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

Logan Beaver

TL;DR

This extended abstracts presents a method to generate energy-optimal trajectories for multi-agent systems as a strategic-form game and demonstrates the performance of this algorithm in simulation and finds an optimal trajectory in 45 milliseconds on a tablet PC.

Abstract

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.

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

TL;DR

This extended abstracts presents a method to generate energy-optimal trajectories for multi-agent systems as a strategic-form game and demonstrates the performance of this algorithm in simulation and finds an optimal trajectory in 45 milliseconds on a tablet PC.

Abstract

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.
Paper Structure (5 sections, 10 equations, 3 figures)

This paper contains 5 sections, 10 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Optimization Problem
  3. Game-Theoretic Formulation
  4. Numerical Results
  5. Conclusions

Figures (3)

  • Figure 1: The two agents, blue and yellow, navigating from their initial state (circles) to goal states (squares) while avoiding obstacles. The red obstacles are inflated to compensate for the size of the agents during motion planning.
  • Figure 2: The pairwise safe distance constraint between the agents for the environment shown in Fig. \ref{['fig:trajectories']}.
  • Figure 3: The relative distance between the agents satisfies the safety constraints when their arrival times are delayed or advanced to avoid collisions.