Affine Formation Algorithms and Implementation Based on Triple-Integrator Dynamics

This paper presents novel affine formation algorithms and implementations in different scenarios for the coordination of multi-agent systems with triple-integrator agent dynamics for both sampled-data and continuous-time settings. The agents in affine maneuver control are to be capable of producing required geometric shapes and simultaneously accomplishing desired maneuvers such as shearing, rotation, translation and scaling. From existing work, these tasks can be accomplished for systems whose agent dynamics are described using double-integrators and the agents communicate continuously in time. In some practical situations, however, the inter-agent communication may be limited to periodic intervals of time. Furthermore, a wide range of systems is governed by complex dynamics described with higher-orders. This paper presents two novel algorithms based on triple-integrator agent dynamics. Four implementation cases comprising of two scenarios each studied in both continuous-time and sampled-data cases are considered. Under the proposed algorithms, the collection of agents are capable of tracking time-varying targets which are affine transforms of the reference formation, if the leaders have knowledge of the required formation maneuvers. Detailed implementation results are presented to demonstrate the efficacy of the proposed algorithms.