Trochoidal Patterns Generation Using Generalized Consensus Strategy for Double-Integrator Dynamic Agents

This article studies a distributed consensus law to achieve a coordinated trochoidal formation among a team of mobile agents. The mobile agents are modeled as double integrators. We generalize an existing consensus algorithm for double-integrator dynamics (1) to achieve trochoidal patterns under a general network topology and (2) to extend the pattern formation in a 3-D plane. Since the trochoidal patterns are 2-D curves, the proposed control law allows us to specify the 2-D plane in the 3-D space on which the patterns will be formed. We modify the standard consensus protocol and manipulate the gains to create trochoidal motion through local information exchange by appropriately placing the eigenvalues of the system. Trochoids have been used in multifaceted robotic applications such as area coverage, hurricane sampling, and orbit designs for satellites, apart from their aesthetic appeal. Computer simulations and multi-robot experiments are presented to validate the theoretical findings.