Passive Decomposition Approach to Formation and Maneuver Control of Multiple Rigid Bodies

[+] Author and Article Information
Dongjun Lee

Department of Mechanical, Aerospace and Biomedical Engineering, University of Tennessee at Knoxville, 502 Dougherty Hall, 1512 Middle Drive, Knoxville, TN 37996djlee@utk.edu

Perry Y. Li

Department of Mechanical Engineering, University of Minnesota, 111 Church Street SE, Minneapolis, MN 55455pli@me.umn.edu

J. Dyn. Sys., Meas., Control 129(5), 662-677 (Feb 15, 2007) (16 pages) doi:10.1115/1.2764507 History: Received May 02, 2006; Revised February 15, 2007

A passive decomposition framework for the formation and maneuver controls for multiple rigid bodies is proposed. In this approach, the group dynamics of the multiple agents is decomposed into two decoupled systems: The shape system representing internal group formation shape (formation, in short), and the locked system abstracting the overall group maneuver as a whole (maneuver, in short). The decomposition is natural in that the shape and locked systems have dynamics similar to the mechanical systems, and the total energy is preserved. The shape and locked system can be decoupled without the use of net energy. The decoupled shape and locked systems can be controlled individually to achieve the desired formation and maneuver tasks. Since all agents are given equal status, the proposed scheme enforces a group coherence among the agents. By abstracting a group maneuver by its locked system whose dynamics is similar to that of a single agent, a hierarchical control structure for the multiple agents can be easily imposed in the proposed framework. A decentralized version of the controller is also proposed, which requires only undirected line communication (or sensing) graph topology.

Copyright © 2007 by American Society of Mechanical Engineers
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This can be obtained by using the definitions (ωi,τi,δi)≔(Ji−1(ζi)ωib,JiT(ζi)τib,JiT(ζi)δib) and the attitude dynamics in SO(3) w.r.t. the body frame Iiω̇ib=pib×ωib+τib+δib, where ωib is the angular rate, Ii is the inertia matrix, pib is the angular momentum, τib,δib are the controls and disturbances, respectively, all in the body frame, and Ji(ζi) is the Jacobian map that is nonsingular if −π∕2<θi<π∕2, see (28-29).


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Figure 1

Hierarchy by abstraction: Each group Σi0 abstracted by its locked system ∇Li1; group of groups Σ11 again abstracted by its locked system ∇L12; formation among agents/groups described by their shape systems (not shown)

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Figure 2

A circuit-network representation of the passive decomposition, where κL(q,vL)≔12vLTML(q)vL and κE(q̇,vE)≔12q̇ETME(q)q̇E

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Figure 3

Communication topology of centralized control: Decentralized control uses only decentralizable communication (black solid lines)

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Figure 4

3D and 2D simulation snapshots: Position and attitude of agent represented by sphere and body-fixed frame

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Figure 5

Detailed data of the snapshots in Fig. 4

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Figure 6

Effect of disturbance on agent 3: Agent position/pitch angle represented by vertex of triangle and bar stemming from it

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Figure 7

Hierarchy by abstraction: Snapshots of nine agents, three groups (triangles), and their locked systems (solid lines)

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Figure 8

Hierarchy by abstraction: Agent 5’s actuation temporarily failed and recovered

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Figure 9

Formation-maneuver decoupling with the centralized control

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Figure 10

Formation-maneuver coupling with the decentralized control



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