Proceedings of the 2021 IEEE International
Conference on Intelligence and Safety for Robotics
Nagoya, Japan, March 4-6, 2021

Proposal of Fail-Safe Contact Motion Control and its Simulation using
CRANE-X7
Hiroki Kito, Yoji Yamada, Jian Liu, Yasuhiro Akiyama and Shogo Okamoto
Abstract— Currently, human-robot collaboration has attracted remarkable interest among researchers. It is being
considered for application in the ﬁeld of manufacturing andan attention of a new risk regarding runaway motion on the
robot side has been paid by our group. For example, if the robot
runs away owing to a single fault, the robot and the worker
may collide. Therefore, the runaway motions of robots need to
be examined. We focus on not only a joint running away but
also other active joints. If we can control them and reduce theamount of collision impact, a safe operation can be achieved
at a fully secured level. Thus, we propose a fail-safe contact
motion control and simulate its usefulness using CRANE-X7.

stopping. Based on this, we extend the concept of PRAM-t
and propose fail-safe contact motion control (FSCMC) as asafety strategy that may further improve the productivity ofthe system. The goal is to maintain human contact motion ina fail-safe manner at a fully secured level, which means thateven in highly unlikely runaway conditions of manipulators,
the risk of contact can be avoided. In this paper, the concept
of FSCMC is proposed, and the practicality of FSCMC isevaluated by simulating a collision between a manipulator
and a dummy skin.

I. I NTRODUCTION

II. FAIL - SAFE CONTACT MOTION CONTROLWith the recent introduction of human-robot collaboration,
there has been much debate on the new associated risks. The
protective separation distance (PSD), which quantiﬁes theminimum distance of separation for protection, [1] is deﬁned
as an international standard, and a considerable amount ofresearch has been conducted on the practical application of
speed separation monitoring (SSM), which is a requirement
for the use of the PSD. There have been various studies on
different topics [2] [3], including the introduction of SSM
prototypes [4] safety and productivity evaluation of SSM[5], and implementation of SSM in a collaborative robot
work cell [6]. Some studies have complemented PSD [7][8], and some have examined avoidance behavior [9] [10][10] Moreover, many researchers have debated about safety
based on whether or not contact between robots and humans
is allowed. Suita and Yamada et al. proposed the use ofhuman somatic pain as a criterion for acceptability [11][12] [13]. Other studies have proposed deformation tolerance
limits [14], the correlation between pain and energy [15],and impact experiments using surrogate animal skin [16][17]. In addition, according to the ISO 10218-1 standard[1] [18], the safety of workers must be ensured even in
the event of a single failure in a safety-related system, andfault detection algorithms have been actively researched [19][20] [21]. Here, we consider a case in which a single failure
occurs in a robot. The worst case would be the maximizationof one of the joint torques of the robot owing to a single
failure. Yamada et al. [22] deﬁned the space in which a robot
can move in the event of a runaway situation up to the timeof emergency stop as the potential runaway space of theworkspace representation (PRAM-t). It was used to estimate
the space in which the manipulator could move before

In this chapter, we propose fail-safe contact motion control(FSCMC) as an attempt to reduce the risk of collision byusing a sound joint when the joint of a manipulator runs outof control and contacts the human body.
A. Dynamics of manipulator
The dynamic properties of the manipulator are shown
below.
M (q)q̈ + C(q, q̇) + g(q) = τ − J T f

where q ∈ Rn is the vector of the joint angle, M (q) is
the inertia matrix, C(q, q̇) ∈ Rn is the term for centrifugal
and Coriolis forces, g(q) ∈ Rn is the term for gravity, andf ∈ Rm is the external force applied to the end-effector.
However, if x ∈ Rn is the vector of the position of the endeffector, and J (q) ∈ Rm×n is the Jacobian, the following
equation is obtained:ẍ = JM −1 (τ − C(q, q̇) − G(q)) + J˙ (q)q̇ − JM −1 J T f(2)
The human body is then divided into a ﬁve-element
matrix with viscoelastic parameters, as shown in Fig.
3. Considering the Maxwell model and deﬁning theparametersk1 , k2 , k3 , c2 , c3 , displacement xh , xh2 , xh3 andforce fr , we obtain the following three equations: fr = k1 xh + k2 x2h + k3 x3h
k2 x2h = c2 (ẋh − ẋ2h )
k3 x3h = c3 (ẋh − ẋ3h )(3)Let the unit for indicating the direction of danger be thevector h ∈ R3 , and f be represented by
f = fr h.

All are with the Department of Mechanical Systems Engineering, Nagoya
University, Nagoya, Japan.

978-0-7381-4674-4/21/$31.00 ©2021 IEEE

(1)

161

We deﬁne u ∈ R3 as follows:(4)u = J M −1 (τ − C(q, q̇) − G(q)) + J˙ (q)q̇(5)

And Eq. 2 becomes like following;ẍ = −JM −1 J T uh f r + u(6)Taking the inner product of both sides of the above
equation and h, and substituting fr , the following equation
is obtained:ẍh = −Mh (k1 x + k2 x2h + k3 x3h ) + uh

Fig. 1.

The dummy skin

(7)

With ẍh = hT ẍ, Mh = hT JM −1 J T h, uh = hT u,
let the Laplace-transformed xh ，x2h ，x3h , and uh be Xh ，
X2h ，X3h , and Uh , respectively. By Laplace-transforming
the equations and eliminatingX2h and X3h , we obtainsk3 c3sk2 c2+)Xh + Uh (8)s Xh = −Mh (k1 +k2 + sc2
k3 + sc3
Let U be the input and Xh be the output. Transfer function
G is obtained for the system. Then, based on G, we obtain astate-space model with an input of uh and an output of xh .

Fig. 2.

The impact experimental apparatus

2

B. Running away part
This section deals with the orbit calculation of the endeffector in the runaway part. As an example, consider thecase in which the i-th joint generates a positive torque on
the z-axis of rotation. Let’s deﬁne the max torque of eachjoint as τimax (i = 1, ..., n). The torque vector where thei-th component is τimax and the other components are zerois τi+ , and the torque vector where the i-th component is−τimax and the other components are zero is を τi− . Then,the input is expressed as
uh = hT [JM −1 (τi+ − C(q, q̇) − G(q)) + J˙ (q)q̇] (9)By solving the aforementioned state-space model under
initial conditions, we can obtain the trajectory of the endeffector.
C. Braking part
This section deals with the calculation of the trajectory of
the end-effector in the brake part. As in the previous section,
consider the case where the i-th joint generates a positive
torque on the z-axis to the axis of rotation. Here, we deﬁneτˆj (j = 1, ..., n) as follows:IfhT · JM −1 τj+ ≦ 0, τj = τj+elsetauj = {τj−(10)Then, we deﬁne the torque produced by the braking of thefailed joint and the control of the healthy joint as follows:
τib = (n∑τj ) − τi + τi−(11)

If the reaction time of the system is tr , then the constraintof the state-space model in the brake part is that for t = tr ,moreover, the state variable is the same as the state variablein the runaway part. By solving this state-space model under
the constraints, we can obtain the trajectories of the endeffector. We also deﬁne the stopping time, ts , as the time
when ẋh (ts ) = 0.
III. I MPACT EXPERIMENT
A. Impact experiment using dummy skinIn this study, we assume contact between a dummy skinand a manipulator, which reproduces the characteristics ofhuman skin. Therefore, to represent the dummy skin [23]in the aforementioned ﬁve-element Maxwell model, impact
experiments were conducted to identify the parameters ofthe model. A manipulator with a 14 mm square impactor
attached to an end-effector was used for the impact experiments. The stability forces were set at 5, 10, 15 N, and thecontact speed was set at 250 mm/s. The experiments wererepeated three times under different conditions.
B. Curve ﬁtting
By deﬁning the ﬁve-element Maxwell model, as shown in
the Fig. 3, we obtain the following equation:
{
x=

vt
vtp

(0 ≤ t < tp )(tp ≤ t)
k1 vt + c2 v[1 − exp(− kc22 t)]





(0 ≤ t < tp )+c3 v[1 − exp(− kc33 t)] k1vt + c v[1 − exp(−
k2
t
)]
p
2
c2 p
F =
(14)
 exp[− kc22 (t − tp )]
 +c3 v[1 − exp(− kc 3 tp )]3
exp[− kc33 (t − tp )](tp ≤ t)j=1

Fs = k1 x(tp )Then, the input can be deﬁned as follows:uh = hT [JM −1 (τib − C(q, q̇) − G(q)) + J˙ (q)q̇] (12)

(13)

(15)

where x is the displacement, v is the contact velocity, F
is the contact force, Fs is the stable contact force, and tp

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Fig. 3.

5-element Maxwell modelFig. 5.

Fig. 6.
Fig. 4. Results of the impact experiments and curve ﬁtting (from the top
to bottom, stable force is 5 N, 10 N, 15 N)

is the peak value timing (or stop timing). Curve ﬁtting was
performed using these equations to optimize the viscoelastic
parameters.
C. Result of curve ﬁtting
The results of the curve ﬁtting are presented in Fig. 4.
The average value of the parameters obtained for each trial
was used as the viscoelasticity parameter in the simulation.
Table 1 shows the result of estimating the parameters of the
5-element Maxwell model for the dummy skin.
IV. S IMULATION OF FSCMC
A. Condition of simulation
This section presents the simulations for evaluating the
FSCMC. In this study, we focus on the CRANE-X7, amanipulator with three degrees of freedom by ﬁxing 1,3,5
and 7 joints which are deﬁned in Fig.5. We compare the
combination of stopping only by braking without active
joints and speed reduction via braking with active joints.
The positional relationship between the manipulator and thedummy skin is shown in Fig. 6. It is assumed that the dummyskin is pressed against the workbench with a set initial
velocity. The initial velocity is changed between 0 mm/s and
100 mm/s. And the reaction time of the system is deﬁned
as tr = 50 ms. In this time of simulation, each normallyoperating joint rotates in the opposite direction to that where
the robot moves to cause more hazardous situation.
B. Result of simulation
A part of the simulation results are shown in Fig. 7
through Fig. 9. In each graph, the horizontal axis is time

CRANE-X7

The condition of the simulationand the vertical axis is contact displacement of end-effector,
and a legend is shown in the Fig. 7. The results show thatthe contact depth can be reduced by up to 1mm by using
FSCMC.
C. Discussion
If there is a risk of robot-human contact, risk assessment
shall take into account the severity of the risk and theprobability of occurance of thebcontact. We have shownthat the proposed FSCMC could reduce the severity of risk
associated with injuries caused by such a contact. In thecase where a contact is quasi-static (contact speed is nearly
0mm/s), the displacement curve appears convex during the
runaway phase while the curve is drawn concave in the casewhere the contact speed is 100mm/s. With the proposed
FSCMC incorporated, it is revealed to cause harmless eventsin the case of the quasi-static contact while harmful events
can be anticipated in the situation of completely clamping ahuman hand. To what extent of speed can avoid any harmful
event can become a novel criterion of HRC in contact tasks.
V. C ONCLUSION
A fail-safe contact safety control (FSCMC) is proposed toreduce the contact risk of a human and a robot by making
the most of healthy joints that can be controlled when asingle failure occurs in a joint. The concept of fail-safe
contact safety control is formulated and a method is proposedto generate torque to reduce contact risk using an active
joint. Impact experiments were conducted to identify theviscoelastic parameters for a ﬁve-element Maxwell modelof a dummy skin. Using simulations on CRANE-X7, theusefulness of FSCMC was investigated and it was shownthat the displacement of end-effector can be reduced by up to
1 mm in the case where the contact speed is 100mm/s. These

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TABLE IO PTIMIZED PARAMETERS OF THE 5- ELEMENT M AXWELL MODEL FOR THE DUMMY SKIN
Force (N )51015Mean value

k1(N/mm)
0.36520.38650.41430.3869k2(N/mm)
0.13590.19440.24670.1923k3(N/mm)
0.041540.04928
0.066810.05254

results show that the method can possibly avoid serious
accidents during a runaway caused by a single failure ofa manipulator.
VI. ACKNOWLEDGE
This paper was ﬁnancially supported by ”Knowkedge
Hub Aichi” research project: R7 and conducted through”Construction of Risk Assessment System for Service Robot
Applications: Establishment of A V and V Testing Method.”This paper is also ﬁnancially supported by Kakenhi (Grant
20H02114: A novel strategy for safety control of a manipulator with a single fault detection capability to mitigate theseverity of injury during a contact between the end effectorof the manipulator and human skin under the worst case
impact scenario.

Fig. 7.

Simulated result (Conﬁg. I, 0 mm/s,left=w/o AJ, right=w/ AJ)

Fig. 8.

Simulated result (Conﬁg. I, 50 mm/s,left=w/o AJ, right=w/ AJ)

Fig. 9.

Simulated result (Conﬁg. I, 100 mm/s,left=w/o AJ, right=w/ AJ)

c2(N/(mm/s))
0.02470.03037
0.038140.03107c3(N/(mm/s))
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