Passivity Shortageに基づく離散時間3次元位置姿勢同期制御

抄録

This paper investigates discrete-time pose (position and attitude) synchronization for a group of networked rigid bodies in three dimensions. The challenge is how to deal with 3D attitude motion dynamics on the Special Orthogonal group: SO(3) or the Special Eucledian group: SE(3) in the discrete-time domain. To cope with this issue, in this study, attitude dynamics are rigorously considered by employing exponential mapping. The rigid body network consisting of multiple bodies with discrete-time pose dynamics, relative pose measurements, and directed interconnection topology between the bodies is defined. Then, attitude synchronization is first investigated for the rigid body network. As the main feature of this work, it is shown that attitude dynamics of each rigid body have a passivity shortage-like property, and a distributed attitude synchronization law based on the property is proposed. Pose synchronization is next investigated with Euler approximations for position dynamics. Here, a passivity shortage-like property is also derived for approximated pose dynamics, and passivity shortage-based distributed pose synchronization laws are presented. The proposed techniques are verified via convergence analysis and simulations.