Sampled-data collective rotating consensus for second-order networks under directed interaction

• DOI: 10.1007/s12555-014-0260-8
• Publication Date: 2015-07-14T01:14:26Z
• Authors: Yintao Wang; Qi Sun
• Keywords: Relative velocity; Line (geometry)

This paper investigates collective rotating motions of second-order multi-agent systems in 3-D under a sampled-data setting. A rotating consensus protocol was proposed and conditions on sampling period, damping gain, communication topology and rotating angle such that the vehicles will eventually move on a straight-line path, cylindrical spirals and logarithmic, respectively, were derived. In particular, when the vehicles move along circular orbits, the relative radii of the orbits (respectively, the relative phases of the vehicles on their orbits) are equal to the relative magnitudes (respectively, the relative phases) of the components of a right eigenvector associated with the critical eigenvalue of the nonsymmetric Laplacian matrix. Simulations are performed to validate the theoretical results.