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Research Papers

Rapid Swing-Free Transport of Nonlinear Payloads Using Dynamic Programming

[+] Author and Article Information
Daniel Zameroski

Department of Mechanical Engineering, The University of New Mexico, Albuquerque, NM 87131daniel.zameroski@lord.com

Gregory Starr

Department of Mechanical Engineering, The University of New Mexico, Albuquerque, NM 87131starr@unm.edu

John Wood

Department of Mechanical Engineering, The University of New Mexico, Albuquerque, NM 87131jw@unm.edu

Ron Lumia

Department of Mechanical Engineering, The University of New Mexico, Albuquerque, NM 87131lumia@unm.edu

J. Dyn. Sys., Meas., Control 130(4), 041001 (Jun 04, 2008) (11 pages) doi:10.1115/1.2936384 History: Received June 12, 2006; Revised February 13, 2008; Published June 04, 2008

Residual vibration suppression in freely suspended payload transports has been the focus of extensive work in the past. Many methods have been used to address this problem, including both open-loop motion planning and closed-loop control techniques. However, to be effective, most of these methods require linearization of the system and, in turn, have been restricted in their maneuver speeds. The inherent nonlinearity of suspended payload systems suggests the need for a more rigorous method, where the complete dynamic description can be retained throughout the optimization. Dynamic programming (DP) is such a method. This paper will outline the development of the DP algorithm for a discrete time system as well as its application to the rapid transport of a doubly suspended payload, a nonlinear system. The system consists of a long slender payload, suspended by a cable at each end. The two cables are each held by an independent robot manipulator. We will show that DP is effective at reducing residual oscillations for nonlinear systems, as demonstrated by both simulations and experimental validation. Residual oscillations were suppressed to less than 5% of their original magnitudes.

Copyright © 2008 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Rotary jib-crane dynamic model

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Figure 2

Optimal jib trajectory for 3.5s swing-free motion

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Figure 3

Swing angles for 3.5s jib-crane maneuver

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Figure 4

Optimal jib trajectory for 2.3s swing-free motion

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Figure 5

Swing angles for 2.3s jib-crane maneuver

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Figure 6

Schematic of experimental setup and constraint

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Figure 7

Description of Cartesian motion reference frame

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Figure 8

Schematic of system geometry as functions of θ2 and θ3

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Figure 9

d approximating surface

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Figure 10

Comparison of simulated continuous time response versus discrete approximation for time step sizes of 10ms and 1ms (MATLAB ®)

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Figure 11

Photo of experimental setup

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Figure 12

Peak-to-peak residual oscillations present after each convergence pass (MATLAB ®)

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Figure 13

Optimal x, y, and ϕ trajectories

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Figure 14

Optimal versus cubic trajectory for the x component of maneuver

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Figure 15

y motion trajectory position, velocity, and acceleration characteristics (MATLAB ®)

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Figure 16

Oscillation amplitude of cubic versus optimal trajectories (MATLAB ®)

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Figure 17

Residual oscillations during the 2s after an optimal maneuver (ADAMS ®)

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