Citation: Su, C.; Xu, J. A
Sampling-Based Unfixed Orientation
Search Method for Dual Manipulator
Cooperative Manufacturing. Sensors
2022, 22, 2502. https://doi.org/
10.3390/s22072502
Academic Editors: Yuansong Qiao
and Seamus Gordon
Received: 1 January 2022
Accepted: 15 February 2022
Published: 24 March 2022
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Article
A Sampling-Based Unfixed Orientation Search Method for Dual
Manipulator Cooperative Manufacturing
Chang Su
1,
* and Jianfeng Xu
2
1
School of Mechanical Science & Engineering, Huazhong University of Science & Technology,
Wuhan 430074, China
2
State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science
& Technology, Wuhan 430074, China; jfxu@hust.edu.cn
* Correspondence: suchang@hust.edu.cn
Abstract:
The case of dual manipulators with shared workspace, asynchronous manufacturing tasks,
and independent objects is named a dual manipulator cooperative manufacturing system, which
requires collision-free path planning as a vital issue in terms of safety and efficiency. This paper
combines the mathematical modeling method with the time sampling method in the classification
of robot path-planning algorithms. Through this attempt we can achieve an optimal local search
path during each sampling period interval. Our strategy is to build the corresponding non-linear
optimization functions set based on the motion characteristics of the dual manipulator system. In
this way, the path-planning problem can be turned into a purely mathematical problem of solving
the non-linear optimization programming equations set. The spatial geometric analysis is used to
linearize the predicted dual-manipulator minimum distance equation, thus linearizing the non-linear
optimization equations set. Finally, this system of linear optimization equations will be mapped
directly into a virtual Euclidean space and then solved intuitively using the spatial geometry theory.
By simulation and comparing with the previous strategies, we find that the planning results of the
newly proposed planning strategy are smoother and have shorter deviations as well as a higher
algorithmic efficiency in terms of spatial geometric properties.
Keywords:
dual manipulator system; cooperative manufacturing; collision-free path planning;
non-linear optimization programming; minimum distance prediction
1. Introduction
1.1. Subsection
At present, six-degree-of-freedom (6-DOF) industrial manipulators play an increas-
ingly important role in automated manufacturing due to numerous advantages, including
the provision of tireless repetitive labor, faster-moving speeds, and a higher accuracy per-
formance [
1
]. Thus, tasks requiring numerous workers can undoubtedly be accomplished
cooperatively by multiple manipulators, meaning that multi-manipulators will not only
work side-by-side but as dyads and teams. Analogous to the definition of Human–Robot
Interaction (HRI) [
2
,
3
], the case of a dual manipulator manufacturing system can be divided
into cooperation and collaboration according to the arrangement of the tasks. For the case of
a collaborative manufacturing system, all manipulators together with the executed mecha-
nism constitute a complete multi-degree-of-freedom closed-loop or parallel manufacturing
system. Thus, the non-collision manufacturing control strategy under such circumstances
can be transformed into the currently mature internal obstacle avoidance strategy [
4
]. How-
ever, for the case of the multiple manipulator cooperative manufacturing system, problems
and limitations arise in the small overlapping workspaces that accommodate numerous
cooperative manipulators, resulting in collisions if no related countermeasures are put
in place. Under this circumstance, a path-planning algorithm that can circumvent the
Sensors 2022, 22, 2502. https://doi.org/10.3390/s22072502 https://www.mdpi.com/journal/sensors
