Contributions To Pursuit-Evasion Game Theory.

This dissertation studies adversarial conflicts among a group of agents moving in the plane, possibly among obstacles, where some agents are pursuers and others are evaders. The goal of the pursuers is to capture the evaders, where capture requires a pursuer to be either co-located with an evader, or in close proximity. The goal of the evaders is to avoid capture. These scenarios, where different groups compete to accomplish conflicting goals, are referred to as pursuit-evasion games, and the agents are called players. Games featuring one pursuer and one evader are analyzed using dominance, where a point in the plane is said to be dominated by a player if that player is able to reach the point before the opposing players, regardless of the opposing players' actions. Two generalizations of the Apollonius circle are provided. One solves games with environments containing obstacles, and the other provides an alternative solution method for the Homicidal Chauffeur game. Optimal pursuit and evasion strategies based on dominance are provided. One benefit of dominance analysis is that it extends to games with many players. Two foundational games are studied; one features multiple pursuers against a single evader, and the other features a single pursuer against multiple evaders. Both are solved using dominance through a reduction to single pursuer, single evader games. Another game featuring competing teams of pursuers is introduced, where an evader cooperates with friendly pursuers to rendezvous before being captured by adversaries. Next, the assumption of complete and perfect information is relaxed, and uncertainties in player speeds, player positions, obstacle locations, and cost functions are studied. The sensitivity of the dominance boundary to perturbations in parameters is provided, and probabilistic dominance is introduced. The effect of information is studied by comparing solutions of games with perfect information to games with uncertainty. Finally, a pursuit law is developed that requires minimal information and highlights a limitation of dominance regions. These contributions extend pursuit-evasion game theory to a number of games that have not previously been solved, and in some cases, the solutions presented are more amenable to implementation than previous methods.PhDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/120650/1/dwoyler_1.pd

Simultaneous Search and Monitoring by Unmanned Aerial Vehicles

Although robot search and monitoring are two problems which are normally addressed separately, this work conceives the idea that search and monitoring are both required in realistic applications. A problem of simultaneous search and monitoring (SSM) is studied, which innovatively combines two problems in a synergistic perspective. The single pursuer SSM of randomly moving or evasive targets are studied first, and are extended to the cases with multiple pursuers. The precise mathematical frameworks for this work are POMDP, POSG and Dec-POMDP. They are all intractable and non-scalable. Different approaches are taken in each scenario, to reduce computation cost and achieve online and distributed planning, without significantly undermining the performance. For the single pursuer SSM of randomly moving targets, a novel policy reconstruction method is combined with a heuristic branching rule, to generate a heuristic reactive policy. For the single pursuer SSM of evasive targets, an assumption is made and justified, which simplifies the search evasion game to a dynamic guaranteed search problem. For the multiple-pursuer SSM of randomly moving targets, the partial open-loop feedback control method is originally applied to achieve the cooperation implicitly. For the multiple-pursuer SSM of evasive targets, the assumption made in the single pursuer case also simplifies the cooperative search evasion game to a cooperative dynamic guaranteed search problem. In moderate scenarios, the proposed methods show better performance than baseline methods, and can have practical computation efficiency. The extreme scenarios when SSM does not work are also studied

Synchronous intercept strategies for a robotic defense-intrusion game with two defenders

We study the defense-intrusion game, in which a single attacker robot tries to reach a stationary target that is protected by two defender robots. We focus on the "synchronous intercept problem", where both robots have to reach the attacker robot synchronously to intercept it. Assume that the attacker robot has the control policy which is based on attraction to the target and repulsion from the defenders, two kinds of synchronous intercept strategies are proposed for the defense-intrusion game, introduced here as Attacker-oriented and Neutral-position-oriented. Theoretical analysis and simulation results show that: (1) the two strategies are able to generate different synchronous intercept patterns: contact intercept pattern and stable non-contact intercept pattern, respectively. (2) The contact intercept pattern allows the defender robots to intercept the attacker robot in finite time, while the stable non-contact intercept pattern generates a periodic attractor that prevents the attack robot from reaching the target for infinite time. There is potential to apply the insights obtained into defense-intrusion in real systems, including aircraft escort and the defense of military targets or territorial boundaries

Games of Pursuit-Evasion with Multiple Agents and Subject to Uncertainties

Over the past decade, there have been constant efforts to induct unmanned aerial vehicles (UAVs) into military engagements, disaster management, weather monitoring, and package delivery, among various other applications. With UAVs starting to come out of controlled environments into real-world scenarios, uncertainties that can be either exogenous or endogenous play an important role in the planning and decision-making aspects of deploying UAVs. At the same time, while the demand for UAVs is steadily increasing, major governments are working on their regulations. There is an urgency to design surveillance and security systems that can efficiently regulate the traffic and usage of these UAVs, especially in secured airspaces. With this motivation, the thesis primarily focuses on airspace security, providing solutions for safe planning under uncertainties while addressing aspects concerning target acquisition and collision avoidance. In this thesis, we first present our work on solutions developed for airspace security that employ multiple agents to capture multiple targets in an efficient manner. Since multi-pursuer multi-evader problems are known to be intractable, heuristics based on the geometry of the game are employed to obtain task-allocation algorithms that are computationally efficient. This is achieved by first analyzing pursuit-evasion problems involving two pursuers and one evader. Using the insights obtained from this analysis, a dynamic allocation algorithm for the pursuers, which is independent of the evader's strategy, is proposed. The algorithm is further extended to solve multi-pursuer multi-evader problems for any number of pursuers and evaders, assuming both sets of agents to be heterogeneous in terms of speed capabilities. Next, we consider stochastic disturbances, analyzing pursuit-evasion problems under stochastic flow fields using forward reachability analysis, and covariance steering. The problem of steering a Gaussian in adversarial scenarios is first analyzed under the framework of general constrained games. The resulting covariance steering problem is solved numerically using iterative techniques. The proposed approach is applied to the missile endgame guidance problem. Subsequently, using the theory of covariance steering, an approach to solve pursuit-evasion problems under external stochastic flow fields is discussed. Assuming a linear feedback control strategy, a chance-constrained covariance game is constructed around the nominal solution of the players. The proposed approach is tested on realistic linear and nonlinear flow fields. Numerical simulations suggest that the pursuer can effectively steer the game towards capture. Finally, the uncertainties are assumed to be parametric in nature. To this end, we first formalize optimal control under parametric uncertainties while introducing sensitivity functions and costates based techniques to address robustness under parametric variations. Utilizing the sensitivity functions, we address the problem of safe path planning in environments containing dynamic obstacles with an uncertain motion model. The sensitivity function based-approach is then extended to address game-theoretic formulations that resemble a "fog of war" situation.Ph.D

Threat assessment for safe navigation in environments with uncertainty in predictability

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2011.Cataloged from PDF version of thesis.Includes bibliographical references (p. 213-224).This thesis develops threat assessment algorithms to improve the safety of the decision making of autonomous and human-operated vehicles navigating in dynamic and uncertain environments, where the source of uncertainty is in the predictability of the nearby vehicles' future trajectories. The first part of the thesis introduces two classes of algorithms to classify drivers behaviors at roads intersections based on Support Vector Machines (SVM) and Hidden Markov Models (HMM). These algorithms are successfully validated using a large real-world intersection dataset, and can be used as part of future driver assistance systems. They are also compared to three popular traditional methods, and the results show significant and consistent improvements with the developed algorithms. The second part of the thesis presents an efficient trajectory prediction algorithm that has been developed to improve the performance of future collision avoidance and detection systems. The proposed approach, RR-GP, combines the Rapidly-exploring Random Trees (RRT) based algorithm, RRT-Reach, with mixtures of Gaussian Processes (GP) to compute dynamically feasible paths, in real-time, while embedding the flexibility of GP's nonparametric Bayesian model. RR-GP efficiently approximates the reachability sets of surrounding vehicles, and is shown in simulation and on naturalistic data to improve the performance over two standard GP-based algorithms. The third part introduces new path planning algorithms that build upon the tools that have been previously introduced in this thesis. The focus is on safe autonomous navigation in the presence of other vehicles with uncertain motion patterns. First, it presents a new threat assessment module (TAM) that combines the RRT-Reach algorithm with an SVM-based intention predictor, to develop a threat-aware path planner. The strengths of this approach are demonstrated through simulation and experiments performed in the MIT RAVEN testbed. Second, another novel path planning technique is developed by integrating the RR-GP trajectory prediction algorithm with a state-of-the-art chance-constrained RRT planner. This framework provides several theoretical guarantees on the probabilistic satisfaction of collision avoidance constraints. Extensive simulation results show that the resulting approach can be used in real-time to efficiently and accurately execute safe paths. The last part of the thesis considers the decision-making problem for a human-driven vehicle crossing a road intersection in the presence of other, potentially errant, drivers. The proposed approach uses the TAM framework to compute the threat level in real-time, and provides the driver with a warning signal and the best escape maneuver through the intersection. Experimental results with small autonomous and human-driven vehicles in the RAVEN testbed demonstrate that this approach can be successfully used in real-time to minimize the risk of collision in urban-like environments.by Georges Salim Aoudé.Ph.D

Advanced Mobile Robotics: Volume 3

Mobile robotics is a challenging field with great potential. It covers disciplines including electrical engineering, mechanical engineering, computer science, cognitive science, and social science. It is essential to the design of automated robots, in combination with artificial intelligence, vision, and sensor technologies. Mobile robots are widely used for surveillance, guidance, transportation and entertainment tasks, as well as medical applications. This Special Issue intends to concentrate on recent developments concerning mobile robots and the research surrounding them to enhance studies on the fundamental problems observed in the robots. Various multidisciplinary approaches and integrative contributions including navigation, learning and adaptation, networked system, biologically inspired robots and cognitive methods are welcome contributions to this Special Issue, both from a research and an application perspective

A review of task allocation methods for UAVs

Unmanned aerial vehicles, can offer solutions to a lot of problems, making it crucial to research more and improve the task allocation methods used. In this survey, the main approaches used for task allocation in applications involving UAVs are presented as well as the most common applications of UAVs that require the application of task allocation methods. They are followed by the categories of the task allocation algorithms used, with the main focus being on more recent works. Our analysis of these methods focuses primarily on their complexity, optimality, and scalability. Additionally, the communication schemes commonly utilized are presented, as well as the impact of uncertainty on task allocation of UAVs. Finally, these methods are compared based on the aforementioned criteria, suggesting the most promising approaches

Game-Theoretic Safety Assurance for Human-Centered Robotic Systems

In order for autonomous systems like robots, drones, and self-driving cars to be reliably introduced into our society, they must have the ability to actively account for safety during their operation. While safety analysis has traditionally been conducted offline for controlled environments like cages on factory floors, the much higher complexity of open, human-populated spaces like our homes, cities, and roads makes it unviable to rely on common design-time assumptions, since these may be violated once the system is deployed. Instead, the next generation of robotic technologies will need to reason about safety online, constructing high-confidence assurances informed by ongoing observations of the environment and other agents, in spite of models of them being necessarily fallible.This dissertation aims to lay down the necessary foundations to enable autonomous systems to ensure their own safety in complex, changing, and uncertain environments, by explicitly reasoning about the gap between their models and the real world. It first introduces a suite of novel robust optimal control formulations and algorithmic tools that permit tractable safety analysis in time-varying, multi-agent systems, as well as safe real-time robotic navigation in partially unknown environments; these approaches are demonstrated on large-scale unmanned air traffic simulation and physical quadrotor platforms. After this, it draws on Bayesian machine learning methods to translate model-based guarantees into high-confidence assurances, monitoring the reliability of predictive models in light of changing evidence about the physical system and surrounding agents. This principle is first applied to a general safety framework allowing the use of learning-based control (e.g. reinforcement learning) for safety-critical robotic systems such as drones, and then combined with insights from cognitive science and dynamic game theory to enable safe human-centered navigation and interaction; these techniques are showcased on physical quadrotors—flying in unmodeled wind and among human pedestrians—and simulated highway driving. The dissertation ends with a discussion of challenges and opportunities ahead, including the bridging of safety analysis and reinforcement learning and the need to ``close the loop'' around learning and adaptation in order to deploy increasingly advanced autonomous systems with confidence