Smoothed-Particle-Hydrodynamics for the Control of Robotic Swarms, and Parametric Associations

Abstract

A swarm of robots has several macroscopic properties that are extraneous to an individual robot. This is a direct consequence of the fact that a swarm is a coupled high-dimensional system that is characterized by interactions between individual robots. In a smoothed-particle-hydrodynamics-based control of a swarm of robots, the equations of motion may be parameterized by key parameters that affect the macroscopic properties of the swarm such as separation, compressibility, cohesivity, and velocity matching. In this article, we analyze this relation between the parameters in the equations of motion and the properties of the swarm. The resulting analysis enables the design of a versatile, scalable controller that may be modified and adopted to suit the desired objectives of individual applications. We also present a new interaction potential that enables controlling the robot-robot separation, beyond maintaining the robot density, and providing a swarm cohesive force that keeps the robots in the swarm together. The constructed interaction potential is conservative, and the overall swarm stability may still be established using passivity arguments in the presence of a dissipative process. In this article, we use Lyapunov methods on the total energy to establish this stability. The salient features of the proposed controller are verified using simulations and experiments. The experiments are conducted using two real physical airplanes to demonstrate the practical feasibility of the proposed controller.