Abstract
SummaryThis paper addresses the finite‐time formation tracking control problem for multiple rigid bodies whose dynamics are defined on the matrix Lie groups, including the special Euclidean group SE(2),SE(3) as specific cases. The reference trajectory in a form of rotational and translational motions is generated offline in advance as the virtual leader for tracking. Moreover, the formation time is specified according to the task, and the desired formation shape is given a priori with respect to the virtual leader. By virtue of the system decomposition approach, intrinsic formation tracking laws are derived for arbitrary initial velocities for the rigid bodies. The tracking controllers are intrinsic meaning that the dynamics and controllers are developed in the body‐fixed frame without a global reference frame. Moreover, based on the geometric convex combination on SE(3), the result is extended to the distributed case where only the neighboring agents' state are used. Two numerical simulations on SE(2) and SE(3) are given respectively to illustrate the validity and robustness of the proposed controllers. Copyright © 2017 John Wiley & Sons, Ltd.
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