Affine Formation Maneuver Control of Multi-Agent Systems with Triple-Integrator Dynamics

This paper addresses the affine formation maneuver control of multi-agent systems with triple-integrator dynamics for both continuous-time and sampled-data settings. In affine formation control, the agents are supposed to form a desired geometric pattern and simultaneously achieve required maneuvers, such as rotation, scaling and translation. In existing literature, it is understood that this can be achieved for systems with double-integrator dynamics where the inter-agent communications occur continuously in time. However, agents may only be able to communicate in periodic time intervals and a broad range of systems have complex dynamics requiring higher-order dynamics in some practical situations. In this paper, we propose novel maneuver control laws using triple-integrator dynamics. The proposed approach is based on stress matrix, which allows the communication graph weights to be positive or negative, and it can be considered as a generalized Laplacian matrix of a graph. Under the proposed control laws, the group of agents are able to track time-varying targets that are affine transformations of a given nominal formation, and the desired formation maneuvers are only known by the leaders.