Swing-Free Movement of Simply Suspended Objects Employing Parameter Estimation Page: 3 of 10
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Sandia National Laboratories is currently inves-
tigating the feasibility of using intelligent ma-
chines at nuclear wastestorage sites. One class
of operations that is necessary at a waste stor-
age site is the transportation of nuclear waste
shipping casks and other heavy objects to vari-
ous locations throughout the installation. Dur-
ing. overhead crane transportation, an object is
free to swing. If any oscillation of the object be-
gins, it must be sufficiently damped by the op-
erator, or allowed to decay naturally before the
next operation can begin. Either option is time
consuming and reduces the availability of the fa-
cility. However, damping the oscillation of sim-
ply suspended payloads during transportation is
possible if the acceleration of the crane is pro-
grammable. Jones and Petterson  discuss ac-
celeration profile shaping for a trajectory planner
in detail and define the necessary conditions for
This paper presents an extension of their work:
the analytical development and experimental im-
plementation of an adaptive, swing-free trajec-
tory planner. Other researchers, for example
Tzes and Yurkovich  and Nelson and Mitra ,
have developed parameter estimation schemes for
closed-loop control of flexible structures. Our
open-loop planner is made adaptive by employ-
ing a batch, nonlinear least square estimator to
predict the parameters of the suspended object
which are necessary for swing-free motion from a
set of force sensor measurements. Initially, an ob-
ject with unknown parameters is picked up and
moved (which causes the object to oscillate) and
force measurements are taken. Next, the estima-
tor processes the data and extracts the parame-
ters of interest while the force-damping (closed-
loop) controller  damps the object's oscillation.
Finally, the planner calculates the swing-free tra-
jectory from the estimated parameters and in-
structs the robot to move. Note that the only re-
quired parameter for swing-free motion is the pe-
riod of oscillation , but the estimator includes
the initial conditions and the mass of the sus-
pended object to increase the robustness of the
Dire LIon of
Figure 1: Diagram of Transporting Device
estimation process. The robustness of the esti-
mator became an issue when a simple scheme to
calculate the period of the pendulum (measure
the time between peaks of the force sensor out-
put) did not produce adequate results. The sim-
ple scheme was limited in resolution by the 47mns
update rate of data sampling and subject to 47 ms
increments of error due to noise in the dat a.
2 Mathematical Foundation
There are many ways to produce a swing-free
move of a simply suspended object (Figure 1).
One of the most general methods is described
by Jones and Petterson  where a double pulse
train is employed. The basic ingredient neces-
sary for every approach to developing swing-free
trajectories is knowledge of the frequency of os-
cillation of the suspended object, Consequently,
the period of oscillation must be measured each
time a different object is moved in order to pro-
duce a, swing-free move. In this section, we de-
scribe a batch, nonlinear least square estimator
that, enables the computer to automatically cal-
culate the period of oscillation of the suspended
object from force sensor measurements and pro-
duce swing-free trajectories.
The nonlinear least square estimator is bas( d
on the Gaussian least square differential cor-
rection (GLSDC) algorithm described by Junk-
ins . The GLSDC algorithm is choreii because
it is easy to implement and highly f( \ible (refer
to References  and ). The algorithm applies
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Werner, Jill C.; Robinett, Rush D. & Petterson, Ben J. Swing-Free Movement of Simply Suspended Objects Employing Parameter Estimation, report, June 1, 1990; Albuquerque, New Mexico. (https://digital.library.unt.edu/ark:/67531/metadc1193169/m1/3/: accessed March 24, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.