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6-DOFs Robot Placement Based on the Multi-Criteria Procedure for Industrial Applications

October 2024
Robotics 13(10):153

DOI:10.3390/robotics13100153

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CC BY 4.0

Authors:

Francesco Aggogeri

University of Brescia

Nicola Pellegrini

University of Brescia

Robot acceptance is rapidly increasing in many different industrial applications. The advancement of production systems and machines requires addressing the productivity complexity and flexibility of current manufacturing processes in quasi-real time. Nowadays, robot placement is still achieved via industrial practices based on the expertise of the workers and technicians, with the adoption of offline expensive software that demands time-consuming simulations, detailed time-and-motion mapping activities, and high competencies. Current challenges have been addressed mainly via path planning or robot-to-workpiece location optimization. Numerous solutions, from analytical to physical-based and data-driven formulation, have been discussed in the literature to solve these challenges. In this context, the machine learning approach has proven its superior performance. Nevertheless, the industrial environment is complex to model, generating extra training effort and making the learning procedure, in some cases, inefficient. The industrial problems concern workstation productivity; path-constrained minimal-time motions, considering the actuator’s torque limits; followed by robot vibration and the reduction in its accuracy and lifetime. This paper presents a procedure to find the robot base location for a prescribed task within the robot’s workspace, complying with multiple criteria. The proposed hybrid procedure includes analytical, physical-based, and data-driven modeling to solve the optimization problem. The contribution of the algorithm, for a given user-defined task, is the search for the best robot base location that enables the target points, maximizing the manipulability, avoiding singularities, and minimizing energy consumption. Firstly, the established method was verified using an anthropomorphic robot that considers different levels of a priori kinematics and system dynamics knowledge. The feasibility of the proposed method was evaluated through various simulations for small- and medium-sized robots. Then, a commercial offline program was compared, considering three scenarios and fourteen robots demonstrating an energy reduction in the 7.6–13.2% range. Moreover, the unknown joint dependency in real robot applications was investigated. From 11 robot positions for each active joint, a direct kinematic was appraised with an automatic DH scheme that generates the 3D workspace with an RMSE lower than 65.0 µm. Then, the inverse kinematic was computed using an ANN technique tuned with a genetic algorithm showing an RMSE in an S-shape task close to 702.0 µm. Finally, three experimental campaigns were performed with a set of tasks, repetitions, end-effector velocity, and payloads. The energy consumption reduction was observed in the 12.7–22.9% range. Consequently, the proposed procedure supports the reduction in workstation setup time and energy saving during industrial operations.

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Citation: Aggogeri, F.; Pellegrini, N.

6-DOFs Robot Placement Based on the

Multi-Criteria Procedure for

Industrial Applications. Robotics 2024,

13, 153. https://doi.org/10.3390/

robotics13100153

Received: 9 September 2024

Revised: 15 October 2024

Accepted: 15 October 2024

Published: 16 October 2024

Licensee MDPI, Basel, Switzerland.

This article is an open access article

distributed under the terms and

conditions of the Creative Commons

Attribution (CC BY) license (https://

creativecommons.org/licenses/by/

4.0/).

robotics

Article

6-DOFs Robot Placement Based on the Multi-Criteria Procedure

for Industrial Applications

Francesco Aggogeri and Nicola Pellegrini *

Department of Mechanical and Industrial Engineering, University of Brescia, Via Branze, 38, 25123 Brescia, Italy;

francesco.aggogeri@unibs.it

*Correspondence: nicola.pellegrini@unibs.it; Tel.: +39-030-3715580

Abstract: Robot acceptance is rapidly increasing in many different industrial applications. The

advancement of production systems and machines requires addressing the productivity complexity

and ﬂexibility of current manufacturing processes in quasi-real time. Nowadays, robot placement

is still achieved via industrial practices based on the expertise of the workers and technicians, with

the adoption of ofﬂine expensive software that demands time-consuming simulations, detailed time-

and-motion mapping activities, and high competencies. Current challenges have been addressed

mainly via path planning or robot-to-workpiece location optimization. Numerous solutions, from

analytical to physical-based and data-driven formulation, have been discussed in the literature

to solve these challenges. In this context, the machine learning approach has proven its superior

performance. Nevertheless, the industrial environment is complex to model, generating extra training

effort and making the learning procedure, in some cases, inefﬁcient. The industrial problems concern

workstation productivity; path-constrained minimal-time motions, considering the actuator’s torque

limits; followed by robot vibration and the reduction in its accuracy and lifetime. This paper presents

a procedure to ﬁnd the robot base location for a prescribed task within the robot’s workspace,

complying with multiple criteria. The proposed hybrid procedure includes analytical, physical-based,

and data-driven modeling to solve the optimization problem. The contribution of the algorithm, for a

given user-deﬁned task, is the search for the best robot base location that enables the target points,

maximizing the manipulability, avoiding singularities, and minimizing energy consumption. Firstly,

the established method was veriﬁed using an anthropomorphic robot that considers different levels

of a priori kinematics and system dynamics knowledge. The feasibility of the proposed method was

evaluated through various simulations for small- and medium-sized robots. Then, a commercial

ofﬂine program was compared, considering three scenarios and fourteen robots demonstrating an

energy reduction in the 7.6–13.2% range. Moreover, the unknown joint dependency in real robot

applications was investigated. From 11 robot positions for each active joint, a direct kinematic

was appraised with an automatic DH scheme that generates the 3D workspace with an RMSE

lower than 65.0

m. Then, the inverse kinematic was computed using an ANN technique tuned

with a genetic algorithm showing an RMSE in an S-shape task close to 702.0

m. Finally, three

experimental campaigns were performed with a set of tasks, repetitions, end-effector velocity, and

payloads. The energy consumption reduction was observed in the 12.7–22.9% range. Consequently,

the proposed procedure supports the reduction in workstation setup time and energy saving during

industrial operations.

Keywords: industrial robot; multi-criteria; modeling; energy consumption; optimization

1. Introduction

The positioning of a robot base inﬂuences the high repeatability, reliability, and dexter-

ity performance of robots in manufacturing, welding, packaging, and assembly applications.

Although the perception paradigm is tangible for enhancing the level of automation, in

Robotics 2024,13, 153. https://doi.org/10.3390/robotics13100153 https://www.mdpi.com/journal/robotics

Robotics 2024,13, 153 2 of 27

an industrial context, the current system ability may be signiﬁcantly enhanced by eval-

uating different factors: the safety-related boundaries, the maximum accelerations, the

end-effector’s arrangement, and the singularity avoidance. In addition, the existing layout

adjustment cannot be easily managed due to physical constraints, such as workpiece inertia

or geometry, and other input/output interdependencies that impact the placement of the

robotic system. Moreover, the robot’s accuracy is affected by geometric errors, deformation

and distortion errors, payloads, and temperature proﬁles [

–

]. The workstation layout

is a central factor in satisfying the user-deﬁned tasks and the workspace complexity that

is still determined through a time-consuming trial-and-error process, and it is usually

managed via the high skills and expertise of operators, technicians, and engineers. In

recent years, the literature has presented several studies that may be classiﬁed into two

approaches: path planning and robot-to-workpiece location optimization. Robot path

planning aims to search for a collision-free path between the starting and ﬁnal target frame

in the robot space that meets a set of constraints [

]. Planning methods are described with

graph-based search procedures [

], and the algorithms were developed in particular for

cooperative unmanned mobile robots. The artiﬁcial potential ﬁeld-based method [

] is

a technique that presents ofﬂine and online path adaptations with unknown obstacles

with resultant errors of lower than 16.6% and 17.4%, respectively. Then, machine learning

(ML) methodologies and simulation have been adopted for online planning in time-variant

conditions [

–

]. In [

], an experimental study of the vibrations of a roller shutter gripper

on a robotic palletizing station was presented using a FANUC Robotguide environment,

demonstrating effective vibration reduction. In [

], Bucinskas et al. provide a method-

ology for the online deep Q-learning-based approach intended to increase positioning

accuracy at key points by analyzing experimentally predetermined robot properties and

their impact on overall accuracy. The KUKA-YouBot robot has been used, and the proposed

ML-based compensation method resulted in a positioning error decrease at the trajectory

of 30% of the tolerance declared. In [

], a deep neural network is presented for path

estimation using reinforcement learning. Although ML has proven its superior perfor-

mance in many studies, several challenges are open: The environment is often signiﬁcantly

complex to model, generating an extra training effort and making the learning procedure

inefﬁcient [

]. Another concern is the over-ﬁtting problem—real robot positioning is time-

consuming for the training phase and shows inadequate model extension in unstructured

environments [

]. In an industrial context, the robotic applications are determined in

path-constrained minimal-time motions to increase workstation productivity, considering

the actuator’s torque limits. The practical consequence is the increase in the robot tool

center point (TCP) and vibration, and a reduction in its accuracy and lifetime. The second

approach—robot-to-workpiece placement—has been studied and investigated to address

the aforementioned issues. The aim is to focus on planning the manipulator operations

determined by the robot base location to accomplish a given task under a set of criteria. The

problem’s objective functions mostly comprise the manipulability and velocity index [16],

the cycle time, and the joint motion bounds. Nevertheless, the robot placement solution

was discussed as a multi-dimensional function in a controlled time-variant workspace.

Numerous analytical, physical-based, and data-driven formulation methods have been pre-

sented to solve this challenge. In [

], Guanhua et al. address a technique for robot location

in drilling applications based on a bidimensional manifold in joint space using a particle

swarm optimization (PSO) procedure applied to identify the best parameters. The indus-

trial context is aircraft machining, such as shaped panel drilling and isometric positioning.

A procedure is proposed to model the positioning error to predict and compensate for the

deviations. A dual solution of bifurcation was studied and simulated. The experimental

campaign conducted on a KUKA robot veriﬁed the improvement in terms of position error

of 12–22%, with 255 real targets positioned and a resultant average positioning error of close

to 0.50–0.69 mm. Ur-Rehman et al. in [18] present a multi-objective placement for parallel

kinematics machines based on power consumption and shaking forces. The proposed

approach is veriﬁed using the Orthoglide, a three-degrees-of-freedom (DoF) robot. The

Robotics 2024,13, 153 3 of 27

four-sided trajectory was evaluated to gather pocketing operations. The shaking forces

analyses revealed that the inertial contributions exerted on the PKM base inﬂuenced the

energy consumption. A multi-objective genetic algorithm was used to ﬁnd the boundaries

for a rectangular test trajectory, with a width of 30.0 mm, a length of 60.0 mm, and a TCP

velocity of 600.0 mm/s. In the work, a campaign demonstrated a reduction of 60% in the

power consumption and a decrease of 17% in the shaking forces. In addition, refs. [

]

describe optimization techniques for minimizing robot energy consumption. In [

], Doan

and Lin focus on the redundancy resolution scheme to evaluate welding equipment for

offshore assembly of buildings. The welding technology is applied to large workpieces

and compared with the robot’s workspace. The robot position is analyzed based on joint

limitation, singularities, and collision avoidance. Non-differentiable terms are determined

by applying a modiﬁed particle swarm optimization (MPSO) that is designed and devel-

oped. The feasibility is demonstrated via simulation using ABB RobotStudio digital twin

commercial software and using an experimental dry run welding test bench. The workpiece

size is 2.0 m

3.0 m, the area of interest for welding is a diameter of 355.6 mm, and the

identiﬁed placement is 200 mm

350 mm

250 mm. Son and Kwon, in [

], propose a

method based on a convex programming approach for the location of an anthropomorphic

robot with a spherical wrist. The procedure determines a convex solution without solving

the inverse kinematics (IK). The KUKA KR6 R900-2 robot was selected as a representative

system; formulation and simulation were completed to verify the reachability, singularity

avoidance, and manipulability criteria via MATLAB and KUKA Sim Pro software. Ren

et al. and works by other researchers described constrained optimization problems for

painting robot manipulators [

–

]. The proposals refer to the penalty cost function and

Lagrange index to search for the optimal robot base position. The works test the algorithms

using the IRB5500 robot, obtaining a residual error of close to 10% for ﬂat, cylindrical, and

truncated conical surfaces. Spensieri et al., in [

], present a derivative-free model to attain

multiple task positions. The results are stated via simulation for cycle time minimization;

nevertheless, the work does not study rotations due to computation boundaries. Other

methodologies focus on searching for a likely robot location for slow-motion application.

In [

], the authors investigate the available workspace and the ability to sustain the resul-

tant forces at the end effector during motion. Successive solutions are computed with a

searching method by incrementally ﬁxing the constraints.

Although several advances have been investigated in earlier studies, a large portion is

inappropriate for real-time or shop ﬂoor practical applications due to user-deﬁned ad hoc

criteria, computational limits, and time-consuming procedures. Likely functions, bound-

aries, and industrial efﬁciency indexes differ signiﬁcantly on robot workspace complexity,

while the best robot position may be appraised differently depending on the selected ap-

plication criteria. Robot positioning for predeﬁned tasks, considering the reachability, is

inadequate for avoiding robot singularity and guaranteeing collision avoidance. Moreover,

it is necessary to react to production mix variability and layout modiﬁcations promptly,

including time and cost efﬁciency, with a procedure that could be implemented directly by

a technician or operator. Limited a priori kinematics knowledge of the robot usually leads

to a bang-bang motion. In contrast, the overﬁtting of robot modeling drives complexities

for online implementation.

Beyond the industrial practices and research lab developments, in the standardization

context the focus is centered on the safety of industrial robots and service robots to enable

innovative products to be brought to the market. ISO/TC 299 [

] has the goal of fostering

the growth of the robotics market by introducing standards in ﬁelds like terminology,

performance measurement, and modularity. In a similar vein, ISO-10218 Part 1 (“Safety

of Robots”) [

] and Part 2 (“Safety of Robot Integration”) [

] were intended to set forth

safety requirements for robots and robot systems in general. Moreover, safety requirements

for designing and implementing industrial robot systems are speciﬁed in the voluntary

industry consensus standard ANSI/RIA R15.06-2012 (“R15.06”). Finally, the technical

report (TR) ANSI RIA TR R15.506 [

] deﬁnes the guidelines for existing industrial robot

Robotics 2024,13, 153 4 of 27

applications. These standards ensure that technologies are used safely, efﬁciently, and in

harmony. The authors’ contribution to the progress of industrial, laboratory, and standard

scenarios is to validate a procedure to ﬁnd the robot base location for a prescribed task

within the robot’s workspace, complying with multiple criteria for industrial application.

The four-step methodology is veriﬁed by simulations and experimental campaigns consid-

ering a set of tasks and scenarios that explore the a priori knowledge of kinematic/dynamic

modeling and the unknown joint dependency in a real test setup. Given the user-deﬁned

task in the cell layout reference frame, the contribution of the proposed technique is to

search for the optimal robot base location and conﬁgurations that consider the reachable

target points and joint range of motions, maximize the manipulability, avoid singularities,

and minimize the energy consumption. The procedure uses analytical formulation to

examine the reaching ability of the user task. Then, for an unknown model, a scheme leads

the operator to obtain the direct kinematic model via digital twin software or using a real

robot to provide the input for the appraisal of the data-driven model based on the artiﬁcial

neural network technique tuned via a genetic algorithm. Consequently, the criteria are

evaluated to identify a feasible robot base location from collision avoidance to singularity

and manipulability analyses and energy consumption computation. In case there is no

suitable performance, the iterative procedure updates the robot base position—the whole

procedure may be conducted in minutes rather than the hours or days that conventional

methods require.

2. Integrated Multi-Criteria Procedure for Robot Base Location

In this section, a selection of criteria have been investigated for the 6-DOF articulated

robot placement deﬁnition. The industrial input synthesis as the layout description, the

existing equipment, the ﬁxturing systems/tooling, and the surrounding environmental

considerations are the starting point for the problem formulation. Optimal robot positioning

searching requires iterative multi-criteria computations considering the following areas:

1. Task speciﬁcation, workspace deﬁnition, and reachability measure;

2. Robot inverse kinematic data-driven modeling for collision avoidance;

3. Singularity and manipulability analyses;

4. Energy consumption appraisal.

2.1. Task Speciﬁcation, Workspace Deﬁnition, and Reachability Measure

Conventional manipulators comprise an open chain of serially connected joints (revo-

lute or prismatic) to accomplish three-dimensional motions in the Cartesian workspace.

The 6-DoF robot is the usual architecture of industrial manipulators, as shown in Figure 1a.

A task T

is a combination of user-deﬁned points-to-points that the robot needs to approach

via the TCP positions. To verify the robot’s reachability for a deﬁned task, it is required to

conﬁrm that all these positions are within the robot’s workspace. The preliminary reacha-

bility assessment is the measure of the feasible tasks that the robot can achieve considering

the manipulator geometrical features and mechanical structure abilities. The measure can

be attained by approximating the wrist of the robot and the position center for joint J

as described in Figure 1b. Let bbe the robot base location for a speciﬁc task T

, and the

reachability mis formulated in Equations (1)–(3):

m=Di−rc(1)

Di=



wi−b



2(2)

rc=r+R

2(3)

Robotics 2024,13, 153 5 of 27

where D

is the Euclidean distance between the TCP position w

and the robot base location

b, and r

is the distance concerning the base position for the centroid of the robot for the

task Ti.

Robotics 2024, 13, x FOR PEER REVIEW 5 of 27

(a) (b)

Figure 1. The 6-DOF robot representation: serial-linked revolute joints (a); preliminary reachability

of the ABB IRB1200-5/0.9 robot for reference (b).

As shown in Figure 2a, the workspace is expressed using the coordinate P

, which

identiﬁes the reference frame of the starting point in the task T

to the coordinate P

(re-

ferring to the termination point), following the trajectory Γ. Consequently, the plane 𝝅

parallel to the ground base is formulated, where z is the vertical position of 𝝅, 𝑧 is the

vertical coordinate of the robot base, and ∆𝑧 is the geometrical feature of the robot as the

distance between the robot base and the J

centroid. The 𝜏 region in Figure 2a represents

the area where it is possible to place the centroid in the J

joint of the 6-DOF robot to reach

points P

and P

for a selected task T

(a) (b)

Figure 2. Workspace analysis based on task T

(a); region of the J

robot based on task T

(b).

The 𝛕 region is formulated as in Equation (4). The π plane’s vertical location bounds

𝜋[] are analytically expressed in Equations (5) and (6).

𝜏=(𝑥,𝑦,𝑧)|𝑥−𝑥



+𝑦−𝑦



≤𝑟 , 𝑥−𝑥



+𝑦−𝑦



≤𝑟 , 𝑧 =𝜋

(4)

𝜋

[]

: [𝑧



−ℎ; 𝑧



+ℎ] (5)

ℎ=𝑅



+⎝

⎛

𝑥





−𝑥









+𝑦





−𝑦









+𝑧





−𝑧









2⎠

⎞



𝑐𝑜𝑠sin



|𝑧





−𝑧





𝑑2

 (6)

where d is the Euclidean diﬀerence relating the P

and P

reference coordinates.

2.2. Robot Data-Driven Modeling for Collision Avoidance

The user deﬁned task T

is stated as S composed of n Cartesian frames [x, y, z, R

, R

] and the corresponding time t, as stated in Equation (7):

𝑆=(𝑡,𝑥,𝑦,𝑧)|𝑡≤𝑡≤𝑡,(𝑋,𝑦,𝑧)∈𝑅 (7)

For a given set S of a known task T

, the inverse kinematics are computed. The model

may be formulated with analytical, numerical, or data-driven representation. In the

Figure 1. The 6-DOF robot representation: serial-linked revolute joints (a); preliminary reachability of

the ABB IRB1200-5/0.9 robot for reference (b).

As shown in Figure 2a, the workspace is expressed using the coordinate P

, which

identiﬁes the reference frame of the starting point in the task T

to the coordinate P

(referring to the termination point), following the trajectory

. Consequently, the plane

parallel to the ground base is formulated, where z is the vertical position of

is the

vertical coordinate of the robot base, and

∆z

is the geometrical feature of the robot as the

distance between the robot base and the J

centroid. The

region in Figure 2a represents

the area where it is possible to place the centroid in the J

joint of the 6-DOF robot to reach

points Paand Pbfor a selected task Ti.

Robotics 2024, 13, x FOR PEER REVIEW 5 of 27

(a) (b)

Figure 1. The 6-DOF robot representation: serial-linked revolute joints (a); preliminary reachability

of the ABB IRB1200-5/0.9 robot for reference (b).

As shown in Figure 2a, the workspace is expressed using the coordinate P

, which

identiﬁes the reference frame of the starting point in the task T

to the coordinate P

(re-

ferring to the termination point), following the trajectory Γ. Consequently, the plane 𝝅

parallel to the ground base is formulated, where z is the vertical position of 𝝅, 𝑧 is the

vertical coordinate of the robot base, and ∆𝑧 is the geometrical feature of the robot as the

distance between the robot base and the J

centroid. The 𝜏 region in Figure 2a represents

the area where it is possible to place the centroid in the J

joint of the 6-DOF robot to reach

points P

and P

for a selected task T

(a) (b)

Figure 2. Workspace analysis based on task T

(a); region of the J

robot based on task T

(b).

The 𝛕 region is formulated as in Equation (4). The π plane’s vertical location bounds

𝜋[] are analytically expressed in Equations (5) and (6).

𝜏=(𝑥,𝑦,𝑧)|𝑥−𝑥



+𝑦−𝑦



≤𝑟 , 𝑥−𝑥



+𝑦−𝑦



≤𝑟 , 𝑧 =𝜋

(4)

𝜋

[]

: [𝑧



−ℎ; 𝑧



+ℎ] (5)

ℎ=𝑅



+⎝

⎛

𝑥





−𝑥









+𝑦





−𝑦









+𝑧





−𝑧









2⎠

⎞



𝑐𝑜𝑠sin



|𝑧





−𝑧





𝑑2

 (6)

where d is the Euclidean diﬀerence relating the P

and P

reference coordinates.

2.2. Robot Data-Driven Modeling for Collision Avoidance

The user deﬁned task T

is stated as S composed of n Cartesian frames [x, y, z, R

, R

] and the corresponding time t, as stated in Equation (7):

𝑆=(𝑡,𝑥,𝑦,𝑧)|𝑡≤𝑡≤𝑡,(𝑋,𝑦,𝑧)∈𝑅 (7)

For a given set S of a known task T

, the inverse kinematics are computed. The model

may be formulated with analytical, numerical, or data-driven representation. In the

Figure 2. Workspace analysis based on task Ti(a); region of the J2robot based on task Ti(b).

The

region is formulated as in Equation (4). The

plane’s vertical location bounds

π[min−max]are analytically expressed in Equations (5) and (6).

τ=(x,y,z)qx−xJ2a2+y−yJ2a2≤ra,qx−xJ2b2+y−yJ2b2≤rb,z=π(4)

π[min−max]:[zπ−h;zπ+h](5)

h=v

tR2+

qxPa−xPb2+yPa−yPb2+zPa−zPb2

2



cos



sin−1





zPa−zPb

2







(6)

where dis the Euclidean difference relating the Paand Pbreference coordinates.

Robotics 2024,13, 153 6 of 27

2.2. Robot Data-Driven Modeling for Collision Avoidance

The user deﬁned task T

is stated as S composed of n Cartesian frames [x, y, z, R

, R

Rz] and the corresponding time t, as stated in Equation (7):

S=n(t,x,y,z)t0≤t≤tf,(X,y,z)∈R3o(7)

For a given set S of a known task T

, the inverse kinematics are computed. The model

may be formulated with analytical, numerical, or data-driven representation. In the present

work, the problem is solved by implementing a sequential data-driven approach [

]. The

scheme applies an automated Denavit–Hartenberg (D-H) estimation tool to compute the

direct kinematics (DK) model, which is needed to generate the workspace dataset [

Additionally, the artiﬁcial neural network (ANN) is chosen as the reference algorithm.

The number of layers and the number of hidden neurons per layer are set via a genetic

algorithm (GA) computation for each joint. The advantages of the simulated data points

derived from the DK model is fewer experimental trials or virtual robot posiitons that

impact the total setup time.

The indicator of position error at each point is selected as the distance between the TCP

position and the position computed by model via the ANN algorithm, and the formulation

is reported in Equation (8). The position error is negligible if the accuracy is lower than a

deﬁned threshold ε(set equal to 5.0 µm).

Erri=0i f TCPpose −Tn

AN N b<ε

TCPpose −Tn

AN N b(8)

where b,

TCPpose

, and

AN N

are the robot base location, the TCP position, and the kinematic

model via the ANN algorithm of the n-DOF manipulator, respectively.

Moreover, collision avoidance is a safety requirement that is integrated following

Equation (9). The constraint condition is applied to all n: 6 robot joints and the kexternal

objects and entities present in the industrial environment.

Cnj ≥On+Ojn={1, . . . , 6}∧j={1, . . . , k}(9)

where C

is the distance between two reference frame origins (reference n, reference j), and

Onand Ojare the effective radius of the nth robot joints and the jth obstacle, respectively.

2.3. Singularity and Manipulability Analyses

In addition, the manipulator configuration in 3D workspace influences the task execu-

tion during industrial operation. The joint variables are represented by q = [q

, q

. . .

, q

]

and the TCP position and orientation by p = [p

, p

. . .

, p

]

, assuming g

≤

n. The Jacobian

matrix J

∈

6×6

is the transformation relating to the joint and TCP movements, as stated in

Equation (10): .

xn=J·.

θ(10)

where

xn∈

6×1

and

θ∈

6×1

are the TCP and joint motion vectors, respectively. The

analysis is added in the proposed procedure to avoid the arrangements with rank(J) < 6.

Correspondingly, the manipulability evaluation

is adopted to assess the dexterity of the

robot, as indicated with Equation (11):

µ=qdet(J·JT)=∏

δi(11)

where

δi

indicates the singularity of the Jacobian matrix J. Therefore, the manipulabil-

ity

tending to null is an index of singularity approaching. Similarly, the greater the

manipulability index, the higher the ability to prevent singular conﬁgurations.

Robotics 2024,13, 153 7 of 27

2.4. Energy Consumption Appraisal

In the present work, the dynamics are a signiﬁcative factor for the robot base position-

ing deﬁnition. The estimation of power consumption for a prescribed task T

is derived

from the determination of the generalized resultant forces of vector

. The relation between

energy and force is coupled to the n-joint at the instant period [t

; t

]. Then, the mechanical

power is described as in Equation (12):

MP=

∑

n=1Ztf

t0hτn(t).

θn(t)i2dt (12)

The procedure calculates the robot base location to minimize Equation (12) for a

selected area. In the case of an industrial 6-DOF robot, the

τ2

is signiﬁcantly larger than

others; therefore, the expected contribution to the energy consumption is affected by J2.

3. Objective Function Formulation for Robot Positioning

The procedure to determine the optimal robot base position has been described con-

sidering the selected multi-criteria industrial drivers deﬁned in Section 2. Figure 3shows a

ﬂow diagram of the integrated scheme for establishing the brute-force robot base position.

The starting phase is the selection of the robot with the geometrical properties, the user

requirement, and the task deﬁnition under investigation. Then, a set of robot placements

and the assessment of the reachability measure, including the space limits within the scope

for searching optimization, are carried out. In phase 2, the robot model formulation is

performed to conﬁrm the workspace and robot conﬁguration for the tasks based on a

data-driven approach, assuring collision avoidance. The degree of accordance between

model and scenario could be appraised numerically or via experimental tests. In phase

3, the robot positioning for a singularity-free task is investigated using a manipulability

index that needs to be maximized. During the subsequent phase 4, the iterations are

related to the energy appraisal for each base position to determine the minimum energy

consumed to validate the procedure. The robot location may be obtained considering all

the described criteria, and the objective function fthat needs to be minimized is formulated

in the following Equations (13)–(16):

f=α·f1

+(1−α)·f2

+f3

0≤α≤1 (13)

f1=

∑

task=1

∑

g=1

∑

n=1T7

AN N (g,n)−TPC7

pose (g,n)2

i(14)

f2=

∑

task=1 1

µ2

i!(15)

f3=

∑

n=1

β·Ztf

t0hτn(t).

θn(t)i2dt 0≤β≤1 (16)

where f

represents the deviation contribution between the estimated TCP positions and the

related predeﬁned positions, f

is the sum of the inversed manipulability measures, and f3

is the mechanical power contribution at task T

. The values f

, and f

are derived from

the calculation of IK-ANN modeling, manipulability, and energy consumption, respectively.

In particular,

µi

is the manipulability index for the robot in position I,

is a weighting

factor of the accuracy–manipulability compromise, and

is the weight factor of each joint’s

contribution to energy consumption. Additionally, the initial and ﬁnal velocity conditions

are given in Equation (17) to represent a point-to-point motion:

Robotics 2024,13, 153 8 of 27

θn(t0)=0n=1, . . . , n

θntf=0n=1, . . . , n(17)

where t0and tfare the initial and ﬁnal task times for each joint n, respectively.

Robotics 2024, 13, x FOR PEER REVIEW 8 of 27

𝜃󰇗(𝑡)=0 𝑛=1,…,𝑛

𝜃󰇗𝑡=0 𝑛=1,…,𝑛 (17)

where t

and t

are the initial and ﬁnal task times for each joint n, respectively.

Figure 3. Flow chart of the multi-criteria procedure for brute-force robot base location.

Robotics 2024,13, 153 9 of 27

4. Simulation of Robot Base Placement and Case Studies

The robot placement procedure was validated analytically and using the digital twin

technique for a pick-and-place task application that is signiﬁcant in the manufacturing

industry. Some Ti tasks with two to eight target frames are presented, considering the

outcomes of the multi-criteria objective function.

4.1. Robot-to-Workpiece Placement: Analytical Method

The ﬁrst step of the proposed procedure is the collection of the following inputs: the

robot link dimensions, the layout constraints, and the TCP positions (coordinates and

orientation), as shown in Table 1—Case 1. The handled working volume based on the

pick-and-place reference frames, the robot base horizontal plane, and the user-deﬁned

positions (pick, place, b—manual position) are illustrated in Figure 4in the MATLAB

environment.

Table 1. Input variables, bounds, and parameters.

Case 1

Target

TCP Position

Position [X, Y, Z]

Rotation

[RX, RY, RZ] deg

Robot J1–J2 Link

Robot Base

Height

z-Axis Robot

Placement mm

b-Manual

Position [X, Y]

TCP Pick [−100, −200, 1200] [0, 0, 0] 448.0 339.1 670.0 [200, 100]

TCP Place [500, 400, 800] [0, 0, 0]

Robotics 2024, 13, x FOR PEER REVIEW 9 of 27

4. Simulation of Robot Base Placement and Case Studies

The robot placement procedure was validated analytically and using the digital twin

technique for a pick-and-place task application that is signiﬁcant in the manufacturing

industry. Some Ti tasks with two to eight target frames are presented, considering the

outcomes of the multi-criteria objective function.

4.1. Robot-to-Workpiece Placement: Analytical Method

The ﬁrst step of the proposed procedure is the collection of the following inputs: the

robot link dimensions, the layout constraints, and the TCP positions (coordinates and ori-

entation), as shown in Table 1—Case 1. The handled working volume based on the pick-

and-place reference frames, the robot base horizontal plane, and the user-defined positions

(pick, place, b—manual position) are illustrated in Figure 4 in the MATLAB environment.

Figure 4. Case 1—graphic representation: pick reference frame, place reference frame; π plane, b-

manual position.

Table 1. Input variables, bounds, and parameters.

Case 1

Target

TCP Position Position [X, Y, Z] mm Rotation [R

, R

] deg

Robot J1–J2

Link mm

Robot Base

Height

z-Axis Robot

Placement mm

b-Manual

Position [X,

Y] mm

TCP

Pick

[−100, −200, 1200] [0, 0, 0] 448.0 339.1 670.0 [200, 100]

TCP

Place

[500, 400, 800] [0, 0, 0]

In Case 1, the weighting factor β related to energy consumption is assumed to be

identical for each joint. To maximize the manipulability and the robot dexterity, the α

value is a signiﬁcative assumption that also impact the acceptable TCP positional devia-

tion; therefore, the initial set is equal to 0.15.

Table 2 summarizes the analytical results of Case 1, comparing the proposed b-posi-

tion on the XY plane for a chosen z-plane placement of 670.0 mm and the b-position man-

ually identiﬁed qualitatively by the user. The b-position proposed is placed at [X, Y] =

[600.0 mm, 300.0 mm], and the manual b-position is assessed at [X, Y] = [200.0 mm, 100.0

mm].

Figure 4. Case 1—graphic representation: pick reference frame, place reference frame;

plane,

b-manual position.

In Case 1, the weighting factor

related to energy consumption is assumed to be

identical for each joint. To maximize the manipulability and the robot dexterity, the

value is a signiﬁcative assumption that also impact the acceptable TCP positional deviation;

therefore, the initial set is equal to 0.15.

Table 2summarizes the analytical results of Case 1, comparing the proposed b-position

on the XY plane for a chosen z-plane placement of 670.0 mm and the b-position manually

identiﬁed qualitatively by the user. The b-position proposed is placed at [X, Y] = [600.0 mm,

300.0 mm], and the manual b-position is assessed at [X, Y] = [200.0 mm, 100.0 mm].

Figure 5a–c show the proposed b-position of the robot placement on the XY plane,

corresponding to the solution using an identical weighting factor for each DOF—here,

the J

, J

, and J

joints of the robot conﬁguration. To demonstrate the achievement of the

proposed procedure concerning manual position appraisal, Figure 5a shows the impact of

the b-position on the J

range of motion; similarly, Figure 5b reports the J

inﬂuence, and

Robotics 2024,13, 153 10 of 27

Figure 5c shows the J

effect. Case 1 is considerably affected by the range of motion of J

and J3, impacting TCP accuracy, manipulability, and energy consumption criteria.

Table 2. Output variables: b-manual comparison with b-proposed positions on the XY plane.

Case 1

Target Position [X, Y, Z] mm Rotation

[RX, RY, RZ] deg

Robot Placement

z-Axis mm

b-Manual

Position [X, Y] mm

b-Proposed

Position [X, Y] mm

TCP Pick [−100, −200, 1200] [0, 0, 0] 670.0 [200, 100] [600, −300]

TCP Place [500, 400, 800] [0, 0, 0]

Robotics 2024, 13, x FOR PEER REVIEW 10 of 27

Table 2. Output variables: b-manual comparison with b-proposed positions on the XY plane.

Case 1

Target Position [X, Y, Z] mm Rotation [R

, R

] deg

Robot Placement

z-Axis mm

b-Manual

Position [X, Y] mm

b-Proposed

Position [X, Y] mm

TCP

Pick

[−100, −200, 1200] [0, 0, 0] 670.0 [200, 100] [600, −300]

TCP

Place

[500, 400, 800] [0, 0, 0]

Figure 5a–c show the proposed b-position of the robot placement on the XY plane,

corresponding to the solution using an identical weighting factor for each DOF—here, the

, J

, and J

joints of the robot conﬁguration. To demonstrate the achievement of the pro-

posed procedure concerning manual position appraisal, Figure 5a shows the impact of the

b-position on the J

range of motion; similarly, Figure 5b reports the J

inﬂuence, and Fig-

ure 5c shows the J

eﬀect. Case 1 is considerably aﬀected by the range of motion of J

and

, impacting TCP accuracy, manipulability, and energy consumption criteria.

(a) (b)

(c)

Figure 5. Case 1—angular joint contribution based on the b-position of the robot placement on the

π-plane: J

contribution (a); J

contribution (b); J

contribution (c).

Case 2 is evaluated in order to investigate the contribution of the vertical position of

the

centroid on the robot base location. The task T

is equivalent to that in Case 1, and

the robot conﬁguration is selected with vertical z-axis moved from 670.0 mm to 400.0 mm.

Figure 5. Case 1—angular joint contribution based on the b-position of the robot placement on the

π-plane: J1contribution (a); J2contribution (b); J3contribution (c).

Case 2 is evaluated in order to investigate the contribution of the vertical position of

the J

centroid on the robot base location. The task T

is equivalent to that in Case 1, and

the robot conﬁguration is selected with vertical z-axis moved from 670.0 mm to 400.0 mm.

The output variables, b-manual, and b-proposed positions on the XY plane are reported in

Table 3.

Robotics 2024,13, 153 11 of 27

Table 3. Output variables: b-manual comparison with b-proposed positions on the XY plane.

Case 2

Target Position [X, Y, Z] mm Rotation [RX, RY, RZ]

deg

Robot Placement

z-Axis mm

b-Manual

Position [X, Y] mm

b-Proposed

Position [X, Y] mm

TPick [−100, −200, 1200] [0, 0, 0] 400.0 [200, 100] [−300, 400]

TPlace [500, 400, 800] [0, 0, 0]

The manual b-position is considered constant in Case 1 at [X, Y] = [200.0 mm, 100.0 mm].

The b-position analytical results are computed for Case 2 as [X, Y] = [

−

300.0 mm, 400.0 mm];

meanwhile, the results of Case 1 are [X, Y] = [600.0 mm,

−

300.0 mm], highlighting a differ-

ence in the location in the two scenarios and conﬁrming the goodness of the preliminary

assessment.

Figure 6a–c shows the b-position determined by joints’ contribution to altering the

vertical placement. The weighing factor

of joints J

–J

are the same, although the impact

is signiﬁcant for J

and J

in Figure 6a,c, respectively. The observed difference in [X, Y]

relating to Case 1 and Case 2 in terms of robot location is [X, Y] as [900.0 mm, 700 mm].

The energy consumption comparison of Case 2 for the b-manual and b-proposed robot

placement is shown in Figure 7a,b—which is based on the ABB IRB1200-5/0.9 features for

reference. In Figure 7a, the energy consumption in the Joule bar chart shows the beneﬁt

of lower energy consumption of close to 7.2% of proposed b-position under the same

trajectory motion conditions (e.g., velocity, ﬂy-by parameter, motion type). In Figure 7b,

the power–time chart highlights the lower instantaneous request, within the 11.6–24.3%

range, for the b-proposed position, guaranteeing task execution. Further scenarios have

been carried out to study the analytical outcome for pick-and-place task execution using a

robot with lower payload of maximum 3.0 kg. Table 4reports the input/output data used

for the procedure to fulﬁl the TCP positions. Case 3 and Case 4 differ for the speciﬁed robot

placement on the z-axis, which is moved from 670.0 mm to 400.0 mm, respectively. The

proposed b-position is placed for Case 3 at [X, Y] = [0.0 mm,

−

100.0 mm] and in Case 4 at

[X, Y] = [0.0 mm, −500.0 mm].

Table 4. Input variables, bounds, and parameters.

Case 3—Input

Target Position

[X, Y, Z] mm

Rotation

[RX, RY, RZ] deg

Robot J1–J2

link mm

Robot Base Height

mm z-Axis Robot Placement mm

b-Manual

Position

[X, Y] mm

TPick [0, 0.1, 1200] [0, 0, 0] 448.0 339.1 670.0 [500, 500]

TPlace [0, 0.1, 1000] [0, 0, 0]

Case 3—Output

Target Position

[X, Y, Z] mm

Rotation

[RX, RY, RZ] deg Robot Placement z-Axis mm b-Manual

Position [X, Y] mm

b-Proposed

Position [X, Y] mm

TPick [0, 0.1, 1200] [0, 0, 0] 670.0 [500, 500] [0, −100]

TPlace [0, 0.1, 1000] [0, 0, 0]

Case 4—Output

Target Position

[X, Y, Z] mm

Rotation

[RX, RY, RZ] deg Robot Placement z-Axis mm b-Manual

Position [X, Y] mm

b-Proposed

Position [X, Y] mm

TPick [0, 0.1, 1200] [0, 0, 0] 400.0 [500, 500] [0, −500]

TPlace [0, 0.1, 1000] [0, 0, 0]

Robotics 2024,13, 153 12 of 27

Robotics 2024, 13, x FOR PEER REVIEW 11 of 27

The output variables, b-manual, and b-proposed positions on the XY plane are reported

in Table 3.

Table 3. Output variables: b-manual comparison with b-proposed positions on the XY plane.

Case 2

Target Position [X, Y, Z] mm Rotation [R

, R

] deg

Robot Placement

z-Axis mm

b-Manual

Position [X, Y] mm

b-Proposed

Position [X, Y] mm

Pick

[−100, −200, 1200] [0, 0, 0] 400.0 [200, 100] [−300, 400]

Place

[500, 400, 800] [0, 0, 0]

The manual b-position is considered constant in Case 1 at [X, Y] = [200.0 mm, 100.0

mm]. The b-position analytical results are computed for Case 2 as [X, Y] = [−300.0 mm,

400.0 mm]; meanwhile, the results of Case 1 are [X, Y] = [600.0 mm, −300.0 mm], highlight-

ing a diﬀerence in the location in the two scenarios and conﬁrming the goodness of the

preliminary assessment.

Figure 6a–c shows the b-position determined by joints’ contribution to altering the

vertical placement. The weighing factor β of joints J

–J

are the same, although the impact

is signiﬁcant for J

and J

in Figure 6a,c, respectively. The observed diﬀerence in [X, Y]

relating to Case 1 and Case 2 in terms of robot location is [X, Y] as [900.0 mm, 700 mm].

The energy consumption comparison of Case 2 for the b-manual and b-proposed robot

placement is shown in Figure 7a,b—which is based on the ABB IRB1200-5/0.9 features for

reference. In Figure 7a, the energy consumption in the Joule bar chart shows the beneﬁt

of lower energy consumption of close to 7.2% of proposed b-position under the same tra-

jectory motion conditions (e.g., velocity, ﬂy-by parameter, motion type). In Figure 7b, the

power–time chart highlights the lower instantaneous request, within the 11.6–24.3%

range, for the b-proposed position, guaranteeing task execution. Further scenarios have

been carried out to study the analytical outcome for pick-and-place task execution using

a robot with lower payload of maximum 3.0 kg. Table 4 reports the input/output data used

for the procedure to fulﬁl the TCP positions. Case 3 and Case 4 diﬀer for the speciﬁed

robot placement on the z-axis, which is moved from 670.0 mm to 400.0 mm, respectively.

The proposed b-position is placed for Case 3 at [X, Y] = [0.0 mm, −100.0 mm] and in Case

4 at [X, Y] = [0.0 mm, −500.0 mm].

(a) (b)

Robotics 2024, 13, x FOR PEER REVIEW 12 of 27

(c)

Figure 6. Case 2—angular joint contribution based on the b-position of the robot placement on the

π-plane: J

contribution (a); J

contribution (b); J

contribution (c).

(a)

(b)

Figure 7. ABB IRB1200-5/0.9 robot: energy consumption bar chart (a); power-time chart (b).

Figure 8a–f illustrates the proposed b-position of the robot placement on the XY

plane, corresponding to the solution using an identical weighting factor for each DOF—

548.708

509.286

480.00

490.00

500.00

510.00

520.00

530.00

540.00

550.00

560.00

Energy consumption [J]

Jb-proposed

Jb-Manual

-600.00

-400.00

-200.00

0.00

200.00

400.00

600.00

800.00

1000.00

1200.00

1 7 13 19 25 31 37 43 49 55 61 67 73 79 85 91 97 103 109 115 121 127 133 139 145 151

W b-manual

W b-proposed

Time [s]

Power [W]

Figure 6. Case 2—angular joint contribution based on the b-position of the robot placement on the

π-plane: J1contribution (a); J2contribution (b); J3contribution (c).

Figure 8a–f illustrates the proposed b-position of the robot placement on the XY plane,

corresponding to the solution using an identical weighting factor for each DOF—here,

the J

, J

, and J

joints of the robot conﬁguration in Case 3 and Case 4. Compared to the

previous Case 1 and Case 2, the impact of J

and J

are not predominant in either Case 3

or Case 4. The observed difference in [X, Y] between Case 3 and Case 4 in terms of robot

location is [0.0 mm, 400 mm]. The joint perturbation on the b-placement estimation is an

open challenge that needs to be addressed.

Robotics 2024,13, 153 13 of 27

Robotics 2024, 13, x FOR PEER REVIEW 12 of 27

(c)

Figure 6. Case 2—angular joint contribution based on the b-position of the robot placement on the

π-plane: J

contribution (a); J

contribution (b); J

contribution (c).

(a)

(b)

Figure 7. ABB IRB1200-5/0.9 robot: energy consumption bar chart (a); power-time chart (b).

Figure 8a–f illustrates the proposed b-position of the robot placement on the XY

plane, corresponding to the solution using an identical weighting factor for each DOF—

548.708

509.286

480.00

490.00

500.00

510.00

520.00

530.00

540.00

550.00

560.00

Energy consumption [J]

Jb-proposed

Jb-Manual

-600.00

-400.00

-200.00

0.00

200.00

400.00

600.00

800.00

1000.00

1200.00

1 7 13 19 25 31 37 43 49 55 61 67 73 79 85 91 97 103 109 115 121 127 133 139 145 151

W b-manual

W b-proposed

Time [s]

Power [W]

Figure 7. ABB IRB1200-5/0.9 robot: energy consumption bar chart (a); power-time chart (b).

Robotics 2024, 13, x FOR PEER REVIEW 13 of 27

here, the J

, J

, and J

joints of the robot conﬁguration in Case 3 and Case 4. Compared to

the previous Case 1 and Case 2, the impact of J

and J

are not predominant in either Case

3 or Case 4. The observed diﬀerence in [X, Y] between Case 3 and Case 4 in terms of robot

location is [0.0 mm, 400 mm]. The joint perturbation on the b-placement estimation is an

open challenge that needs to be addressed.

Table 4. Input variables, bounds, and parameters.

Case 3—Input

Target Position [X,Y,Z] mm Rotation

] deg

Robot J1-J2

link mm

Robot Base

Height

z-Axis Robot

Placement mm

b-Manual

Position

[X,Y] mm

Pick

[0, 0.1, 1200] [0, 0, 0] 448.0 339.1 670.0 [500, 500]

Place

[0, 0.1, 1000] [0, 0, 0]

Case 3—Output

Target Position [X,Y,Z] mm Rotation

] deg

Robot Placement

z-Axis mm

b-Manual

Position [X, Y] mm

b-Proposed

Position [X, Y] mm

Pick

[0, 0.1, 1200] [0, 0, 0] 670.0 [500, 500] [0, −100]

Place

[0, 0.1, 1000] [0, 0, 0]

Case 4—Output

Target Position [X,Y,Z] mm Rotation

] deg

Robot Placement

z-Axis mm

b-Manual

Position [X, Y] mm

b-Proposed

Position [X, Y] mm

Pick

[0, 0.1, 1200] [0, 0, 0] 400.0 [500, 500] [0, −500]

Place

[0, 0.1, 1000] [0, 0, 0]

(a) (b)

Figure 8. Cont.

Robotics 2024,13, 153 14 of 27

Robotics 2024, 13, x FOR PEER REVIEW 14 of 27

(e) (f)

Figure 8. Case 3 and Case 4 - angular joint contribution based on the b-position of the robot place-

ment on the π-plane: J

contribution Case 3 (a); J

contribution Case 4 (b); J

contribution Case 3 (c)

contribution Case 4 (d); J

contribution Case 3 (e); J

contribution Case 4 (f).

4.2. Robot-to-Workpiece Placement: Simulation Method

To evaluate the procedure, a comparison with a digital twin tool was conducted, as-

suming prior knowledge of the model for a selected set of robots. The models were ob-

tained with Windows PC with Intel-Core4.8GHz-i7. The industrial layout was repre-

sented with commercially I/O systems for machine-tending applications. The layout ar-

chitecture and a set of workstation elements with their target positions (5 to 8 references)

are described in Table 5. Fourteen ABB robots were analyzed, with reach characteristics in

the 1440.0 mm–2500.0 mm range, using ABB RobotStudio software. The TCP velocity was

set at 1.50 m/s. The digital twin SW may reproduce the motion of the robotic system,

providing kinematic constraints and detecting the potential collisions.

Tab le 5. Simulation scenario representation: layout, input/output equipment, and related task posi-

tions.

Layout Type I/O System Position [X mm, Y mm, Z mm] and

Rotation [R

deg, R

deg]

Linear Input system conveyor [1830, 250, 630] [−90, 0, 90]

Output system conveyor [4670, 250, 630] [−90, 0, −90]

Figure 8. Case 3 and Case 4 - angular joint contribution based on the b-position of the robot placement

on the

-plane: J

contribution Case 3 (a); J

contribution Case 4 (b); J

contribution Case 3 (c) J

contribution Case 4 (d); J3contribution Case 3 (e); J3contribution Case 4 (f).

4.2. Robot-to-Workpiece Placement: Simulation Method

To evaluate the procedure, a comparison with a digital twin tool was conducted, as-

suming prior knowledge of the model for a selected set of robots. The models were obtained

with Windows PC with Intel-Core4.8GHz-i7. The industrial layout was represented with

commercially I/O systems for machine-tending applications. The layout architecture and a

set of workstation elements with their target positions (5 to 8 references) are described in

Table 5. Fourteen ABB robots were analyzed, with reach characteristics in the 1440.0 mm–

2500.0 mm range, using ABB RobotStudio software. The TCP velocity was set at 1.50 m/s.

The digital twin SW may reproduce the motion of the robotic system, providing kinematic

constraints and detecting the potential collisions.

Robotics 2024,13, 153 15 of 27

Table 5. Simulation scenario representation: layout, input/output equipment, and related task

positions.

Layout Type I/O System Position [X mm, Y mm, Z mm] and

Rotation [RXdeg, RYdeg, RZdeg]

Linear

Input system conveyor [1830, 250, 630] [−90, 0, 90]

Output system conveyor [4670, 250, 630] [−90, 0, −90]

Workstation

Target 1 [3250, 1750, 620] [−90, 0, 0]

Target 2 [2980, 1750, 750] [0, 90, 90]

Target 3 [3250, 1750, 750] [0, −90, −90]

U-type

Input system conveyor [670, 250, 430] [−90, 0, 0]

Output system conveyor [670, 750, 730] [−90, 0, 0]

Workstation

Target 1 [250, 750, 620] [−90, 0, 90]

Target 2 [−250, −1020, 750] [0, 90, −180]

Target 3 [−250, −480, 750] [0, −90, 0]

U-type

Input system conveyor [670, 1100, 730][−90, 0, 0]

Output system pallet

Position 1 [370, 70, 270] [−90, 0, 0]

Position 2 [370, 730, 270] [−90, 0, 0]

Position 3 [1430, 70, 270] [−90, 0, 0]

Position 4 [1430, 730, 270] [−90, 0, 0]

Workstation

Target 1 [−250, −750, 620] [−90, 0, 90]

Target 2 [−250, −1020, 750] [0, 90, −180]

Target 3 [−250, −480, 750] [0, −90, 0]

The simulation problem was presented with three variables, X, Y, and Z, of the b-

placement position. The searching area was identiﬁed to reduce the computation time

and to satisfy the reachability and manipulability criteria. In the considered scenarios,

the maximum pick-and-place trajectory distance was selected as 1100.0 mm. The robot

placement verifications in 2D-space were completed. The results are displayed in Figure 9a–c

and the selected index was the ratio between the trajectory distance and the robot reach

feature. The results for each layout architecture are shown in Figure 9a for linear—conveyor

to conveyor, in Figure 9b for side—conveyor to conveyor, and in Figure 9c for side—

conveyor to pallet. Six to fourteen veriﬁed robots are shown for the three layouts. The

b-placement coordinate in blue color shows compliance with four criteria, the green color

indicates medium risk for the reachability criteria, and the red color indicates high risk of

not satisfying the four criteria. The difference between the digital twin and the proposed

procedure was less than 5% in terms of energy consumption estimation for the same

robot placement. The results of the scenarios in Table 5show an energy consumption

reduction from red positions (high risk) to blue positions (satisfy criteria) in the range of

24.5% to 26.4%. The beneﬁt of appropriate robot selection and b-placement was reduced in

7.6–13.2%

in the case of medium risk to satisfy the reachability and manipulability criteria.

The goodness and effectiveness of the proposed method were veriﬁed in comparison with

scenarios of high expertise in prior robots and time consumption for the maturity of a

representative digital twin.

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(a)

(b)

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(c)

Figure 9. Normalized index of the 6-DOF robot base position on the XY plane in diﬀerent scenarios

using ABB RobotStudio: linear - conveyor to conveyor (a); side - conveyor to conveyor (b); side -

conveyor to pallet (c).

5. Experimental Validation: Results and Discussion

A series of experimental veriﬁcations of the robot placement scheme were carried out

on the industrial FANUC robot equipped with an external sensor for TCP position recog-

nition and redundant system of power consumption measurement. The robot locations

were obtained considering the unknown IK model and without a prior knowledge of joint

dependency. Evaluating the optimized multi-criteria positioning results and the manual

placement, the feasibility and validity of procedure were conﬁrmed.

The conﬁguration of robotic system is shown in Figure 10, and an LR Mate 200ic was

employed for the test campaign. The speciﬁcation of the robot arm can be stated: number

of axes, 6; maximum robot payload, 5.0 kg; maximum reach, 704.0 mm; repeatability, ±

0.02 mm; and an R-30iA controller. In addition, the joint maximum speed and range of

motion are stated in Table 6.

Figure 9. Normalized index of the 6-DOF robot base position on the XY plane in different scenarios

using ABB RobotStudio: linear-conveyor to conveyor (a); side-conveyor to conveyor (b); side-

conveyor to pallet (c).

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