Robotics and Computer Integrated Manufacturing 61 (2020) 101819

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Robotics and Computer Integrated Manufacturing
journal homepage: www.elsevier.com/locate/rcim

Estimating probability of human hand intrusion for speed and separation
monitoring using interference theory

T⁎

Eugene Kim ,a, Robin Kirschnerb, Yoji Yamadaa, Shogo Okamotoaab

Department of Mechanical Systems Engineering, Nagoya University, Furo-Cho, Chikusa-ku, Nagoya, 464-8603, Japan
Department of Mechanical Engineering, Chemnitz University of Technology, Reichenhainer Strasse 70, Chemnitz 09126, Germany

A R T I C LE I N FO

A B S T R A C T

Keywords:
Human-robot collaboration
Speed and separation monitoring
Interference theory
Unstructured manufacturing

Human Robot Collaboration (HRC) has attracted high attention in modern manufacturing. Recently, a safety
standard for collaborative robots has been launched (ISO/TS 15066). It cover the safety function of Speed andSeparation Monitoring (SSM) which includes velocities and positions of the human and the robot. However, risk
should be discussed with probability, while the SSM is not. Therefore, the probability of intrusion was calculated
according to the stopping time of the robot and the maximum speed of the robot. Since the SSM was testiﬁed
along the simulation by far, actual adhesive applying task was carried out in this paper.

1. Introduction
Industrial robots have been used for several decades and collaborative operation that enables collaboration between the humans andthe robots has become increasingly of practical interest in the manufacturing industry [1]. Industrial robots, which have high precision in
the manufacturing processes, can overcome the physical limitations ofhumans and perform risky tasks. However, it can be time consuming
and ineﬃcient to use industrial robots when the production is small.
Furthermore, it is not easy to alter a process immediately to satisfy
market needs. Therefore, it is diﬃcult to use industrial robots in factories that produce products that require ﬂexibility and complexity[2,3]. Consequently, human–robot collaboration (HRC) has been introduced to improve product quality and utilize a manufacturing layout
where the robot carries out the simple and repetitive work while theworker operates on complicated assembly tasks [4].
For humans and robots to share work spaces, the safety integrity
level of collaborative systems based on international safety standards[5,6] must be satisﬁed. The safety standard ISO/TS 15,066 (“Robots
and robotic devices-collaborative robots”) [7] describes safety functions
to secure the safety of the workers. Speed and separation monitoring(SSM) is one of these functions that maintain suﬃciently large distances
to ensure safety by detecting the position and velocity of the human.
Unlike other safety functions included in this standard, SSM allows
mutual movement of the human and robot while ensuring that physicalcontact is avoided, helping robots and humans to work together.

⁎

Therefore, by using SSM, sharing of workspaces can be expected [8]and the eﬃciency of production processes can also be improved.
Over the past few years, many researchers have shown an interest in
the SSM method. In an early stage of the SSM development history, anevaluation mechanism for the SSM function was presented focusing on
safety and productivity [9]. Further, an analysis of the current SSM
function was reported based on simulation results [10]. In this study,
the eﬀect of the method measuring the speed of the robot on the SSM
and the rationality of the elements constituting the SSM were studied
and discussed. In another research, a likelihood analysis of the collaborative tasks based on tracking the human motion and the frequency
of a cell in a space occupied by a human was carried out [11]. In addition, a dynamic SSM has been proposed, diﬀerent from the existing
calculation method of conventional safety distance, and its beneﬁts andperformance evaluation have been reported [12]. General safety factors, including SSM, were also investigated in terms of human presence
sensing [13], collision avoidance [14–16], and danger ﬁelds [17].
Despite these eﬀorts, the safety evaluation of the SSM function
based on simulations has only been attempted for a two-dimensional
analysis and has not been evaluated from the actual end-eﬀector distance to the human. For this reason, the function of the SSM was likely
to introduce or include an extra distance between the human and therobot. However, it is expected that the eﬃciency of the SSM will be
increased by using a three-dimensional (3D) safety-related sensor. It is,therefore, important to investigate which of the parameters of the SSM
function are sensitive to inﬂuence the safety distance with the growing

Corresponding author.
E-mail address: kim.eugene@a.mbox.nagoya-u.ac.jp (E. Kim).
URL: http://www.mech.nagoya-u.ac.jp/asi/en/ (E. Kim).

https://doi.org/10.1016/j.rcim.2019.101819
Received 15 June 2018; Received in revised form 29 May 2019; Accepted 31 May 20190736-5845/ © 2019 Elsevier Ltd. All rights reserved.

Robotics and Computer Integrated Manufacturing 61 (2020) 101819

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where Sh is the distance the human is expected to move from the time
the stop signal is issued to the robot until the time taken by the robot tostop completely. Thus, in addition to the net time at which the robot
must stop after receiving the stop signal, the additional reaction time,such as the time required for the communication between the safetyrelated sensor and the robot system, must be considered. Sr represents
the reaction distance of the robot until the stop signal is issued by thesafety-related sensors based on the human intrusion. It is assumed thatthe robot is moving with a constant speed until it receives the stop
signal and reacts. The reaction time typically includes the response timeof the safety-related equipment, the robot controller, and the communication latency. Furthermore, Ss is the distance that the robot travels
from the time it receives the stop signal until it stops completely.
Consequently, Ss is highly dependent on the stopping performance ofthe robot, the speed of the robot during the speciﬁc task, and the weightof the payload. In addition, C is an intrusion distance through which apart of the body (usually a hand) can move past the detected zone towards the hazard zone prior to actuation of the safety functions [21].
For example, safety sensors that monitor a two-dimensional plane,
should consider the intrusion of the human body parts from the undetected intrusion, which can depend on the distance between theneighboring beams in case of a light curtain. Finally, Zd and Zr are themeasurement uncertainties of the positions of the human and the robot,
respectively. Zd varies according to the performance of the safety-related sensor [22,23], and Zr varies according to the accuracy of therobot’s measurement system.
Furthermore, (1) can be written in more detail by substituting eachterm as follows:increase in the use of 3D sensors [18,19]. The question remains how toquantitatively estimate the intrusion in the workspace in the designingstage of implementing SSM. In addition, the challenge lies to determine
how to maintain work cell productivity without hampering the performance of the robot. Therefore, the present study was undertaken to
examine the robot’s performance and the eﬀect of the environmental
factors on the probability of intrusions in an actual collaboration scenario with a statistical interpretation.
In this study, a battery assembly task that includes an adhesive
application by a robot was chosen as the collaborative task and implemented to measure the probability of human hand intrusion into therobot’s protective separation distance (PSD). All tasks were based on
HRC to investigate the probability of intrusion, and a statistical interpretation from interference theory (IT) was used for the analysis. Basedon the actual HRC, we analyzed the tendency of intrusion probabilities
into the PSD based on the stopping time and the parameters of the robotthat supplement the PSD.
2. Speed and separation monitoring in human-robot collaboration
2.1. Protective separation distance
PSD is the smallest distance allowed between the human and themoving robot in a collaborative operation used by the SSM function.
According to the ISO/TS 15,066 technical speciﬁcation, when the separation distance, which is the distance between the human and therobot, decreases to a value below the PSD, a protective stop function
should be executed immediately [20]. However, depending on theoperation state of the robot, the speed and the inertia of the robot canvary on the basis of its payload or its pose and motion, which can increase the stopping distance. Therefore, it is necessary to maintain asafe distance between the robot and the worker to stop the robot, evenwhen the operator cannot respond to the threat. Thus, PSD is expressedas the distance traveled by the human and the robot towards each otheruntil the robot completely stops.
As shown in Fig. 1, assuming that the PSD Sp(t) is a function of timet, the PSD at time t0 can be expressed as follows:

Sp (t0) = Sh + Sr + Ss + C + Zd + Zr ,Sp (t0) = vh (t0)(Tr + Ts ) + vr (t0) Tr + Ss + M .

(2)

It is assumed that Tr is the time elapsed from the moment the humanenters the PSD until the robot reacts and Ts is the time elapsed from theissuing of the stop signal until the robot stops completely. Thus, thedistance traveled by the human until the robot completely stops can be
expressed as the product of the velocity of the human vh at time t0 andthe sum of Ts and Tr. Next, the distance traveled by the robot until it
responds is expressed as the product of the velocity vr and Tr.
Furthermore, the distance traveled until the robot completely stops canbe predicted by integrating the speed vs along Ts while the robot is
decelerating.

(1)

Ss =

t0 + Tr + Ts

∫t +T
0

r

vs (t ) dt .

(3)

Finally, the uncertainties in the measurements of Zd, Zr, and the
intrusion distance C can be expressed to simplify to the equation using amargin factor M.
3. Human and robot interference theory
In HRC, human safety can be broadly classiﬁed into two types:
psychological and physical safety [24]. Psychological safety refers to
keeping the worker safe from threats such as mental fatigue or stress,
which are constantly experienced in the work environment. Physicalsafety refers to keeping the operator safe from personal fatigue andinjury from physical interactions of the robot with the worker. It is
required to mitigate the risk to a tolerable limit through reasonable risk
assessment and corresponding mitigation measures [25]. However, in
this study, only physical safety is discussed to focus on the SSM functionality.
Physical safety can be interpreted as a guarantee of avoidance fromunintended or unwanted contact between the human and the robot.
Physical contact can occur only when the operator is at a distance closeenough to collide with the robot and when the sensor system does notrecognize the operator or the robot fails to stop. Therefore, in theprocess designing stage, it is important to know the probability of intrusion into the hazard zone based on the positions of the operator andFig. 1. Diagram of the safety function of Speed and Separation Monitoring.
Protective Separation Distance consists of the minimum permissible distance
between the robot and the human, Sh (distance that the human moves from stop
issued until the robot stops), Sr (distance that the robot moves until it reacts), Ss(distance that the robot moves during braking), Intrusion distance C, andUncertainties of measurement. Zd and Zr [7].
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Fig. 2. Comparison of Protective Separation Distance Sp and the separation
distance S distribution. Collision between the human and the robot can only
occur when S is smaller than Sp. The distance is calculated along in direction ofclosest distance between the human and the robot.

Fig. 3. Human and Robot Interference Theory comparing Protective Separation
Distance and separation distance considering time variable. By considering thetime variable when calculating the probability of intrusion, it is possible toprevent the probability of intrusion from being calculated excessively.

the robot. Herein, we propose the use of IT to investigate the probability of intrusion during the collaboration between the operator andthe robot [26,27].
The concept of IT shows how the failure of the system can appear
from a mechanical perspective [28]. By using IT, the PSD and the separation distance between the human and the robot are compared, as
shown in Fig. 2. The projected area in Fig. 2 shows the portion of theinterference between the two variables. When the distributions of the
PSD and the closest distance are known, the general expression for the
probability of intrusion can be written as

POI = P (Sp ≥ S ) = P (Sp − S ≥ 0),(4)

where POI is the probability of intrusion and each Sp and S represents a
random variable of the PSD and separation distance, respectively.
Therefore, a statistical expression of the POI using the PSD and closest
distance can be rewritten as

POI =

∞

∞

∫−∞ fSp (Sp) ⎡⎢ ∫S fS (S ) dS⎤⎥ dSp,⎣p

Fig. 4. The red sphere is the PSD that is calculated based on the velocity vh of
the operator’s hand and the velocity vr of the end eﬀector of the robot particularly deﬁned in direction of the closest distance from each other. Accordingly,
the velocity vh′ of the worker’s hand projected on closest distance vector and the
projected velocity vr′ of the end eﬀector of the robot is used in the calculation.

(5)⎦

where fSp and fS are the probability density function of the PSD and theseparation distance between the human and the robot, respectively.
However, because both fSp and fS terms are time dependent, if POI is
calculated taking the time into account, the equation can be expressed
as follows:

POI (t ) =∞vector. As shown in Fig. 4, instead of using the velocity of the human vhand the robot vr, each of the velocities projected on the closest distancevector, vh′ and vr′, is used in the calculation. Furthermore, the maximum
limit of the margin factor M in the calculation of the PSD (2) is assumed
to be lower or equal to 850 mm [21], assuming that all 3D motions aredetectable. In this study, only the collision between the end eﬀector of
the robot and the hand of the operator is considered as the most hazardous collision event. Therefore, the measured closest distance between the human hand and the end eﬀector of the robot is used as theseparation distance between the operator and the robot.

∞∫0 fSp (t, Sp) ⎡⎢ ∫S fS (t, S ) dS⎤⎥ dSp.
⎣

p

⎦

(6)

As shown in Fig. 3, by comparing the PSD and the separation distance including the time variable, it is possible to estimate the probability of intrusion in each time interval. In the analysis, because thedomain of the PSD uses the physical parameter of the distance, only
positive values were used in the integral domain. Note that POI is afunction of t, and fSp and fS are the probability density functions at atime interval [t , t + Δt ) . Therefore, the POI can be deﬁned by the time t
and time interval Δt, and the POI for the total time T is expressed asfollows:

1
POI =
T

T

∞

4. Experimental setups
4.1. Task setup∞∫0 ∫0 fSp (t, Sp) ⎡⎢ ∫S fS (t, S ) dS⎤⎥ dSp dt,⎣

p⎦A battery assembling task was chosen to demonstrate the HRC task.
An adhesive material must be applied to the corresponding battery
junction in each direction to ﬁx the battery cell into the case and theinjection quantity should be adjusted by the proper amount. Therefore,
the robot performed the adhesive application task and the battery-(7)

where POI denotes an averaged POI over the total time T.
To calculate POI more accurately, PSD must be calculated from thecomponents of the velocities in the direction of the closest distance3

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4.2. Robot conﬁguration and measurement setup
During the collaboration between the robot and the operator described above, it was assumed that the contact between the end eﬀectorof the robot and the hand of the operator was the most dangerous andwas accompanied by the risk of injury. Therefore, the distance between
the human and the robot was determined by measuring the distance ofthe hand (left or right hand) of the operator closest to the end eﬀector of
the robot. In this experiment, a motion capture system (Venus 3D),
calibrated with a measurement error of less than 1 mm, was used todetect the movement of the robot end eﬀector and the human hand in
three dimensions with high accuracy. Seven cameras were used in theexperiment, and the markers were attached to the tip of the end eﬀectorof the robot and both hands of the operator.
A six-axis robot arm, Denso VS-060, was used in the experiment andits maximum speed was set at 0.9 m/s. The stopping time of the robot
was calculated based on the speed of the robot at every moment basedon the data provided by the robot manufacturer. Based on the speciﬁcation of the braking performance, stopping distance at every moment
is calculated linearly from the instantaneous speed of the robot including the reaction time of the robot 0.1 s. The end eﬀector was replaced by a soft urethane material, as unintended contact between the
robot and the person that can occur during the experiment. In addition,
to allow the operator to manually bring the robot to a safe state whendesired, an emergency-stop button was placed close to the operator.
Participants worked parallel to the robot at a distance of about 1.5 mfrom the center of the robot during the task so that the workers could
not physically contact the robot, even if the workers reached out theirhand. Ten healthy people participated in the experiment, and eachparticipant assembled ten batteries.

Fig. 5. Schematic diagram of human-robot collaboration work used in the experiment. The used battery assembly cooperative work is accomplished by
combining (a) the battery case and (b) the battery cell. Here, the robot performs
the work on the adhesive, and the E-stop is arranged within the workers reach.

5. Experimental results
5.1. Comparison of protective separation distance and separation distanceFig. 7shows an example of the comparison of the calculated PSD andthe separation distance using both the distance and the speed of theparticipant and the robot with respect to the world coordinate frame
spanned at the motion capture system. The PSD was computed based on
the relative speed of the robot and the operator. The intrusion distance
C, which supplements the margin factor M, is the assumed distancerequired to detect human body parts successfully using the 3D safetyrelated sensor. No collisions between the human and the robot occurredFig. 6. One of the participants doing the battery assembly work. Some of thelayouts have been changed to make it easier to do the work for each of theparticipant and have improved the proﬁciency through several exercises.

assembling task was conducted by the human participant. Fig. 5 shows
the schematic diagram of the experimental layout and Fig. 6 shows anactual image of the layout. However, only the application motion of therobot was demonstrated without actually using the adhesive. Next, tocomplete the task, a battery cell was inserted into each junction of thebottom case, and the battery case was assembled in the order of bottom,
middle, and upper case.

• Battery assembly task:

1. The operator installs the bottom case to the robot working space.
2. The robot starts applying the adhesive to the bottom battery case.
3. After the robot completes the operation, the operator installs theupper case in the robot’s working space.
4. The robot starts applying adhesive to the upper battery case.
5. The operator inserts the battery cells into the bottom case during
the upper case operation of the robot.
6. The operator assembles the middle case.
7. The operator assembles the upper case when the adhesive processof the upper case of the robot is completed.

Fig. 7. Comparison of Protective Separation Distance (Sh, Sr and Ss only) andseparation distance, which is derived by the actual speed and position of boththe human hand and the robot end eﬀector during experiment.
4

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Fig. 8. Histogram of averaged distribution of closest distance between the operator and robot and the Protective Separation Distance of the ten participants
until the task was completely over.

Fig. 10. Probability of intrusion into the Protective Separation Distance of ten
participants in the experiment according to a margin factor M, which involves
the intrusion distance C and uncertainties Zd, Zr. P1-P10 indicate the ten participants.

in this experiment.
As shown in Fig. 8, the PSD and the separation distance between theend eﬀector of the robot and the separation distances of the ten people
participating in the experiment were statistically compared. The
average separation distance from the end eﬀector of the robot to theoperator was 0.74 m, and it required 7.5 min on an average to assemble
ten batteries. Accordingly, the probability of the hand intrusion POI
into the PSD using the IT in the battery assembly task was 1.2%.
In addition, Fig. 9 shows an example of the comparison between the
PSD and the separation distance obtained by considering the time
variable when setting the time interval Δt to 8 s. Consequently, theaverage POI for all of the ten participants was calculated to be
5.6 × 10−3 .

predetermined constant. Fig. 10 shows the simulation results of the POI
in the PSD for each of the ten subjects when applying a diﬀerent margin
factor M in the PSD. The time interval Δt was set as 1 s, which includes
100 measured position samples of subjects and the robot. Accordingly,
the probability of the human hand intrusion increased rapidly from
170 mm on an average, and over 1% of the intrusions were observed
when a margin factor of 240 mm was applied. In addition, when using amargin factor greater than 650 mm, an intrusion probability of morethan 15% was expected for the experimented task. By contrast, whenexcluding the margin factor, the probability of the human hand intrusion POI of all participants was 4.9 × 10−5 .
The stopping distance of the robot diﬀers based on the robot inertia
including the payload, robot pose, and velocity. Fig. 11 shows the simulation of the probabilities of the human hand intrusion into the PSD
according to the diﬀerent stopping time of the robot from the maximum

5.2. Simulation results of margin factor and stopping time in the probabilityof intrusion
As shown in the formula of PSD function (2), the calculation of thesafety distance between the human and the robot comprises the margin
factor M. Thus, the POI depends on the margin factor M, which is a

Fig. 11. Simulation of the probability of intrusion into the Protective
Separation Distance using a robot with each stopping time according to themargin factor M when the maximum speed of the robot is 0.9 m/s. The stopping
time is calculated linearly proportional to the instant speed of the robot. The
greater the stopping time, the greater the probability of intrusion into theProtective Separation Distance.

Fig. 9. Histogram of Protective Separation Distance and separation distance ineach time period when the time interval is set 8 s.
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2.70 × 10−2

during the reaction time of the robot system. Moreover, the maximum
velocity vhmax of the human is assumed to be 1600 mm/s when theseparation distance is greater than 500 mm and 2000 mm/s when it islesser than 500 mm. However, the conﬁguration of C can diﬀer by theuse of various safety measures including fences and safety doors.
Meanwhile, intrusion distance C can be diminished by detecting the
intrusion of the hand by use of the 3D safety-related sensor making the
HRC task faster and allowing the human and the robot to work in closer
proximity. Furthermore, the workspace using the SSM function can beadditionally conﬁgured and adjusted based on the probability of ahuman intrusion into the robot workspace. Speciﬁcally, even if thelayout of the task process does not violate the SSM function and a smallchange in human behavior in actual collaboration causes a frequent
halt of the robot, the layout of the workspace should be reorganized tomeet the requirement of the safety regulation while maintaining thedesired productivity in the process designing stage.

1.55 × 10−606.2. Probability of intrusion and practicality

Table 1
Calculation of PSD and POI using parameters of typical industrial robot parameters. The maximum velocity of a human was assumed to be 1.6 m/s and thereaction time of the robot was assumed as 0.1 s.
Physical parameters

Calculated results

Stopping time(Ts)

Margin factor(M)

Maximum protective
separation distance (Spmax)

POI

0.05 s0.03 s0.01 s0.05 s0.05 s

850 mm
850 mm
850 mm
550 mm
350 mm2.13 m1.72 m1.31 m1.83 m1.63 m

0.353
0.352
0.351
0.175

2.94 × 10−2

0.05 s

150 mm1.43 m

1.48 × 10−4

0.05 s

10 mm

1.29 m0.03 s0.03 s

550 mm
350 mm1.42 m1.22 m

4.86 × 10−50.175

0.01 s

150 mm0.61 m0.01 s

10 mm

0.47 mThe IT used in this study is a discrete statistical analysis method
over time used to calculate the probability of intrusion. However, if theprobability of intrusion is simply calculated for the entire collaborative
work time, the characteristics of the partial intrusion tendency are ignored. Consequently, this creates diﬃculty in assessing how much of
the interaction is involved in the detailed task and how much theycause intrusion. Conversely, if IT is used to calculate the probabilities of
intrusion between the human and the robot, we can calculate how
likely an intrusion is, in the local episodes between the time intervals of
the intrusion distribution. For example, it is possible to predict how
much the local probability of intrusion increases or decreases quantitatively as the number of tasks increases based on the data obtained
during the work. This can limit or change the maximum speed of therobot to control the value of the probability of intrusion. In the process
designing stage, it is possible to predict changes in the likelihood of an
intrusion into the HRC system when the margin factors of the SSM
function are changed. It is preferable that the arrangement of the tasks
is set again if the robots are stopped frequently and the productivity islowered, even though human presence detection is performed and thetasks are arranged by calculating the PSD using the SSM in the conﬁguration step of the collaborative system. In addition, from an economic point of view, widening the distance between the robot and thehuman, reducing the speed of the robot, or reducing the payload could
possibly reduce the probability of intrusion, which can bring about
productivity beneﬁts.
However, design of the time interval and the application of the POI
also depends on the type of the collaborative task. If the task allows thehuman and the robot to interact continuously over a short distance, thetime interval can be kept low to calculate the frequency with which thework was performed without violating the PSD. In this case, setting alarger time interval may lead to a higher POI than necessary. However,if the worker frequently needs to leave the collaborative space, or if thework is done in a large layout, it is more desirable to calculate the POI
by generalizing the work time according to the categorized work, rather
than using a constant time interval.
In this study, the POI was calculated with the distance between thehuman operator’s hand and the end eﬀector of the robot, which has thewidest moving range in general. However, in reality, not only thehuman hand but also any part of the upper or lower body or any part of
the robot could be involved in a collision. For example, when an operator performs an operation of bending the upper body to inspect the
product, the head of the operator is positioned closer to the robot thanthe hand. Similarly, each joint of the robot may collide with the bodypart of the worker. The estimation method using the IT proposed in thisstudy can be improved by expanding the consideration to various
human body parts. Therefore, to eﬃciently make use of the POI, 3D
sensing technology is essential to the function of the SSM.

speed Ts which aﬀects the stopping distance of the robot Ss. Fig. 11 was
generated with the average experimental data of the ten subjects. Whenthe stopping time of the robot increased, the POI increased as well.
Once the margin factor of 170 mm was exceeded a very rapid increase
was observed. Finally, the simulation results based on the typicalparameters of the stopping time and the margin factor are shown in
Table 1.
6. Discussions
6.1. Application of speed and separation monitoring and limits
In comparison with the safety functions listed in ISO/TS 15066, SSM
function has a strong advantage as it can enable HRC while using
standard industrial robots [12]. For example, another collaborative
principle, Power and Force Limiting, requires robots capable of detecting human contact. In addition, it is diﬃcult to apply for tasks suchas using heavy payloads or sharp tools where contact between thehuman and the robot is not allowed. In this respect, there is no doubtthat SSM has a lot of potential in terms of application of collaborative
work requiring non-contact and utilization of existing resources.
However, robots designed with HRC in mind prefer the Power andForce Limiting function rather than the SSM function [10]. This may be
because there are few safety-related sensors that can utilize the SSM
functionality. Nevertheless, there are some constraints and applicationdiﬃculties when implementing the SSM function.
One critical limit of the SSM is that each term in the PSD calculation
is not easily deﬁned, and it is diﬃcult to choose the proper parametervalues [10]. Although the explanations of the coeﬃcients are provided
in the ISO/TS 15066, the options to select the appropriate parametersspeciﬁc to a situation depends heavily on the discretion of the safety
integrator. Consequently, an evaluation method for each parametermust be provided subsequently and it is necessary to grasp the continuous technology trend for the SSM function to be applied with easeto all the robots.
For instance, the margin factor M in the PSD is subordinate to theworkspace layout, which is not easily obtained speciﬁcally. The international standard, ISO 13,855 (”Safety of Machinery Positioning ofProtective Equipment with Respect to the Approach Speeds of Parts ofthe Human Body”) [21], suggests guidelines for human physical parameters, especially including the choice of the intrusion distance C andmaximum velocity of the human being. For example, the required intrusion distance C can be assumed as 850 mm maximum when the twodimensional sensors cannot detect the human hand continuously. In
this case, the robot should be separated by a distance greater than the
intrusion distance C, and the worst-case distance the human can travel
6

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Acknowledgment

6.3. Inﬂuence of the margin factor and the stopping time on the probabilityof intrusion

This study was conducted through “Knowledge Hub Aichi” project(Stage II - R6) which is ﬁnancially supported by the Aichi Science andTechnology Foundation.

The margin factor can be reduced by improving the performance ofthe safety-related sensor and increasing the measurable special dimension. This is because the measurement uncertainty can be reduced
when the performance of the sensor device increases and the intrusion
distance can be shortened when a 3-dimensional measurement is implemented. However, once the workspace is structured, the margin
factor is likely ﬁxed. Therefore, to construct the most eﬃcient working
environment it is important to know which variables are adjustable andwhich items are most eﬀective to modify the margin factor.
During the simulation, reducing the margin factor and the stopping
time can decrease the probability of intrusion. Increasing the margin
factor, can be interpreted as reducing the distance between the humanand the robot such that the diﬀerence between the PSD and an actual
separation distance is reduced. Therefore, it can be seen that theprobability of intrusion increases in the workspace of the robot when
the distance between the human and the robot is slightly reduced
through the simulation without actually changing the layout of thecooperative work.
With a high probability of intrusion, reducing the stopping time of
the robot does not signiﬁcantly decrease this tendency. This can be
expected in the situation where the robot uses various tools, such as
welding, drilling, moving, light, and heavy tools, and the change of theprobability of intrusion based on the stopping speed caused by inertia
diﬀerence. However, when the robot is light enough or does not use
heavy tools, it is more eﬀective to decrease the margin factor to reduce
the probability of intrusion.

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7. Conclusion
In this study, an experiment was conducted to investigate theProbability of Intrusion (POI) of a human hand into the Protective
Separation Distance (PSD) in Human and Robot Collaboration (HRC)with the Speed and Separation Monitoring (SSM) function presented in
the ISO/TS 15066. Throughout the presented experiment, Interference
Theory (IT) was used to analyze the results, and its application for SSMtype applications was proposed. In particular, it was experimentally
proven that if the time variable is considered in the IT, it is possible toprevent the POI of the human hand into the PSD from being overestimated.
In addition, to investigate the contribution of each component of the
PSD to the POI of the human hand, a simulation based on typicalparameters was executed. Consequently, it was shown that reducing the
POI of the human hand is possible by modifying parameters such as the
stopping time, the margin factors of the robot, and the safety-related
sensor system, which represents the intrusion distance and the measurement uncertainties. Therefore, when using the SSM, the POI can beused as an index to validate the productivity while meeting the requirement of the safety regulation of the SSM based on the parametersthat supplement to the PSD.

Conﬂict of interest
The authors declare no conﬂict of interest.

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