Formation Tracking of Nonholonomic Systems on the Special Euclidean Group under Fixed and Switching Topologies: An Affine Formation Strategy

2021 ◽  
Vol 59 (4) ◽  
pp. 2850-2874
Author(s):  
Junyi Yang ◽  
Feng Xiao ◽  
Tongwen Chen
Keyword(s):  
Nonholonomic Systems ◽  
Euclidean Group ◽  
Switching Topologies ◽  
Formation Tracking ◽  
Special Euclidean Group

scholarly journals Distributed Adaptive Formation Tracking Control under Fixed and Switching Topologies: Application on General Linear Multi-Agent Systems

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 941
Author(s):  
Tianhao Sun ◽  
Huiying Liu ◽  
Yongming Yao ◽  
Tianyu Li ◽  
Zhibo Cheng
Keyword(s):  
Switching Topology ◽  
General Linear ◽  
Time Varying ◽  
Multi Agent System ◽  
Multi Agent Systems ◽  
Agent System ◽  
Switching Topologies ◽  
Formation Tracking ◽  
Leader Following ◽  
Multi Agent

In this paper, the time-varying formation tracking problem of the general linear multi-agent system is discussed. A distributed formation tracking protocol based on Riccati inequalities with adaptive coupling weights among the follower agents and the leader agent is designed for a leader-following multi-agent system under fixed and switching topologies. The formation configuration involved in this paper is expressed as a bounded piecewise continuously differentiable vector function. The follower agents will achieve the desired formation tracking trajectory of the leader. In traditional static protocols, the coupling weights depend on the communication topology and is a constant. However, in this paper, the coupling weights are updated by the state errors among the neighboring agents. Moreover, the stability analysis of the MAS under switching topology is presented, and proves that the followers also could achieve pre-specified time-varying formation, if the communication graph is jointly connected. Two numerical simulations indicate the capabilities of the algorithms.

scholarly journals Polynomial Invariants of the Euclidean Group Action on Multiple Screws

2021 ◽  
Author(s):  
◽  
Deborah Crook
Keyword(s):  
Group Action ◽  
Three Dimensions ◽  
Euclidean Group ◽  
Polynomial Invariants ◽  
Generating Sets ◽  
Special Euclidean Group ◽  
The One

<p>In this work, we examine the polynomial invariants of the special Euclidean group in three dimensions, SE(3), in its action on multiple screw systems. We look at the problem of finding generating sets for these invariant subalgebras, and also briefly describe the invariants for the standard actions on R^n of both SE(3) and SO(3). The problem of the screw system action is then approached using SAGBI basis techniques, which are used to find invariants for the translational subaction of SE(3), including a full basis in the one and two-screw cases. These are then compared to the known invariants of the rotational subaction. In the one and two-screw cases, we successfully derive a full basis for the SE(3) invariants, while in the three-screw case, we suggest some possible lines of approach.</p>

scholarly journals A Mobility Determination Method for Parallel Platforms Based on the Lie Algebra of SE(3) and Its Subspaces

2021 ◽  
pp. 1-12
Author(s):  
Alejandro de Jesús Sánchez-García ◽  
José M. Rico ◽  
J. Jesús Cervantes-Sánchez ◽  
Pablo Lopez-Custodio
Keyword(s):  
Lie Algebra ◽  
Screw Theory ◽  
Determination Method ◽  
Mobility Analysis ◽  
Euclidean Group ◽  
Second Stage ◽  
Direct Sum ◽  
Three Stages ◽  
Last Stage ◽  
Special Euclidean Group

Abstract This contribution presents a screw theory-based method for determining the mobility of fully parallel platforms. The method is based in the application of three stages. The first stage involves the application of the intersection of the subalgebras of Lie algebra, se(3), of the special Euclidean group, SE(3), associated with the legs of the platform. The second stage analyzes the possibility of the legs of the platform generating a sum or direct sum of two subalgebras of the Lie algebra, se(3). The last stage, if necessary, considers the possibility of the kinematic pairs of the legs satisfying certain velocity conditions; these conditions allow to reduce the platform's mobility analysis to one that can solved using one of the two previous stages.

scholarly journals Time-varying output formation-tracking of heterogeneous multi-agent systems with time-varying delays and switching topologies

2021 ◽  
Vol 54 (9-10) ◽  
pp. 1371-1382
Author(s):  
Shiyu Zhou ◽  
Yongzhao Hua ◽  
Xiwang Dong ◽  
Jianglong Yu ◽  
Zhang Ren
Keyword(s):  
Tracking Error ◽  
Lyapunov Theory ◽  
Reference Trajectory ◽  
Time Varying ◽  
Multi Agent Systems ◽  
Agent Systems ◽  
Switching Topologies ◽  
Formation Tracking ◽  
Multi Agent ◽  
Control Feedback

This paper focuses on the time-varying output formation (TVOF) tracking control of heterogeneous linear multi-agent systems (HL-MASs) with both delays and switching topologies, where the followers’ outputs can move along the reference trajectory generated by the leaders and maintain the desired time-varying formation. First, a distributed observer is proposed for each follower, aiming to estimate the convex combination of leaders’ state with both communication delays and switching graphs. The observer’s error for heterogeneous MASs is analyzed based on Lyapunov theory and linear matrix inequality (LMI) technique. Second, the observer is incorporated into the output formation tracking protocol. Then, an algorithm is put forward to calculate the control feedback gains and the formation tracking feasibility constraint is also provided. Furthermore, the convergence of the formation tracking error is proved. At last, the effectiveness of this proposed method is validated through a numerical simulation.

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