Article
Trajectory Extrapolation for Manual Robot Remote Welding
Lucas Christoph Ebel
1,
*
,†
, Jochen Maaß
2,†
, Patrick Zuther
1
and Shahram Sheikhi
2
Citation: Ebel, L.C.; Maaß, J.; Zuther,
P.; Sheikhi, S. Trajectory Extrapolation
for Manual Robot Remote Welding.
Robotics 2021, 10, 77. https://doi.org/
10.3390/robotics10020077
Academic Editor: Dario Richiedei
Received: 15 April 2021
Accepted: 20 May 2021
Published: 23 May 2021
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4.0/).
1
Institute for Material Science and Welding Techniques, University of Applied Science Hamburg,
Berliner Tor 5, 20099 Hamburg, Germany; patrick.zuther@haw-hamburg.de
2
Research and Transfer Center FTZ-3i, University of Applied Science Hamburg, Berliner Tor 5,
20099 Hamburg, Germany; j.maass@haw-hamburg.de (J.M.); shahram.sheikhi@haw-hamburg.de (S.S.)
* Correspondence: lucas.ebel@haw-hamburg.de; Tel.: +49-40-428-75-8988
† These authors contributed equally to this work.
Abstract:
This article describes an algorithm for the online extrapolation of hand-motion during
remote welding. The aim is to overcome the spatial limitations of the human welder’s arms in
order to cover a larger workspace with a continuous weld seam and to substantially relieve the
welder from strain and fatigue. Depending on the sampled hand-motion data, an extrapolation
of the given motion patterns is achieved by decomposing the input signals in a linear direction
and a periodic motion component. An approach to efficiently determine the periodicity using a
sampled autocorrelation function and the subsequent application of parameter identification using a
spline function are presented in this paper. The proposed approach is able to resemble all practically
relevant motion patterns and has been validated successfully on a remote welding system with
limited input space and audio-visual feedback by an experienced welder.
Keywords: hand-motion tracking; extrapolation; autocorrelation; spline; remote welding
1. Introduction
To decrease programming effort, improve ergonomics, and reduce hazards to the
welder, remote welding applications are pursued [
1
–
9
]. The typical setup consists of
a motion input device and a standard industrial robot with a welding torch attached.
The input devices range from complex applications of VR technology [
10
] to simpler
methodologies using infrared optical motion sensors [
11
,
12
]. A comprehensive overview
of different approaches is given in Section 3 of the review paper [
13
]. The common problem
with those approaches is the limited tracking region of the input device, whereas longer,
and even more important, continuous welding seams are to be manufactured [
14
]. To
achieve these long continuous welding seams, solutions have been presented [
15
–
18
] that
apply 2D laser-scanning before the welding in order to pre-calculate a trajectory. However,
it is still beneficial to directly control the torch’s motion to save time and to respond
to unexpected variations in material properties, as they are frequently present in repair
applications [19].
Recent work performed by the authors of the paper [
20
] introduces a promising ap-
proach to tackle the problem of the limited workspace of the motion input devices, as
illustrated in Figure 1. When the motion of the input device, which is tracked by the
robot, reaches the boundary of the input device’s acquisition space, the robot’s motion is
continued by extrapolation of the input trajectory for a period of time. In the meantime,
the input device can be re-positioned into a convenient position and the control is resumed
to the tracking of the input device thereafter. The extrapolation algorithm uses a discrete
Fourier transformation (DFT) approach to isolate the dominant spatial frequency and is
able to generate the continuous motion pattern for the weaving motion in concave and
convex shapes by estimating parameters of a sine template function. As a result, spatial
motions must be composable by a single sine function per degree of freedom. Thus, the
practically relevant Christmas-tree-shaped motion pattern is extrapolated with limited
Robotics 2021, 10, 77. https://doi.org/10.3390/robotics10020077 https://www.mdpi.com/journal/robotics
