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Research Papers: Mechanisms and Robotics

Dynamic Workspace and Control of Planar Active Tensegritylike Structures

[+] Author and Article Information
Andrew P. Schmalz

Mechanical Systems Laboratory, Department of Mechanical Engineering, University of Delaware, Newark, DE 19716apschmalz@comcast.net

Sunil K. Agrawal1

Mechanical Systems Laboratory, Department of Mechanical Engineering, University of Delaware, Newark, DE 19716agrawal@udel.edu

1

Corresponding author.

J. Mech. Des 130(12), 122301 (Oct 07, 2008) (12 pages) doi:10.1115/1.2988474 History: Received July 05, 2007; Revised August 21, 2008; Published October 07, 2008

This paper addresses the issues of control and workspace determination of planar active tensegrity or tensegritylike structures. The motion of such structures is generally produced by actuated cables, which cannot tolerate compressive forces. Hence, a controller, which not only satisfies the system dynamic equations but also maintains positive tension in cables, is necessary. A null-space controller based on feedback linearization theory is developed for this purpose. This controller utilizes redundant active cables to overactuate the system. The concept of a “dynamic workspace” for these structures is then introduced. This workspace consists of all configurations that are achievable from a given initial configuration while maintaining positive tensions throughout the entire system motion, and it is a powerful tool in analyzing the performance of a variety of tensegrity structures. This idea extends the concept of the static workspace, which consists of statically maintainable configurations, by incorporating system motion and dynamics to guarantee positive tensions during transition between the states. A critical benefit of this procedure is that it may be used to find the dynamic workspace of a system regardless of whether actuator redundancy is utilized, and thus it can be used to objectively illustrate the degree to which overactuation improves mobility of a tensegrity structure. The effectiveness of the developed concepts is demonstrated through computer simulation and actual physical experimentation.

Copyright © 2008 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Example of a complex planar tensegrity structure. This may be modeled using the same principles as much simpler structures.

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Figure 2

Planar tensegrity structure with one fixed rod and one free rod

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Figure 3

Planar tensegrity structure with one pivot constraint and one sliding constraint

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Figure 4

Summary of the dynamic workspace generation procedure

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Figure 5

Dynamic workspace for fully-actuated System 1 with parameters described in Table 1 and initial configuration q0=[0.25090deg]T

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Figure 6

Static workspace for System 1 with parameters described in Table 1. The areas containing points eliminated in the dynamic workspace are indicated by arrows.

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Figure 7

Dynamic workspace for overactuated System 1 using null-space controller with parameters given in Table 1

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Figure 8

Portion of feasible volume added by using overactuation, found by subtracting a plot of Fig. 5 from that of Fig. 7

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Figure 9

Dynamic workspace for fully-actuated System 2 with parameters described in Table 2 and initial configuration q0=[45deg135deg0.3536]T

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Figure 10

Static workspace for System 2 with parameters described in Table 2. The areas containing points eliminated in the dynamic workspace are indicated by arrows.

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Figure 11

Dynamic workspace for overactuated System 2 using null-space controller with parameters given in Table 2. The regions expanded by use of the null-space controller are indicated by arrows.

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Figure 12

Setup for System 1 experiment: (A) backboard with rod, cables, pulleys, load cells, and motors; (B) routing pulleys; (C) load cells; and (D) motor shaft with cable spool

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Figure 13

Dynamic workspace for fully-actuated experimental system based on parameters from Table 3 and initial configuration q0=[0.30090deg]T.

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Figure 14

Dynamic workspace for experimental system with additional constraint that no cable becomes shorter than .15m to account for load cells and cable connectors

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Figure 15

From left to right, x, y, and θ tracking for x-y translation experiment, comparing actual and simulation results

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Figure 16

Tension values for x-y translation experiment including actual tensions recorded by load cells, desired tensions calculated by controller, and expected values from simulation. Actual responses for controlled tensions T1, T2, and T3 track their desired values reasonably, though all four measured tensions depart somewhat from the ideal simulation plots.

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