Formation tracking control for multiple rigid bodies on matrix Lie groups: A system decomposition approach

Abstract

Summary This 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.

Trajectory tracking control for nonholonomic mobile robots under arbitrary reference input

“…where θ1 = θ 0 + θ01 . From the definition in (23), it can be observed that the auxiliary configuration g1 has same position as follower g 1 , while its orientation is decided by the leader's attitude θ 0 and the adjoint attitude θ01 .…”

“…Therefore, in this paper the robot is modelled in the Lie group SE (2), with the full name as Special Euclidean group in two dimensions, which is an important class of manifolds for planar rigid body motion. The researches under Lie group framework can be found in [19,20,21,22,23,24].…”

Robust Hierarchical Adaptive Fuzzy Relative Motion Coordination for Feature Points of Two Rigid Bodies With Input and Output Constraints

“…T HE pose motion control of the rigid body is a hot topic in the automation field for many years, since it is the physical nature of many kinds of man-made moving bodies in practice, such as the motions of automotive vehicles [1], aircrafts [2], spacecraft [3], marine vessels [4] and formations [5]. In particular, the relative motion between two vehicles is very common in advanced modern industry, such as the air refueling [6], shipboard landing [7], space docking [8] and underwater docking [9].…”

Trajectory tracking of nonholonomic mobile robots by geometric control on special Euclidean group

“…Therefore, in this article, the configuration of the nonholonomic mobile robot is described by the Lie group SE (2), with the full name as special Euclidean group in two dimensions, which is an important class of manifolds for planar rigid body motion. We recommend [22][23][24][25][26][27][28] for more results under the Lie group framework.…”