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Learning swarm behaviour from a flock of homing pigeons using inverse optimal control

Afreen Islam

Abstract

In this work, Global Position System (GPS) data from a flock of homing pigeons are analysed. The flocking behaviour of the considered homing pigeons is formulated as a swarm optimal trajectory tracking control problem. The swarm problem in this work is modeled with the idea that one or two pigeons at the forefront lead the flock. Each follower pigeon is assumed to follow a leader pigeon immediately ahead of themselves, instead of directly following the leaders at the forefront of the flock. The trajectory of each follower pigeon is assumed to be a solution of an optimal trajectory tracking control problem. An optimal control problem framework is created for each follower pigeon. An important aspect of an optimal control problem is the cost function. A minimum principle based method for multiple flight data is proposed, which can help in learning the unknown weights of the cost function of the optimal trajectory tracking control problem for each follower pigeon, from flight trajectories' information obtained from GPS data.

Learning swarm behaviour from a flock of homing pigeons using inverse optimal control

Abstract

In this work, Global Position System (GPS) data from a flock of homing pigeons are analysed. The flocking behaviour of the considered homing pigeons is formulated as a swarm optimal trajectory tracking control problem. The swarm problem in this work is modeled with the idea that one or two pigeons at the forefront lead the flock. Each follower pigeon is assumed to follow a leader pigeon immediately ahead of themselves, instead of directly following the leaders at the forefront of the flock. The trajectory of each follower pigeon is assumed to be a solution of an optimal trajectory tracking control problem. An optimal control problem framework is created for each follower pigeon. An important aspect of an optimal control problem is the cost function. A minimum principle based method for multiple flight data is proposed, which can help in learning the unknown weights of the cost function of the optimal trajectory tracking control problem for each follower pigeon, from flight trajectories' information obtained from GPS data.

Paper Structure

This paper contains 2 sections, 1 theorem, 37 equations, 4 figures, 4 tables.

Table of Contents

  1. Introduction
  2. The hard-constrained minimum principle-based IOC method

Key Result

Theorem 1

Given the system dynamics $\dot{X}_i(t)=f(X_i(t),U_i(t))$ for a single flight data of a follower pigeon or $\dot{X}_{i_j}(t)=f(X_{i_j}(t),U_{i_j}(t))$ for multiple flight data of a pigeon, the basis function vector $\phi(X_i(t),U_i(t))$ or $\phi(X_{i_j}(t),U_{i_j}(t))$, and a specific system traject

Figures (4)

  • Figure 1: Kinematics diagram for the flight of a pigeon
  • Figure 2: Hierarchy of the pigeons in the flock
  • Figure 3: Leader-follower pairs in the flock of pigeons indicated by dotted circular contours
  • Figure 4: The swarming behaviour of the flock of pigeons is formulated as an optimal control problem. Measurements of trajectories of the pigeons are then used to solve the IOC problem to recover $c_i$

Theorems & Definitions (2)

  • Remark 1
  • Theorem 1