Dynamic Elliptical Shaping Control for Swarm Robots

Abstract

Solving the robotic swarm coverage problem for an elliptical area has various applications for exploring novel environments. Solutions for this problem should cover a specified ellipse and seamlessly adapt to changing numbers of robots. Previous solutions used techniques such as formation control, vector fields, and neural networks. While these techniques were successful, they all lacked one or more of the three key tenants of swarm elliptical attraction: complete coverage of an ellipse with commandable parameters, simplicity for scaling in the number of robots, and adaptive sizing. Additionally, no previous work presented guidelines for ensuring that the swarms could successfully and safely converge to the commanded ellipse without collisions. In contrast, this work presents a novel swarm elliptical attraction behavior with all three key tenants with guidelines for ellipse and swarm parameter selection. First, a new Lyapunov stable elliptical attraction behavior for Reactive Particle Swarms is presented. The behavior commands robots to cover the entire ellipse area for a specific semimajor axis, eccentricity, and orientation. Additionally, dynamic interagent spacing naturally ensures coverage for different numbers of robots. Second, the work presents a novel adaptive sizing algorithm that varies the ellipse’s semimajor axis based on the swarm state. The adaptive sizing algorithm specifies the eccentricity and orientation using time-varying functions. Third, guidelines for selecting the number of robots, commanded ellipse area, obstacle avoidance distance, and robot communication range that allow for successful aggregation to the commanded ellipse are presented. All three of the results are verified using simulation and hardware-in-the-loop trials.