Autonomous Navigation of Multiple Unmanned Aerial Vehicles

Abstract

The focus of the present thesis is on the analysis and design of guidance, control and navigation algorithms for unmanned aerial vehicles, specifi cally in the context of drone warfare and aerospace battles. In aerospace engagement scenarios involving autonomous agents, the synthesis of intelligent actions must consider the potential strategies by the adversary. When analysing the possible outcomes of an engagement, unpredictability of the adversary's decisions presents the main challenge, the design of our strategies must be robust to a very broad set of possible counter strategies employed by the adversary. Differential game theory provides the correct framework to analyse and design optimal strategies in these dynamic engagement scenarios. Here the goal is the nd the state-feedback Nash equilibrium, the optimal outcome of an engagement scenario, in which all parties with knowledge of the strategies deployed, cannot increase their payoff by altering their decision making process. The contents of this thesis uncovers signi ficant new results in the area of pursuit-evasion differential games. The main contributions are, the discovery of a new geometric mechanism to verify the Hamilton-Jacobi-Bellman equations, and uncovering new symmetries in simple- motion pursuit-evasion games. More specifi cally, the thesis primarily examines the differential game of active target de- fence, otherwise known as the Target-Attacker-Defender pursuit-evasion game. This simple- motion, two-team, zero-sum differential game emulates a common aerospace engagement scenario found in defence applications. Here an explosive carrying Attacker is tasked with neutralising a Target, and the Target in its defence launches an agent named the Defender, from another platform in an integrated/fused air defence. The present thesis identi fies and proves the value and optimal state-feedback strategies for both teams in this engagement scenario. This is done via the analysis of the discrete- time turn-based variant of the differential game, also known as the upper or lower value. Moreover, we unearth new symmetries in the differential game, named Target Symmetry and Defender Symmetry. A symmetry is a transformation of the state of the differential game that leaves the optimal strategies unchanged. Using the newly discovered symmetries we develop unifi ed optimality principles, culminating in the Holographic Theorem for the differential game of active target defence, and more generally, the Holographic Principle for simple-motion differential games.