An Asymmetric Version of the Two Car Pursuit-Evasion Game

Copyright © 2014 IEEEPresented at 53rd IEEE Conference on Decision and Control, Los Angeles, CA, Dec. 15-17, 2014DOI: http://dx.doi.org/10.1109/CDC.2014.7040055n this paper we consider a differential game of pursuit and evasion involving two players with constant, but different, speeds, and different maneuverability constraints. Specifically, the evader has limited maneuverability, while the pursuer is completely agile. This problem is an asymmetric version of the well-known Game of Two Cars. The aim of this paper is to derive the optimal strategies of the two players and characterize areas of initial conditions that lead to capture if the pursuer acts optimally, and areas that guarantee evasion regardless of the pursuer's strategy. It is shown that the problem reduces to a special version of Zermelo's Navigation Problem (ZNP) for the pursuer. Therefore, the well-known ZNP solution can be used to validate the results obtained through the differential game framework as well as to characterize the time-optimal trajectories. The results are directly applicable to collision avoidance problems

Trustworthiness and Motivations

Trust can be thought of as a three place relation: A trusts B to do X. Trustworthiness has two components: competence (does the trustee have the relevant skills, knowledge and abilities to do X?) and willingness (is the trustee intending or aiming to do X?). This chapter is about the willingness component, and the different motivations that a trustee may have for fulfilling trust. The standard assumption in economics is that agents are self-regarding, maximizing their own consumption of goods and services. This is too restrictive. In particular, people may be concerned with the outcomes of others, and they may be concerned to follow ethical principles. I distinguish weak trustworthiness, which places no restrictions on B’s motivation for doing X, from strong trustworthiness, where the behaviour must have a particular non-selfish motivation, in finance the fiduciary commitment to promote the interests of the truster. I discuss why strong trustworthiness may be more efficient and also normatively preferable to weak. In finance, there is asymmetric information between buyer and seller, which creates a need for trustworthy assessment of products. It also creates an ambiguity about whether the relationship is one of buyer and seller, governed by caveat emptor, or a fiduciary relationship of advisor and client. This means that there are two possible reasons why trust may be breached: because the trustee didn’t realise that the truster framed the relationship as a fiduciary one, or because the trustee did realise but actively sought to take advantage of the trust. Correspondingly, there are two possible types of agent: normal people who are not always self-regarding and who are trust responsive (if they believe that they are being trusted then they are likely to fulfill that trust), and knaves, after Hume’s character who is always motivated by his own private interest. We can increase the trustworthiness of normal people by getting them to re-frame the situation as one of trust, so they will be strongly trustworthy (i.e. change of institutional culture), and by providing non-monetary incentives (the correct choice of incentive will depend on exactly what their non-selfish motivation is). Knaves need sanctions, which can make them weakly trustworthy. However, this is a delicate balance because sanctions can crowd out normative frames. We can also increase the trustworthiness of financiers by making finance less attractive to knaves; changing the mix of types in finance could help support the necessary cultural change

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

Asymmetric Robot Motion Design for Pursuit-Evasion Games

Symmetric turning control is the typical design choice for most machines. However, historical examples of asymmetric machine design, as well as examples of asymmetry in nature, suggest that asymmetric turning may be a potential advantage in adversarial applications. For instance, aircraft of World Wars I and II were plagued by asymmetric turning controls as a result of gyroscopic forces from the rotating engine. Pilots of the time actually believed this to be a feature, not a bug, suggesting that the asymmetric turning improved strategic evasion and pursuit during battle. As autonomous robots become increasingly critical in military operations, it is imperative that we endow them with strategic designs for better performance. We seek to understand if asymmetric turning is an advantageous design. Using Karaman and Frazzoli's sample-based algorithm for pursuit-evasion games, software simulates robot motion planning in an asymmetric Dubins state space to observe how asymmetric turning influences agent success. We demonstrate mathematically that the Dubins interval path solutions are applicable to asymmetric Dubins vehicles, as both are utilized within the simulation. The Open Motion Planning Library (OMPL) is leveraged to implement the pursuit-evasion game algorithm. To simulate asymmetric action, agents are assigned varying degrees of asymmetric turning constraints, such that as one turn sharpens, the other broadens. Agents then compete in a pursuit-evasion game. Pursuit-evasion games are simulated across a range of asymmetric turning match-ups and agent starting positions. Results show that pursuer success increases as its asymmetry increases. Evader success remains constant, regardless of asymmetric turning influence. Furthermore, the advantages of asymmetric turning can be further augmented when considered in conjunction with relative agent starting position. The results of this research inform more intelligent machine design strategies for vehicles in dynamic spaces

Optimal steering for kinematic vehicles with applications to spatially distributed agents

The recent technological advances in the field of autonomous vehicles have resulted in a growing impetus for researchers to improve the current framework of mission planning and execution within both the military and civilian contexts. Many recent efforts towards this direction emphasize the importance of replacing the so-called monolithic paradigm, where a mission is planned, monitored, and controlled by a unique global decision maker, with a network centric paradigm, where the same mission related tasks are performed by networks of interacting decision makers (autonomous vehicles). The interest in applications involving teams of autonomous vehicles is expected to significantly grow in the near future as new paradigms for their use are constantly being proposed for a diverse spectrum of real world applications. One promising approach to extend available techniques for addressing problems involving a single autonomous vehicle to those involving teams of autonomous vehicles is to use the concept of Voronoi diagram as a means for reducing the complexity of the multi-vehicle problem. In particular, the Voronoi diagram provides a spatial partition of the environment the team of vehicles operate in, where each element of this partition is associated with a unique vehicle from the team. The partition induces, in turn, a graph abstraction of the operating space that is in a one-to-one correspondence with the network abstraction of the team of autonomous vehicles; a fact that can provide both conceptual and analytical advantages during mission planning and execution. In this dissertation, we propose the use of a new class of Voronoi-like partitioning schemes with respect to state-dependent proximity (pseudo-) metrics rather than the Euclidean distance or other generalized distance functions, which are typically used in the literature. An important nuance here is that, in contrast to the Euclidean distance, state-dependent metrics can succinctly capture system theoretic features of each vehicle from the team (e.g., vehicle kinematics), as well as the environment-vehicle interactions, which are induced, for example, by local winds/currents. We subsequently illustrate how the proposed concept of state-dependent Voronoi-like partition can induce local control schemes for problems involving networks of spatially distributed autonomous vehicles by examining different application scenarios.PhDCommittee Chair: Tsiotras Panagiotis; Committee Member: Egerstedt Magnus; Committee Member: Feron Eric; Committee Member: Haddad Wassim; Committee Member: Shamma Jef

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

Illiquidity and All Its Friends

The recent crisis was characterized by massive illiquidity. This paper reviews what we know and don't know about illiquidity and all its friends: market freezes, fire sales, contagion, and ultimately insolvencies and bailouts. It first explains why liquidity cannot easily be apprehended through a single statistics, and asks whether liquidity should be regulated given that a capital adequacy requirement is already in place. The paper then analyzes market breakdowns due to either adverse selection or shortages of financial muscle, and explains why such breakdowns are endogenous to balance sheet choices and to information acquisition. It then looks at what economics can contribute to the debate on systemic risk and its containment. Finally, the paper takes a macroeconomic perspective, discusses shortages of aggregate liquidity and analyses how market value accounting and capital adequacy should react to asset prices. It concludes with a topical form of liquidity provision, monetary bailouts and recapitalizations, and analyses optimal combinations thereof; it stresses the need for macroprudential policies.