, decomposing the agents into multiple single pursuer-single evader pairs. Two decentralized allocation strategies are proposed and implemented in this thesis. At the lower level, each pursuer computes its strategy based on the results of the single pursuer-single evader target-tracking problem. We initially address this problem in an environment containing a semi-infinite obstacle with one corner. The pursuer\u27s optimal tracking strategy is obtained regardless of the evader\u27s strategy using techniques from optimal control theory and differential games. Next, we extend the result to an environment containing multiple polygonal obstacles. We construct a pursuit field to provide a guiding vector for the pursuer which is a weighted sum of several component vectors. The performance of different combinations of component vectors is investigated. Finally, we extend our work to address the case when the obstacles are not polygonal, and the observers have constraints in motion

Multi-vehicle Framework for the Development of Robotic Games: the Marco Polo Case

This thesis presents a multi-vehicle platform and framework for robotics education and research. The framework has been designed primarily as a tool for teaching children about engineering in general and robotics in particular. The framework is composed of a unique combination of hardware components and software libraries that allow users to easily design and implement sophisticated robotics behaviors. Several example games are presented including ``Obstacle Course," ``Scavenger Hunt," ``Robot Jeopardy," and ``Marco Polo." This thesis also introduces ``Marco Polo" as a robotics problem that mimics the pursuit-evasion game often played by children in swimming pools. Specifically, the question of finding an optimal pursuit strategy under the condition of intermittent communication is addressed. Finally, a problem related to ``Marco Polo" involving a multi-agent sensor network optimally placed in an environment for the purpose of detecting and intercepting intruders is presented together with a proposed solution methodology and simulation and experimental results.School of Electrical & Computer Engineerin