arXiv subjects

Michael Dorothy

Publications and source records attributed to Michael Dorothy.

23 records · Page 2Linked to original sources

arXiv2022

One Apollonius Circle is Enough for Many Pursuit-Evasion Games

This paper investigates obstacle-free simple motion pursuit-evasion problems where the pursuer is faster and game termination is point capture. It is well known that the interior of the Apollonius Circle (AC) is the evader's dominance region, however, it was unclear whether the evader could reach outside the initial AC without being captured. We construct a pursuit strategy that guarantees the capture of an evader within an arbitrarily close neighborhood of the initial AC. The pursuer strategy is derived by reformulating the game into a nonlinear control problem, and the guarantee holds against any admissible evader strategy. Our result implies that the evader can freely select the capture location, but only inside the initial AC. Therefore, a class of problems, including those where the payoff is determined solely based on the location of capture, are now trivial.

math.OC↗

arXiv2021

Dynamic Defender-Attacker Blotto Game

This work studies a dynamic, adversarial resource allocation problem in environments modeled as graphs. A blue team of defender robots are deployed in the environment to protect the nodes from a red team of attacker robots. We formulate the engagement as a discrete-time dynamic game, where the robots can move at most one hop in each time step. The game terminates with the attacker's win if any location has more attacker robots than defender robots at any time. The goal is to identify dynamic resource allocation strategies, as well as the conditions that determines the winner: graph structure, available resources, and initial conditions. We analyze the problem using reachable sets and show how the outdegree of the underlying graph directly influences the difficulty of the defending task. Furthermore, we provide algorithms that identify sufficiency of attacker's victory.

eess.SY↗

arXiv2021

Survey of Recent Multi-Agent Reinforcement Learning Algorithms Utilizing Centralized Training

Much work has been dedicated to the exploration of Multi-Agent Reinforcement Learning (MARL) paradigms implementing a centralized learning with decentralized execution (CLDE) approach to achieve human-like collaboration in cooperative tasks. Here, we discuss variations of centralized training and describe a recent survey of algorithmic approaches. The goal is to explore how different implementations of information sharing mechanism in centralized learning may give rise to distinct group coordinated behaviors in multi-agent systems performing cooperative tasks.

cs.MA↗

arXiv2020

Energy-Optimal Motion Planning for Agents: Barycentric Motion and Collision Avoidance Constraints

As robotic swarm systems emerge, it is increasingly important to provide strong guarantees on energy consumption and safety to maximize system performance. One approach to achieve these guarantees is through constraint-driven control, where agents seek to minimize energy consumption subject to a set of safety and task constraints. In this paper, we provide a sufficient and necessary condition for an energy-minimizing agent with integrator dynamics to have a continuous control input at the transition between unconstrained and constrained trajectories. In addition, we present and analyze barycentric motion and collision avoidance constraints to be used in constraint-driven control of swarms.

math.OC↗

arXiv2011

Neurobiologically Inspired Control of Engineered Flapping Flight

This article presents a new control approach and a dynamic model for engineered flapping flight with many interacting degrees of freedom. This paper explores the applications of neurobiologically inspired control systems in the form of Central Pattern Generators (CPG) to control flapping flight dynamics. A rigorous mathematical and control theoretic framework to design complex three dimensional wing motions is presented based on phase synchronization of nonlinear oscillators. In particular, we show the flapping flying dynamics without a tail or traditional aerodynamic control surfaces can be effectively controlled by a reduced set of CPG parameters that generate phase-synchronized or symmetry-breaking oscillatory motions of two main wings. Furthermore, by using Hopf bifurcation, we show that tailless aircraft alternating between flapping and gliding can be effectively stabilized by smooth wing motions driven by the CPG network. Results of numerical simulation with a full six degree-of-freedom flight dynamic model validate the effectiveness of the proposed neurobiologically inspired control approach.

math.OC↗