Proceedings of the 2018 IEEE International
Conference on Intelligence and Safety for Robotics
Shenyang, China, August 24-27, 2018

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Potential Runaway Motion Volume in Task Space for Estimating The
Probability of Occurrence of A Human-Robot Collision
Yoji Yamada1 Shunya Takeda2 Tomoya Nishiyama3 Shogo Okamoto1
in the collaborative environment of manufacturing under thefollowing requlation: It is known that there exist internationalsafety standards in which the and safety requirements quantitatively state the minimum protective separation distance(PSD, hereafter) [2] and further the safety distance taking
the relative motion vectors of both a robot and a humanapproaching to it as shown in the appendix of [3]. The
speed and separation monitoring formula specified in theabove standard is intensively discussed at a practical researchlevel in [4]. Further, applications are already reported bothin practice [5] and in simulation [6] where the speed andseparation monitoring techniques are assumed to be installed.
Among researchers, the primary interest of enhancing the
productivity while securing human safety is to discuss precollision avoidance control or motion planning with constraints in the research frame work of safety human robot
interaction which was categorized by [7]. It is seen that someresearchers try combining the safety preservation problem
with collision avoidance ones Their technical interests havebeen shifted, given a start and a terminal points in thepartially dynamical environments with obstacles, from creating a complete roadmap to dynamically avoiding obstacles
in real time: The former includes the introduction of adangerzone [8] for a generic obstacle avoidance objective,
which is extended to the safety problem with a proposal ofDanger Field [9] for solving the collision avoidance problem
faster. On the other hand, the latter is started by a proposalof introducing potential fields [10] which is historically
categorized as a problem of reactive motion planning. A
magnetic action of electric current serves as an obstacle fielddefinition called a circulatory field [12] which regulates apoint mass robot motion. Later, the circuitry field is applied
to the collision avoidance control of a manipulator[13].
The elastic strips [11] are cnstructed by candidate paths inwhich local potential field are applied again modifies the
trajectory. Modelling of obstacles is one of the main technicalclues to real-time collision avoidance control of a robot,
which directly affects to narrow the distance between the
robot and surrounding obstacles. Representation of obstacles
using circulatory fields is considered to be most effectivefrom the viewpoint of modelling the obstacles because themethod can geometrically reflect their profiles with highfidelity. Human psychological aspect is also promising to
reduce ineffectual space between a human and a robot. An
approach to making use of psychological reactions for path
planning is demonstrated in [14] which discusses how toassess the risk level to improve the safety of the humanrobot interaction and proposes the control algorithm for

Abstract— The paper deals with a critical safety issue on ahuman-robot coexistence system which is highly expected to be
introduced in such fields of manufacturing as cell productionlines. We discuss a method for quantitatively estimating theprobability of occurrence of a collision between a human anda fixed-type robot when it falls into a runaway state. We apply
the concept of dynamic manipulability ellipsoid to computethe potential runaway space of a robot. Then, we conduct a
psychological experiment in which each subject avoids abrupt
approaching motion of the end effector of the robot anddetermine the collision simulation parameters. Further, we show
an estimation procedure of protective separation distance taking
into account the avoidance action on the participants’ side. The
study contributes to obtaining the protective separation distancerequired for a robot to be separated from a worker. We finallyconfirm that the experimental results validate the separation
distance to converge.

I. INTRODUCTION
In the field of manufacturing, the robot safety accomplished development from an isolation technology symbolized by safety fences to collaborative operation technology
allowing the coexistence of industrial robots with workers
following a revision of ISO 10218-1 [1]. From a global
regulation trend, on the other hand, it has come to be possible
these days to determine the operating conditions of a robot
in the collaborative operation mode within the range of an
acceptable risk based upon the result of risk assessment. By
the systematic review of the standard harmonized in 2010
with the machine directive, a manufacturer is allowed toreasonably determine the speed of the robot in the collaborative operation mode under a certain level of technicalrequirements for a safety-related system based on a resultof the risk assessment.
The aim of the collaborative operation of a robot which
can coexist with a worker is to narrow the distance between
both, and thereby further saving of the work space aswell as the work time to enhance the productivity while
ensuring his/her safety．Based upon the change of regulation trend, researchers have discussed the optimality ofcollision avoidance between a human worker and a robot*The work was supported in part by KAKENHI Grant Number 2124604,
MEXT, Japan.
1 Yoji Yamada and 3 Shogo Okamoto are with Department of
Mechanical Systems Engineering, Graduate School of Engineering,
Nagoya University, Furo-cho, Chikusa-ku, Nagoya City 4648603,
Japan
yoji.yamada@mae.nagoya-u.ac.jp,

okamoto-shogo@mech.nagoya-u.ac.jp
2 Shunya Takeda is with Bridgestone Co., Ltd., 1-1, Kyobashi 3-chome,
Chuo-ku, Tokyo 104-8340, Japan
3 Tomoya Nishiyama is with Mitsubishi Electric Co., Ltd., 1, Hishimachi,
Inazawa CVity, Aichi Prefecture 492-8682, Japan

978-1-5386-5546-7/18/$31.00 ©2018 IEEE

34

B

II. POTENTIAL RUNAWAY MOTION VOLUME INTASK SPACE

t + DTp

A. Derivation of probability of occurrence of a collision in
the manipulator’s fault mode
Headt

The trajectory in Fig.1 is supposed to be taught to a robot
in advance for normal operation and the trajectory A-B is repeated in an operation cycle of Tp . A risk assessment reveals
first of all a potential consequence of a collision between
the robot end effector and the human head which, including
eyes, is considered to be one of the most hazardous partson human body and more likely to cause irreversible injury.
From a viewpoint of risk assessment to quantify, the next
demand should be to compute the probability of occurrenceof such a hazardous collision. There has never been any study
conducted on the derivation of this probability.
First, the probability that the human enters the workspaceand by mistake coming close in the vicinity of the robot’s
predetermined trajectory can be estimated statistically under
his/her routine task where the human enters the workspace
periodically. Let this probability be defined as PH (t). Humanerror analysis is well established to compute PH (t) eg. [5].
Then, the probability that the robot fails and runs off
the trajectory in the interval [t˜, t˜ + TP ) of its lifetime t˜ iscomputed [18] by introducing the failure rate of the safetyrelated robot control system as λ (t˜) TP since (λ (t˜) << 1)and therewith

EyeballA

End - effector

Fig. 1. How close a human can approach to a manipulator operated alonga pretaught trajectory A-B?

minimizing the estimated risk. A simulation technique called
extrapolation simulation is developed in [15] which showsthat the avoidable motion range varies depending on a robot
s approach speed and its initial distance from a humansubject based on a psychological experiment in which theend effector of a robot suddenly approaches to human eyesand studied human avoidance motion characteristics against
the approach [16]. However, there has been no report on
how much of volume on the manipulator side we shallprobabilistically estimate in 3D space at an instant. The PSD
criteria can apply only to the situations where a robot isnormally run and start shutting off only by decreasing the
speed from the break-down point. In other words, any fault
originating eg. in a sensor fault which may cause the erratic
sensor output [17] at the joint control level is not taken into
account even though it possibly leads to an instant runabway
state. This aspect is also indispensable to consider from theview point of probabilistically worst case scenario. To stressthe difference of the effect in the event of a fault specificallyin one of the joint torque controller parts, we discuss the
typical case where an industrial manipultor is operated alonga pre-taught trajectory from A to B as shown in Fig. 1.
The problem is how close a human can approach to the
manipulator. In the study, we develop a method for securing
a marginal volume called Potential RunAway Motion volume
in task space (PRAM-t) by which a human body part in thevicinity is distant enough from the end tip of the manipulator under such technical requirements for collaborative
operation of the manipulator that a single fault detection
capability be equipped with the manipulator [1]. We conduct
a psychological experiment in which each participant avoids
abrupt approaching motion of the end effector of the robot
supposing the robot goes to a runaway state to determine
the collision simulation parameters. Further, we show an
estimation procedure of protective separation distance taking
into account the avoidance action on the participants’ side.

F(t˜ + TP ) − F(t˜)
R (t˜)= 1 − e−λ (t˜)TP

(1)≈ λ (t˜)TP(2)

where R (t˜) and F (t˜) are the reliability and the unreliability
at time t˜ respectively.
R (t˜) = e−λ (t˜)t˜
F (t˜) = 1 − R (t˜)
The failure rate is time-dependent in general, but is considered to be constant in the normal life, which leads formula(2) to λ TP .
Further at this moment, the probability that the system
goes into a fault mode and the end-effector tip runs into
the human head is defined as PC|R (t). Such an event that ahuman enters the operational space of the robot, and the eventthat the robot comes into a fault and runs away to collidewith the human head are statistically independent of eachother. Therefore, the probability of occurrence of a collision
between the robot end-effector tip and the human head under
the supposed situation where he/she comes in the vicinity of
the robot trajectory and the robot runs off it is computed by
PC (t) = PH (t) × λ · ∆Tp × PC|R (t)(3)

Fig.1 also shows the time interval ∆Tp for which theprobability of the robot going into a fault mode is computed.
We will revisit this formula (3) later in Section IV for

35

1500

discussing the null probability of occurrence of the collision
event.

1200

B. Runaway motion due to a single fault
Speed [mm/s]

When a robot goes to a fault state at time t, it is consideredthat the robot end-effector tip traces along other path different
from the original one which has been taken in the normal
operation. We can assume that an industrial robot for the
manufacturing environment is required to have a single fault
tolerance i.e. a single fault shall be detected at or before thenext demand upon the safety function of making a protective
stop during the collaborative operation, which is a safety
requirement stated in ISO 10218-1 [1]. The self diagnosis
function of the safety-related control system can commanda protective stop on the robot by detecting any foreseeable
single fault in the system to lead it to the safe stop state
after a certain period of time, i.e. reaction time. Once therobot comes in a runaway state, it is uncertain how muchof angular speed the motor at each joint can exert andtherefore, the transient positioning of the robot end-effector
tip before the robot is led to a stop state becomes also
uncertain and is considered to construct an uncertain volume
after the robot end-effector tip goes out of the trajectorypredetermined for the normal operation of the robot. We
derive the formula representing the volume PRAM-t. Fig.
2 illustrates an ellipsoid volume PRAM-t to be estimatedalong the trajectory.

t = Tp

t =0

600

0
0

Fig. 3.

200

400
600
Time [ms]

800

1000

Speed patterns of the robot end effector during the experimentapDefinitions of the robot motion characteristics for computing
Fig. 4.
PRAM-tB

t + DTp

2000 mm/s. The absolute value of the maximum acceleration(a)(b)(deceleration) represented by either aR or aR defined inFig. 4 is set to be 9000 mm/s2 .
Each of the arm links is modeled by a cylinder with 60 mm
diameter, and the mass is approximately 5.0 kg. Substituting
the above parameter values into formula (9) in subsection
II-D and the formula (13) below which, with the parametricdefinitions in Fig. 3, allows us to compute the runaway
distance dp in the direction toward the human head.

Head

t

900

300

U (ti)
Potentialrun away motion
volume in task spaceof the manipulator
end effector tip

Pattern 1: Far
Pattern 2: Middle
Pattern 3: Near

EyeballA

End - effector
Fig. 2. Illustration of an ellipsoid volume PRAM-t to be estimated along
the trajectory(r)

dp = tR × vRmax −C. Parametric definitions of robot motion characteristics(vRmax − vRp )2
(a)
2aR

+

v2Rmax
(b)

(4)

aR

(r)

where vRp represents the speed at tR . On the other hand,
the human head is modeled by a sphere with 200 millimeter
diameter as shown in Fig. 5. Note that the human eyeballis also defined in the figure: Even though the probabilityof occurrence of collision with a human eye is small, theharm caused by the collision is irreversible i.e. the severity
is comparatively so high that we always take a stab of theeye into consideration.

Fig.4 shows the speed pattern of the robot end-effector tip
at the time when a protective stop is commanded to observe
the maximum change of the speed deceleration. 1(r)First, the reaction time which is defined as tR in Fig.
4 can be estimated through either technical specification orpractical experimentation. A safety PLC is assumed to be(r)
installed as the controller of the robot, and tR is assumed
to be 70 ms in the study. Taking the rated speed of HIRO(b)
into consideration, the maximum speed vR is set to be

D. Computation of potential runaway motion volume in task
space

1 We set the robot to output the same highest possible speed percentage
for each pattern. While the initial acceleration was similar to each other,
the maximum speed inevitably decreased as the travel distance decreased.

The first-order kinematic relationship between the joint
velocity vector q ≡ (q1 , · · · , qN )T ∈ RN and end effector

36considerably critical condition in terms of the closeness of
the range between each of the participants and the robot endeffector tip.
When the participant sits slouchingly, the initial distance
between the participant’s eyes and the robot’s end-effector tip
is shorter. Hence, the results of the previous psychologicalexperiments, which was reported in [16], suggest that theharm-avoidance action characteristics are contingent on theinitial distance between the human’s eyes and the endeffector tip. To investigate this dependence, psychological experiment was conducted with three different initial positionsof the end-effector. The experimental setup and conditions
are similar to those in the psychological experiment.
1) Participants: The nine participants in this experimentwere five males and four females aged ranging from 18 to 28.
Part of them participated also in the previous psychologicalexperiment. Each of the participant was asked to perform
a task of inserting bearings and retainers using a pair oftweezers in a container to assemble cross roller bearings. The
robot end effectors made of urethane form were mounted on
the two arms of the humanoid at the end effector, which were
supposed to be caught by the peripheral visual field of theparticipant.
2) Experimental Setup: Each participant was exposedto the working area of the robot and performed task ofpsychological experiment.
3) Experimental Conditions: In this experiment, statistically random foreperiods were determined by taking the sumof 10 s and an exponentially distributed random value witha mean of 15 s. Foreperiods longer than 60 s were excluded.
Fig. 6 shows a schematic diagram of the locations anddistances for this experiment. The bearing rings were locatedat the position indicated by the bold cross. Three patterns
were chosen for the initial positions of the end effector.
The initial distance between the participant’s eyes and an
end-effector tip was approximately 470, 370, and 270 mm
for patterns 1, 2, and 3, respectively. Each participant was
asked to confirm that the end-effector tips were in his or
her peripheral view when the tips were located at a viewing
angle of approximately 30◦ for all patterns with the task
position in the center of the visual field. In a trial, the endeffector tip arrived at a point approximately 50 mm forwardof the participant’s initial eye position at the end of the robot
motion.
4) Experimental Procedure: Each participant performed
60 trials, and the end-effector speed pattern and the approaching end-effector, either left or right, were both chosen at
random for each trial. HIRO, which is a product made inCo., Ltd. Kawada Industries, was used as the robot in theexperiment. This is an upper-body humanoid robot each of
the right and left arms having five joints (N = 5).

Eyeball Head

22
(not to scale)

200

z
y

Fig. 5.

x

unit [mm]Position relationship between an eyeball included in the headvelocity vector v ∈ R3 is expressed by
v (q) = J(q)q̇(5)

where J is the Jacobian matrix.
The dynamic manipulability ellipsoid is a set of acceleration vector which is realized by the set of joint torque vectorof a robot. Originally, the space volume satisfies ∥τ̃ ∥ ≤ 1.
However, in the context of our proposal,τ̃ (q) = (τ 1 (q) , . . . τ N (q))T(6)

where the i-th joint torque component, τ̃i , is normalized by
the rated value of the actuator installed at the corresponding
joint.

τ̃i (q) =τi (q)
τi max(7)

Let the inertia matrix of the robot be M(q) ∈ RN×N , wecan compute the acceleration of the robot end-effector.
−1ṽ˙ (q) = J(q)M̃ (q)τ̃ (q)

(8)

where
M̃ (q) = T M (q)
)
1
1
,...,
T = diagτ̃ 1 maxτ̃ N max

(9)

(

(10)

By use of the above acceleration ṽ˙ (q), we can compute
PRAM-t which will be shown later in section IV.
Furthermore, Nishiyama et al. monitored avoidance motion in the experimental situation where a worker erroneously intruded the work space of the robot at the wrong
time, and again, the robot end-effector tip approached theworker’s eyes. They reported that avoidance reaction time
also changed depending on the approach speed of the end
effector when the approaching robot was provided withdifferent acceleration patterns.
III. PSYCHOLOGICAL EXPERIMENTS
PRACTICALLY DETERMINING THE
PARAMETERS FOR COLLISION SIMULATION

IV. ESTIMATION OF PROTECTIVE SEPARATIONDISTANCE
Fig. 7 shows a sample of PRAM-t and a time change ofthe human head’s movement induced as an avoidance action.
The figure views the movements of both the space and the

We conducted a psychological experiment which wasapproved by the ethical committee in Nagoya University.
As is shown later, the experiment was conducted under a

37

320

330

50

140

y
O

170
Bearing

100

180

250

x
Pattern 3
Pattern 2

230

Pattern 1
End effector
Participant

110

280

155

t=200
Fig. 7.

O

x

Side viewFig. 6. Schematic diagram of the interactive human–robot locations during
the psychological experiment (unit: mm).
TABLE IR ESULTS OF THE SEPARATION DISTANCES

Average(Right)
Average(Left)
Average(Total)
Maximum(Total)

Participant A
[mm]
558.9
545.5
551.8
580

Participant B
[mm]
553.3
538.5
546.4
586

Participant C
[mm]
568.9
551.6
558.8
597

−1

(q) = Ud Σd Vd T

X pq = BX Hpq

B

B

XR

~
X pq 1 = BX pq
B~~
X pq i +1 = BX pq i +iSimulation with potential run
away space and human head

PC|R (t ) = 0 ?

No(t > 0)(11)

Yes

where Wh (t) is the volume of a part of the human head thatoverlaps with that of the PRAM-t on the robot side which isrepresented by U(t). U(t) is computed from the ellipsoid of
PRAM-t derived from the formula (12) using singular value
decomposition.
J(q)M̃

PRAM-t of the robot and a human headBhuman head in the O-xy coordinate plane defined in Fig.
6. They capture shortly before and after the PRAM-t andthe human head collides with each other, when PC|R (t) turns
to be PC|R (t) ̸= 0. We can compute the collision probability
PC|R (t) expressed by the following formula.
Wk (t)
PC|R (t) =
U(t)

t=300

in x direction to check whether PC|R (t) ̸= 0. It is assumed
that the variation of human avoidance reaction time against
a manipulator’s attack is small unless the change of the
distance between them is too large.
This process is algorithmically repeated until Wh (t) = 0.
The overall process is shown by the flowchart in Fig. 8. The
result of ∆ pq is added to the initial distance of 220mm in thex-axis direction.

z

1125

200

Top view

END
Fig. 8.

Calculation process for obtaining separation distance

X pq ≡B XHpq −B XR(13)X̃ pq =B X pq + ∆ pq + XS

(14)

B

(12)

and the ellipsoid is characterized by the lengths of σd1 , σd2 ,and σd3 in the directions of the principal axes ud1 , ud2 , andud3 .
The PRAM-t gradually approaches the human head as therobot travels, and the PRAM-t of the robot and the humanhead become overlapped with each other at t = 300, when
PC|R (t) ̸= 0.
To determine the minimal protective separation distance∆ pq defined in formula (14), a small quantity of ∆ is shiftedB

where XS is a safety factor to be taken into account if
necessary. We show in Table I the resultant separation
distance computed by (13) and (14).
V. DISCUSSIONSAs was introduced in section I, it was statistically shown in[16] the reaction time on the participant side depends on the38

initial distance between the robot end-effector and the humaneyes. If the resultant ∆ pq obtained by following the processdescribed in the previous section IV becomes so large thatthe avoidance action of the participants are different in termsof the distance, the initial separation distance may need to
be changed: While we conducted experiments at the initial
distance of either 220mm, 300mm, or 380mm, we focus on
the closest positional relationship between the robot and theparticipant in the paper.
Accepting that the number of the participants is small, it
is observed that the results do not provide a large variation in
BX
pq i.e. the data are not considered to be dependent on theinitial distance from the Table I. We can also observe thatthe variation in the data obtained for the three participants
is considerably small.
As was described in Table I, an avoidance action of theparticipant was observed in the transient states before andafter the collision. The amount of his/her moving backward,
without the simulated ∆ pq , was small enough to be counted asseveral centimeter at most. This means that it is indispensable
to allow any avoidance action taken by a participant during
such a psychological experiment from an ethical view point,
but we can say that the separation distance obtained throughthe experiment was considerably optimized that we do notcount the avoidance actions as a part of psychological effectin expectation of making the separation distance further
shorter.

ACKNOWLEDGMENT
This work was supported in part by MEXT KAKENHI
Grant Number 21246041.
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VI. CONCLUSIONSIn the study, we built a method for estimating the probability of occurrence of a collision between a human and afixed-type manipulator when it falls into a fault to generate
a runaway motion. We applied the concept of dynamic
manipulability ellipsoid to compute the potential runaway
motion volume of a robot in task space under the assumptionthat the safety-related control system is capable of detecting
a single fault to command a protective stop. Then, we
computed the minimum separation distance in such a manneras the probability of occurrence of a collision between arobot and a human goes to null who is in the vicinity of therobot s pre-taught trajectory even taking into account his/her
avoidance actions. For the three participants, the minimum
separation distance under the robot operation conditions of
9000 mm/s2 was obtained approximately as 550 mm. By useof the mathematical expression of dynamic manipulability,
the study specifies the amount of a runaway motion volume
in the worst case which was not clearly quantified in the conventional studies even though the same regulatory statement
vr is the directed speed in the direction of an operator isdefined in the formula of the protective separation distance.
It is necessary to collect more statistically abundant dataof experiments verifying how slow the robot speed in the
runaway state should be so that human reflective avoidance
motion surely contributes to narrowing the protective separation distance.

39