Game theoretic control of multi-agent systems: from centralised to distributed control

Differential game theory provides a framework to study the dynamic strategic interactions between multiple decisors, or players, each with an individual criterion to optimise. Noting the analogy between the concepts of "players'' and "agents'', it seems apparent that this framework is well-suited for control of multi-agent systems (MAS). Most of the existing results in the field of differential games assume that players have access to the full state of the system. This assumption, while holding reasonable in certain scenarios, does not apply in contexts where decisions are to be made by each individual agent based only on available local information. This poses a significant challenge in terms of the control design: distributed control laws, which take into account what information is available, are required. In the present work concepts borrowed from differential game theory and graph theory are exploited to formulate systematic frameworks for control of MAS, in a quest to shift the paradigm from centralised to distributed control. We introduce some preliminaries on differential game theory and graph theory, the latter for modeling communication constraints between the agents. Motivated by the difficulties associated with obtaining exact Nash equilibrium solutions for nonzero-sum differential games, we consider three approximate Nash equilibrium concepts and provide different characterisations of these in terms a class of static optimisation problems often encountered in control theory. Considering the multi-agent collision avoidance problem, we present a game theoretic approach, based on a (centralised) hybrid controller implementation of the control strategies, capable of ensuring collision-free trajectories and global convergence of the error system. We make a first step towards distributed control by introducing differential games with partial information, a framework for distributed control of MAS subject to local communication constraints, in which we assume that the agents share their control strategies with their neighbours. This assumption which, in the case of non-acyclic communication graphs, translates into the requirement of shared reasoning between groups of agents, is then relaxed through the introduction of a framework based on the concept of distributed differential games, i.e. a collection of multiple (fictitious) local differential games played by each individual agent in the MAS. Finally, we revisit the multi-agent collision avoidance problem in a distributed setting: considering time-varying communication graph topologies, which enable to model proximity-based communication constraints, we design differential games characterised by a Nash equilibrium solution which yields collision-free trajectories guaranteeing that all the agents reach their goal, provided no deadlocks occur. The efficacy of the game theoretic frameworks introduced in this thesis is demonstrated on several case studies of practical importance, related to robotic coordination and control of microgrids.Open Acces

FaSTrack: a Modular Framework for Real-Time Motion Planning and Guaranteed Safe Tracking

Real-time, guaranteed safe trajectory planning is vital for navigation in unknown environments. However, real-time navigation algorithms typically sacrifice robustness for computation speed. Alternatively, provably safe trajectory planning tends to be too computationally intensive for real-time replanning. We propose FaSTrack, Fast and Safe Tracking, a framework that achieves both real-time replanning and guaranteed safety. In this framework, real-time computation is achieved by allowing any trajectory planner to use a simplified \textit{planning model} of the system. The plan is tracked by the system, represented by a more realistic, higher-dimensional \textit{tracking model}. We precompute the tracking error bound (TEB) due to mismatch between the two models and due to external disturbances. We also obtain the corresponding tracking controller used to stay within the TEB. The precomputation does not require prior knowledge of the environment. We demonstrate FaSTrack using Hamilton-Jacobi reachability for precomputation and three different real-time trajectory planners with three different tracking-planning model pairs.Comment: Published in the IEEE Transactions on Automatic Contro

MULTI-AGENT UNMANNED UNDERWATER VEHICLE VALIDATION VIA ROLLING-HORIZON ROBUST GAMES

Autonomy in unmanned underwater vehicle (UUV) navigation is critical for most applications due to inability of human operators to control, monitor or intervene in underwater environments. To ensure safe autonomous navigation, verification and validation (V&V) procedures are needed for various applications. This thesis proposes a game theory-based benchmark validation technique for trajectory optimization for non-cooperative UUVs. A quadratically constrained nonlinear program formulation is presented, and a "perfect-information reality" validation framework is derived by finding a Nash equilibrium to various two-player pursuit-evasion games (PEG). A Karush-Kuhn-Tucker (KKT) point to such a game represents a best-case local optimum, given perfect information available to non-cooperative agents. Rolling-horizon foresight with robust obstacles are incorporated to demonstrate incomplete information and stochastic environmental conditions. A MATLAB-GAMS interface is developed to model the rolling-horizon game, and is solved via a mixed complementarity problem (MCP), and illustrative examples show how equilibrium trajectories can serve as benchmarks for more practical real-time path planners

Receding Horizon Re-ordering of Multi-Agent Execution Schedules

The trajectory planning for a fleet of Automated Guided Vehicles (AGVs) on a roadmap is commonly referred to as the Multi-Agent Path Finding (MAPF) problem, the solution to which dictates each AGV's spatial and temporal location until it reaches it's goal without collision. When executing MAPF plans in dynamic workspaces, AGVs can be frequently delayed, e.g., due to encounters with humans or third-party vehicles. If the remainder of the AGVs keeps following their individual plans, synchrony of the fleet is lost and some AGVs may pass through roadmap intersections in a different order than originally planned. Although this could reduce the cumulative route completion time of the AGVs, generally, a change in the original ordering can cause conflicts such as deadlocks. In practice, synchrony is therefore often enforced by using a MAPF execution policy employing, e.g., an Action Dependency Graph (ADG) to maintain ordering. To safely re-order without introducing deadlocks, we present the concept of the Switchable Action Dependency Graph (SADG). Using the SADG, we formulate a comparatively low-dimensional Mixed-Integer Linear Program (MILP) that repeatedly re-orders AGVs in a recursively feasible manner, thus maintaining deadlock-free guarantees, while dynamically minimizing the cumulative route completion time of all AGVs. Various simulations validate the efficiency of our approach when compared to the original ADG method as well as robust MAPF solution approaches.Comment: IEEE Transactions on Robotics (T-Ro) preprint, 17 pages, 32 figure

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

Construction of Barrier in a Fishing Game With Point Capture

This paper addresses a particular pursuit-evasion game, called as “fishing game” where a faster evader attempts to pass the gap between two pursuers. We are concerned with the conditions under which the evader or pursuers can win the game. This is a game of kind in which an essential aspect, barrier, separates the state space into disjoint parts associated with each player's winning region. We present a method of explicit policy to construct the barrier. This method divides the fishing game into two subgames related to the included angle and the relative distances between the evader and the pursuers, respectively, and then analyzes the possibility of capture or escape for each subgame to ascertain the analytical forms of the barrier. Furthermore, we fuse the games of kind and degree by solving the optimal control strategies in the minimum time for each player when the initial state lies in their winning regions. Along with the optimal strategies, the trajectories of the players are delineated and the upper bounds of their winning times are also derived