arXiv subjects

Logan Beaver

Publications and source records attributed to Logan Beaver.

7 recordsLinked to original sources

arXiv2025

Flatness-based Finite-Horizon Multi-UAV Formation Trajectory Planning and Directionally Aware Collision Avoidance Tracking

Optimal collision-free formation control of the unmanned aerial vehicle (UAV) is a challenge. The state-of-the-art optimal control approaches often rely on numerical methods sensitive to initial guesses. This paper presents an innovative collision-free finite-time formation control scheme for multiple UAVs leveraging the differential flatness of the UAV dynamics, eliminating the need for numerical methods. We formulate a finite-time optimal control problem to plan a formation trajectory for feasible initial states. This optimal control problem in formation trajectory planning involves a collective performance index to meet the formation requirements to achieve relative positions and velocity consensus. It is solved by applying Pontryagin's principle. Subsequently, a collision-constrained regulating problem is addressed to ensure collision-free tracking of the planned formation trajectory. The tracking problem incorporates a directionally aware collision avoidance strategy that prioritizes avoiding UAVs in the forward path and relative approach. It assigns lower priority to those on the sides with an oblique relative approach, disregarding UAVs behind and not in the relative approach. The high-fidelity simulation results validate the effectiveness of the proposed control scheme.

cs.RO↗

arXiv2025

A Global Games-Inspired Approach to Multi-Robot Task Allocation for Heterogeneous Teams

In this article we propose a game-theoretic approach to the multi-robot task allocation problem using the framework of global games. Each task is associated with a global signal, a real-valued number that captures the task execution progress and/or urgency. We propose a linear objective function for each robot in the system, which, for each task, increases with global signal and decreases with the number assigned robots. We provide conditions on the objective function hyperparameters to induce a mixed Nash equilibrium, i.e., solutions where all robots are not assigned to a single task. The resulting algorithm only requires the inversion of a matrix to determine a probability distribution over the robot assignments. We demonstrate the performance of our algorithm in simulation and provide direction for applications and future work.

cs.RO↗

arXiv2024

Energy-Optimal Multi-Agent Navigation as a Strategic-Form Game

This extended abstracts presents a method to generate energy-optimal trajectories for multi-agent systems as a strategic-form game. Using recent results in optimal control, we demonstrate that an energy-optimal trajectory can be generated in milliseconds if the sequence of constraint activations is known a priori. Thus, rather than selecting an infinite-dimensional action from a function space, the agents select their actions from a finite number of constraints and determine the time that each becomes active. Furthermore, the agents can exactly encode their trajectory in a set of real numbers, rather than communicating their control action as an infinite-dimensional function. We demonstrate the performance of this algorithm in simulation and find an optimal trajectory in 45 milliseconds on a tablet PC.

math.OC↗

arXiv2021

Energy-Optimal Goal Assignment of Multi-Agent System with Goal Trajectories in Polynomials

In this paper, we propose an approach for solving an energy-optimal goal assignment problem to generate the desired formation in multi-agent systems. Each agent solves a decentralized optimization problem with only local information about its neighboring agents and the goals. The optimization problem consists of two sub-problems. The first problem seeks to minimize the energy for each agent to reach certain goals, while the second problem entreats an optimal combination of goal and agent pairs that minimizes the energy cost. By assuming the goal trajectories are given in a polynomial form, we prove the solution to the formulated problem exists globally. Finally, the effectiveness of the proposed approach is validated through the simulation.

cs.MA↗

arXiv2019

A Game-Theoretic Analysis of the Social Impact of Connected and Automated Vehicles

In this paper, we address the much-anticipated deployment of connected and automated vehicles (CAVs) in society by modeling and analyzing the social-mobility dilemma in a game-theoretic approach. We formulate this dilemma as a normal-form game of players making a binary decision: whether to travel with a CAV (CAV travel) or not (non-CAV travel) and by constructing an intuitive payoff function inspired by the socially beneficial outcomes of a mobility system consisting of CAVs. We show that the game is equivalent to the Prisoner's dilemma, which implies that the rational collective decision is the opposite of the socially optimum. We present two different solutions to tackle this phenomenon: one with a preference structure and the other with institutional arrangements. In the first approach, we implement a social mechanism that incentivizes players to non-CAV travel and derive a lower bound on the players that ensures an equilibrium of non-CAV travel. In the second approach, we investigate the possibility of players bargaining to create an institution that enforces non-CAV travel and show that as the number of players increases, the incentive ratio of non-CAV travel over CAV travel tends to zero. We conclude by showcasing the last result with a numerical study.

cs.GT↗

arXiv2018

Simulation to Scaled City: Zero-Shot Policy Transfer for Traffic Control via Autonomous Vehicles

Using deep reinforcement learning, we train control policies for autonomous vehicles leading a platoon of vehicles onto a roundabout. Using Flow, a library for deep reinforcement learning in micro-simulators, we train two policies, one policy with noise injected into the state and action space and one without any injected noise. In simulation, the autonomous vehicle learns an emergent metering behavior for both policies in which it slows to allow for smoother merging. We then directly transfer this policy without any tuning to the University of Delaware Scaled Smart City (UDSSC), a 1:25 scale testbed for connected and automated vehicles. We characterize the performance of both policies on the scaled city. We show that the noise-free policy winds up crashing and only occasionally metering. However, the noise-injected policy consistently performs the metering behavior and remains collision-free, suggesting that the noise helps with the zero-shot policy transfer. Additionally, the transferred, noise-injected policy leads to a 5% reduction of average travel time and a reduction of 22% in maximum travel time in the UDSSC. Videos of the controllers can be found at https://sites.google.com/view/iccps-policy-transfer.

eess.SY↗

arXiv2018

A Decentralized Control Framework for Energy-Optimal Goal Assignment and Trajectory Generation

This paper proposes a decentralized approach for solving the problem of moving a swarm of agents into a desired formation. We propose a decentralized assignment algorithm which prescribes goals to each agent using only local information. The assignment results are then used to generate energy-optimal trajectories for each agent which have guaranteed collision avoidance through safety constraints. We present the conditions for optimality and discuss the robustness of the solution. The efficacy of the proposed approach is validated through a numerical case study to characterize the framework's performance on a set of dynamic goals.

math.OC↗