Optimal Control Methods for Missile Evasion

Optimal control theory is applied to the study of missile evasion, particularly in the case of a single pursuing missile versus a single evading aircraft. It is proposed to divide the evasion problem into two phases, where the primary considerations are energy and maneuverability, respectively. Traditional evasion tactics are well documented for use in the maneuverability phase. To represent the first phase dominated by energy management, the optimal control problem may be posed in two ways, as a fixed final time problem with the objective of maximizing the final distance between the evader and pursuer, and as a free final time problem with the objective of maximizing the final time when the missile reaches some capture distance away from the evader.These two optimal control problems are studied under several different scenarios regarding assumptions about the pursuer. First, a suboptimal control strategy, proportional navigation, is used for the pursuer. Second, it is assumed that the pursuer acts optimally, requiring the solution of a two-sided optimal control problem, otherwise known as a differential game. The resulting trajectory is known as a minimax, and it can be shown that it accounts for uncertainty in the pursuer\u27s control strategy. Finally, a pursuer whose motion and state are uncertain is studied in the context of Receding Horizon Control and Real Time Optimal Control. The results highlight how updating the optimal control trajectory reduces the uncertainty in the resulting miss distance

Reachable sets analysis in the cooperative control of pursuer vehicles

This thesis is concerned with the Pursuit-and-Evasion (PE) problem where the pursuer aims to minimize the time to capture the evader while the evader tries to prevent capture. In the problem, the evader has two advantages: a higher manoeuvrability and that the pursuer is uncertain about the evader's state. Cooperation among multiple pursuer vehicles can thus be used to overcome the evader’s advantages. The focus here is on the formulation and development of frameworks and algorithms for cooperation amongst pursuers, aiming at feasible implementation on real and autonomous vehicles. The thesis is split into Parts I and II. Part I considers the problem of capturing an evader of higher manoeuvrability in a deterministic PE game. The approach is the employment of Forward Reachable Set (FRS) analysis in the pursuers’ control. The analysis considers the coverage of the evader’s FRS, which is the set of reachable states at a future time, with the pursuer’s FRS and assumes that the chance of capturing the evader is dependent on the degree of the coverage. Using the union of multiple pursuers’ FRSs intuitively leads to more evader FRS coverage and this forms the mechanism of cooperation. A framework for cooperative control based on the FRS coverage, or FRS-based control, is proposed. Two control algorithms were developed within this framework. Part II additionally introduces the problem of evader state uncertainty due to noise and limited field-of-view of the pursuers’ sensors. A search-and-capture (SAC) problem is the result and a hybrid architecture, which includes multi-sensor estimation using the Particle Filter as well as FRS-based control, is proposed to accomplish the SAC task. The two control algorithms in Part I were tested in simulations against an optimal guidance algorithm. The results show that both algorithms yield a better performance in terms of time and miss distance. The results in Part II demonstrate the effectiveness of the hybrid architecture for the SAC task. The proposed frameworks and algorithms provide insights for the development of effective and more efficient control of pursuer vehicles and can be useful in the practical applications such as defence systems and civil law enforcement

Multiagent Cooperative Learning Strategies for Pursuit-Evasion Games

This study examines the pursuit-evasion problem for coordinating multiple robotic pursuers to locate and track a nonadversarial mobile evader in a dynamic environment. Two kinds of pursuit strategies are proposed, one for agents that cooperate with each other and the other for agents that operate independently. This work further employs the probabilistic theory to analyze the uncertain state information about the pursuers and the evaders and uses case-based reasoning to equip agents with memories and learning abilities. According to the concepts of assimilation and accommodation, both positive-angle and bevel-angle strategies are developed to assist agents in adapting to their environment effectively. The case study analysis uses the Recursive Porous Agent Simulation Toolkit (REPAST) to implement a multiagent system and demonstrates superior performance of the proposed approaches to the pursuit-evasion game

Analysis of multi-agent systems under varying degrees of trust, cooperation, and competition

Multi-agent systems rely heavily on coordination and cooperation to achieve a variety of tasks. It is often assumed that these agents will be fully cooperative, or have reliable and equal performance among group members. Instead, we consider cooperation as a spectrum of possible interactions, ranging from performance variations within the group to adversarial agents. This thesis examines several scenarios where cooperation and performance are not guaranteed. Potential applications include sensor coverage, emergency response, wildlife management, tracking, and surveillance. We use geometric methods, such as Voronoi tessellations, for design insight and Lyapunov-based stability theory to analyze our proposed controllers. Performance is verified through simulations and experiments on a variety of ground and aerial robotic platforms. First, we consider the problem of Voronoi-based coverage control, where a group of robots must spread out over an environment to provide coverage. Our approach adapts online to sensing and actuation performance variations with the group. The robots have no prior knowledge of their relative performance, and in a distributed fashion, compensate by assigning weaker robots a smaller portion of the environment. Next, we consider the problem of multi-agent herding, akin to shepherding. Here, a group of dog-like robots must drive a herd of non-cooperative sheep-like agents around the environment. Our key insight in designing the control laws for the herders is to enforce geometrical relationships that allow for the combined system dynamics to reduce to a single nonholonomic vehicle. We also investigate the cooperative pursuit of an evader by a group of quadrotors in an environment with no-fly zones. While the pursuers cannot enter the no-fly zones, the evader moves freely through the zones to avoid capture. Using tools for Voronoi-based coverage control, we provide an algorithm to distribute the pursuers around the zone's boundary and minimize capture time once the evader emerges. Finally, we present an algorithm for the guaranteed capture of multiple evaders by one or more pursuers in a bounded, convex environment. The pursuers utilize properties of the evader's Voronoi cell to choose a control strategy that minimizes the safe-reachable area of the evader, which in turn leads to the evader's capture

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

Quasi-Linear Differential-Deference Game of Approach

This is a post-peer-review, pre-copyedit version of a book chapter that is part of “V. A. Sadovnichiy, M. Z. Zgurovsky (eds.). Modern Mathematics and Mechanics. Understanding Complex Systems”. The final authenticated version is available online at: https://link.springer.com/chapter/10.1007/978-3-319-96755-4_26The paper is devoted to the games of approach. We consider a controlled object whose dynamics is described by the linear differential system with a pure time delay or the differential-difference system with commutative matrices in Euclidean space. The approaches to the solutions of these problems are proposed which based on the Method of Resolving Functions and the First Direct Method of L.S. Pontryagin. The guaranteed times of the game termination are found, and corresponding control laws are constructed. The results are illustrated by a model example