Swarm Coordination for Pursuit Evasion Games Using Sensor Networks

Abstract — In this work we consider the problem of pursuit evasion games (PEGs) where a group of pursuers is required to detect, chase and capture a group of evaders with the aid of a sensor network in minimum time. Differently from standards PEGs where the environment and the location of evaders is unknown and a probabilistic map is built based on the pursuer onboard sensors, here we consider a scenario where a sensor network, previously deployed in the region of concern, can detect the presence of moving vehicles and can relay this information to the pursuers. Here we propose a general framework for the design of a hierarchical control architecture that exploit the advantages of a sensor networks by combining both centralized and decentralized real-time control algorithms. We also propose a coordination scheme for the pursuers to minimize the time-to-capture of all evaders. In particular, we focus on PEGs with sensor networks orbiting in space for artificial space debris detection and removal. Index Terms — Sensor networks, pursuit evasion games, vehicle coordination, space vehicles, space debris over the area of interest. This constraint makes designing a cooperative pursuit algorithm harder because lack of complete observability only allows for suboptimal pursuit policies. See Figure 1(left). Furthermore, a smart evaders makes the map-building process dynamic since their location changes over time. The map-learning phase is, by itself, time-consuming and computationally intensive even for simple two-dimensional rectilinear environments [5]. Moreover, inaccurate sensors complicate this process and a probabilistic approach is often required [21]. I

A Survey on Aerial Swarm Robotics

The use of aerial swarms to solve real-world problems has been increasing steadily, accompanied by falling prices and improving performance of communication, sensing, and processing hardware. The commoditization of hardware has reduced unit costs, thereby lowering the barriers to entry to the field of aerial swarm robotics. A key enabling technology for swarms is the family of algorithms that allow the individual members of the swarm to communicate and allocate tasks amongst themselves, plan their trajectories, and coordinate their flight in such a way that the overall objectives of the swarm are achieved efficiently. These algorithms, often organized in a hierarchical fashion, endow the swarm with autonomy at every level, and the role of a human operator can be reduced, in principle, to interactions at a higher level without direct intervention. This technology depends on the clever and innovative application of theoretical tools from control and estimation. This paper reviews the state of the art of these theoretical tools, specifically focusing on how they have been developed for, and applied to, aerial swarms. Aerial swarms differ from swarms of ground-based vehicles in two respects: they operate in a three-dimensional space and the dynamics of individual vehicles adds an extra layer of complexity. We review dynamic modeling and conditions for stability and controllability that are essential in order to achieve cooperative flight and distributed sensing. The main sections of this paper focus on major results covering trajectory generation, task allocation, adversarial control, distributed sensing, monitoring, and mapping. Wherever possible, we indicate how the physics and subsystem technologies of aerial robots are brought to bear on these individual areas

Estimation and stability of nonlinear control systems under intermittent information with applications to multi-agent robotics

This dissertation investigates the role of intermittent information in estimation and control problems and applies the obtained results to multi-agent tasks in robotics. First, we develop a stochastic hybrid model of mobile networks able to capture a large variety of heterogeneous multi-agent problems and phenomena. This model is applied to a case study where a heterogeneous mobile sensor network cooperatively detects and tracks mobile targets based on intermittent observations. When these observations form a satisfactory target trajectory, a mobile sensor is switched to the pursuit mode and deployed to capture the target. The cost of operating the sensors is determined from the geometric properties of the network, environment and probability of target detection. The above case study is motivated by the Marco Polo game played by children in swimming pools. Second, we develop adaptive sampling of targets positions in order to minimize energy consumption, while satisfying performance guarantees such as increased probability of detection over time, and no-escape conditions. A parsimonious predictor-corrector tracking filter, that uses geometrical properties of targets\u27 tracks to estimate their positions using imperfect and intermittent measurements, is presented. It is shown that this filter requires substantially less information and processing power than the Unscented Kalman Filter and Sampling Importance Resampling Particle Filter, while providing comparable estimation performance in the presence of intermittent information. Third, we investigate stability of nonlinear control systems under intermittent information. We replace the traditional periodic paradigm, where the up-to-date information is transmitted and control laws are executed in a periodic fashion, with the event-triggered paradigm. Building on the small gain theorem, we develop input-output triggered control algorithms yielding stable closed-loop systems. In other words, based on the currently available (but outdated) measurements of the outputs and external inputs of a plant, a mechanism triggering when to obtain new measurements and update the control inputs is provided. Depending on the noise environment, the developed algorithm yields stable, asymptotically stable, and Lp-stable (with bias) closed-loop systems. Control loops are modeled as interconnections of hybrid systems for which novel results on Lp-stability are presented. Prediction of a triggering event is achieved by employing Lp-gains over a finite horizon in the small gain theorem. By resorting to convex programming, a method to compute Lp-gains over a finite horizon is devised. Next, we investigate optimal intermittent feedback for nonlinear control systems. Using the currently available measurements from a plant, we develop a methodology that outputs when to update the control law with new measurements such that a given cost function is minimized. Our cost function captures trade-offs between the performance and energy consumption of the control system. The optimization problem is formulated as a Dynamic Programming problem, and Approximate Dynamic Programming is employed to solve it. Instead of advocating a particular approximation architecture for Approximate Dynamic Programming, we formulate properties that successful approximation architectures satisfy. In addition, we consider problems with partially observable states, and propose Particle Filtering to deal with partially observable states and intermittent feedback. Finally, we investigate a decentralized output synchronization problem of heterogeneous linear systems. We develop a self-triggered output broadcasting policy for the interconnected systems. Broadcasting time instants adapt to the current communication topology. For a fixed topology, our broadcasting policy yields global exponential output synchronization, and Lp-stable output synchronization in the presence of disturbances. Employing a converse Lyapunov theorem for impulsive systems, we provide an average dwell time condition that yields disturbance-to-state stable output synchronization in case of switching topology. Our approach is applicable to directed and unbalanced communication topologies.\u2

Optimal control for safety-critical systems

Enforcing safety plays a crucial role within the optimisation and control literature. Despite notable advances in recent years, optimal control for safety-critical and high-dimensional systems remains a challenging problem. Developing a general theoretical framework for integrating safety within optimal control is not tractable as the numerical inaccuracy and computational cost often grow exponentially with the number of states. Furthermore, different notions of safety require different methodologies and present unique theoretical and computational challenges. This thesis focuses on the challenges that arise when addressing scalability and safety considerations simultaneously. Safety is a multi-facet problem that involves hard constraint satisfaction, avoiding sharing information considered as private, as well as robustifying towards uncertainty that could otherwise compromise safety. The initial chapters of the thesis focus on Hamilton-Jacobi reachability, which has become a well-established method of computing reachable sets for complex nonlinear systems. In addition to enforcing that the system remains within a safe part of the state-space, we consider application-specific abstractions to deal with scalability, the interplay between competing performance objectives and safety objectives, and the challenges arising from multi-objective optimal control problems. We then investigate safety considerations due to the amount of information that needs to be shared between agents in a multi-agent networked control setting. Extending classical state-aggregation in approximate dynamic programming, we introduce a method of solving a large-scale Markov Decision Process in a fully distributed manner. The final chapter considers stochastic safety constraints under a statistical learning theoretic lens. Utilising randomised algorithms, we establish probably approximately correct (PAC) bounds on predicting a future label in a binary classification problem whereby the classifier changes in an unknown structured manner

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

Fixed-wing UAV tracking of evasive targets in 3-dimensional space

In this thesis, we explore the development of autonomous tracking and interception strategies for single and multiple fixed-wing Unmanned Aerial Vehicles (UAVs) pursuing single or multiple evasive targets in 3-dimensional (3D) space. We considered a scenario where we intend to protect high-value facilities from adversarial groups employing ground-based vehicles and quadrotor swarms and focused on solving the target tracking problem. Accordingly, we refined a min-max optimal control algorithm for fixed-wing UAVs tracking ground-based targets, by introducing constraints on bank angles and turn rates to enhance actuator reliability when pursuing agile and evasive targets. An intelligent and persistent evasive control strategy for the target was also devised to ensure robust performance testing and optimisation. These strategies were extended to 3D space, incorporating three altitude control algorithms to facilitate flexible UAV altitude control, leveraging various parameters such as desired UAV altitude and image size on the tracking camera lens. A novel evasive quadrotor algorithm was introduced, systematically testing UAV tracking efficacy against various evasive scenarios while implementing anti-collision measures to ensure UAV safety and adaptive optimisation improve the achieved performance. Using decentralised control strategies, cooperative tracking by multiple UAVs of single evasive quadrotor-type and dynamic target clusters was developed along with a new altitude control strategy and task assignment logic for efficient target interception. Lastly, a countermeasure strategy for tracking and neutralising non-cooperative adversarial targets within restricted airspace was implemented, using both Nonlinear Model Predictive Control (NMPC) and optimal controllers. The major contributions of this thesis include optimal control strategies, evasive target control, 3D target tracking, altitude control, cooperative multi-UAV tracking, adaptive optimisation, high-precision projectile algorithms, and countermeasures. We envision practical applications of the findings from this research in surveillance, security, search and rescue, agriculture, environmental monitoring, drone defence, and autonomous delivery systems. Future efforts to extend this research could explore adaptive evasion, enhanced collaborative UAV swarms, machine learning integration, sensor technologies, and real-world testing

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

Sliding Mode Control

The main objective of this monograph is to present a broad range of well worked out, recent application studies as well as theoretical contributions in the field of sliding mode control system analysis and design. The contributions presented here include new theoretical developments as well as successful applications of variable structure controllers primarily in the field of power electronics, electric drives and motion steering systems. They enrich the current state of the art, and motivate and encourage new ideas and solutions in the sliding mode control area