Citation: Bottin, M.; Boschetti, G.;
Rosati, G. Optimizing Cycle Time of
Industrial Robotic Tasks with
Multiple Feasible Configurations at
the Working Points. Robotics 2022, 11,
16. https://doi.org/10.3390/
robotics11010016
Academic Editor: Guangjun Liu
Received: 8 November 2021
Accepted: 13 January 2022
Published: 15 January 2022
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Article
Optimizing Cycle Time of Industrial Robotic Tasks with
Multiple Feasible Configurations at the Working Points
Matteo Bottin
1,
* , Giovanni Boschetti
2
and Giulio Rosati
1
1
Department of Industrial Engineering, University of Padova, 35131 Padova, Italy; giulio.rosati@unipd.it
2
Department of Management and Engineering, University of Padova, 36100 Vicenza, Italy;
giovanni.boschetti@unipd.it
* Correspondence: matteo.bottin@unipd.it
Abstract:
Industrial robot applications should be designed to allow the robot to provide the best
performance for increasing throughput. In this regard, both trajectory and task order optimization
are crucial, since they can heavily impact cycle time. Moreover, it is very common for a robotic
application to be kinematically or functionally redundant so that multiple arm configurations may
fulfill the same task at the working points. In this context, even if the working cycle is composed
of a small number of points, the number of possible sequences can be very high, so that the robot
programmer usually cannot evaluate them all to obtain the shortest possible cycle time. One of the
most well-known problems used to define the optimal task order is the Travelling Salesman Problem
(TSP), but in its original formulation, it does not allow to consider different robot configurations at the
same working point. This paper aims at overcoming TSP limitations by adding some mathematical
and conceptual constraints to the problem. With such improvements, TSP can be used successfully to
optimize the cycle time of industrial robotic tasks where multiple configurations are allowed at the
working points. Simulation and experimental results are presented to assess how cost (cycle time)
and computational time are influenced by the proposed implementation.
Keywords: robot redundancy; travelling salesman problem; robot optimization
1. Introduction
The most common industrial robot applications are related to the handling of products,
the welding, and the assembly of parts [
1
]. In such applications, the performance of
the robotic workcell is usually limited by the performance of the robot, i.e., the time
required by the robot to move between the points. Moreover, usually, these applications
are kinematically redundant; in other words, the robot kinematic chain has more degrees
of freedom than those required by the task; thus, the robot can perform the same task
with several different configurations at one or more working point. The redundancy is
mainly due to the symmetry of the task, in which the products can be handled by rotating
around the tool axis continuously, (e.g., when vacuum grippers are used), or by discrete
angles, (e.g., when standard grippers with two symmetrical fingers are used); thus, it is
possible to rotate 180
◦
around the tool axis to pick up an object. In common industrial
installations, redundancy is disregarded. In fact, setting up a new workcell is usually a
long and tedious process; thus, it is more important to perform a speedy setup instead
of optimizing the robot movements. Fortunately, teach-by-demonstration techniques are
gaining in popularity [
2
], thus speeding up the process while, at the same time, including
redundancy [3].
As the same task can be performed with different robot configurations, it is possible to
choose such configurations so that the movement between points is optimized, i.e., joint
displacement is minimized. Redundant robot movement is a well-known topic in liter-
ature [
4
,
5
] and has been exploited both for the execution of tasks [
6
], to promote safe
human–robot interaction [7] and to implement multiple robot applications [8].
Robotics 2022, 11, 16. https://doi.org/10.3390/robotics11010016 https://www.mdpi.com/journal/robotics
