2021 International Conference on Computer, Control and Robotics

2021 International Conference on Computer, Control and Robotics (ICCCR) | 978-1-7281-9035-8/20/$31.00 ©2021 IEEE | DOI: 10.1109/ICCCR49711.2021.9349377

A Novel Safety-Oriented Control Strategy for Manipulators Based on the
Observation and Adjustment of the External Momentum

Jian Liu, Yoji Yamada, Yasuhiro Akiyama, Shogo Okamoto, Yumena Iki
Graduate School of Engineering
Nagoya University
Nagoya, Japane-mail: liu.jian@k.mbox.nagoya-u.ac.jp
Several control strategies were considered to show theeffectiveness and friendliness of humans in the pHRI
framework, such as either uncontrolled or controlled stop
(safe stop, hereafter) [6], active stiffness control, impedancecontrol, hybrid control. The safe stop is wildly used as a
general method for the motion/contact force limitation toguarantee the safety of pHRI [4] [7] [8]. The stop function istriggered when the measured or estimated external force
exceeds the predetermined threshold value. The external
force exists even after the manipulator stops; therefore, if thehuman body part is clamped by obstacles and themanipulator, it is difficult to escape from such a hazardous
situation. Active stiffness control [9] [10] is part of the
impedance control [11], which intends to make themanipulator softer in the pHRI task to generate a smaller
contact force. However, to adjust the contact force, themechanical properties of the human body part must be taken
into account when optimizing the stiffness parameter [12][13]. The hybrid control [14] [15] can realize different
control modes in one direction of a specified coordinate(generally, the Cartesian coordinate); therefore, for safety
considerations, the control mode switching from motion toforce control should be triggered when the contact force is
detected, which may result in reaction time and instability
problems. Other strategies focus on reducing the reference
torque input; for example, if a collision is detected, thetorque input will be changed into only a gravity compensator[16], which means that a collision occurs due to theremaining kinematic energy and the contact force forstopping the manipulator increases.
The foregoing post-contact control strategies require theinstruction of injury criteria, for example, the contact
velocity/force limitation [17] or transferred energy [18].
However, for the safety of pHRI, it is necessary to take into
account not only the contact velocity vc of the impactor but
also its mass because they are associated directly with theimpulse resulting in contact force. The momentum equals themass multiplied by the velocity or integral of the contact
force. It is expected to establish a bridge of motion and force
variables in the control strategy as well as for the parameterto comply with the injury criteria. The momentum injury
criterion Lindex can be obtained by a simple transformationfrom the accepted maximum transferred energy Eindex bytaking Lindex  2 Eindex vc . It is almost constant as shown in the

Abstract—Human safety assurance in physical human-robot
interactions (pHRIs) has become a challenge for current
robotic applications. Considering the safety assurance of a
pHRI validation experiment, the viscoelastic properties of ahuman body part were investigated in a previous study andwere added in a pHRI simulation. This study focuses on a
threshold momentum value as an injury criterion for
momentum control strategy design. A novel safety-oriented
control strategy is proposed, which consists of a conventional
proportional-derivative (PD) controller, an external
momentum observer-based compensator for monitoring theexternal momentum, and an adjustment loop for shaping the
trajectory motion command to bind the external momentum
within the injury criterion. The proposed control strategy canbe designed without needing to obtain the mechanicalproperties of the environment. The strategy can also be
combined with the related injury criterion. In addition, it
shows the effectiveness of ensuring safety even in the worst
pHRI clamping situation, where a human body part can escapefrom such a situation. Simulation results show that the
proposed control strategy performs well in the trajectory
tracking task, and the adjustment loop successfully shapes thepredetermined trajectory motion command to bind theexternal momentum within the injury criterion.
Keywords-control strategy; safety; human-robot interaction;
momentum injury criteria; viscoelasticity; in-vivo experimentI.

INTRODUCTION

As the application of robots extends to various fields,
there is a strong desire to remove the guiding fence
separating humans from robots [1]. Therefore, humans androbots must share the same physical environment, which
inevitably increases the possibility of the physical humanrobot interaction (pHRI) [2]. Ensuring human safety in thehuman-robot coexistence environment has been one of thecontrol issues for the past 20 years.
The pHRI can be divided into two types: free bumping
and clamping, in which the latter is the worst case andattracts more attention from researchers. The safety oriented
control strategies for this problem are divided into pre- andpost-contact safety strategies [3], and Yamada et al. [4] [5]first proposed a methodology for the latter, which can besummarized as establishing pain tolerances via humanexperiments and inserting such criteria into a control strategy
for limiting the motions of the manipulator.

978-1-7281-9035-8/21/$31.00 ©2021 IEEE80

result of the study [7]. Haddadin et al. [19] studied the injury
criterion associated with mass and velocity values obtained
through collision experiments, and Lindex was seen to be afunction of the velocity or the mass.
From the above consideration, this study aims toestablish a control strategy of a collaborative manipulator
taking into account the momentum as a directly adjustablesignal [20]. Sensors attached to the end effector are generally
used for force measurements and monitoring the contact
force. However, if the contact part of the manipulator is not
the end effector but some parts of the links of themanipulator, the mechanism to guarantee safety will lose
efficacy [21] [22]. Therefore, a second-order external
momentum observer is proposed for estimating andmonitoring the external momentum generated in contact.
The external momentum estimated by the second-orderobserver is fed to the main control loop to give zerocompliance to the entire control structure. Based on theobserver, an adjustment loop converts the momentum signal
into the motion signal for reshaping the motion trajectorycommand when the external momentum exceeds the injury
criterion in the pHRI. In this study, a novel safety-oriented
control strategy is proposed consisting of a conventional
proportional-derivative (PD) controller, an external
momentum observer-based compensator, and an adjustment
loop, with the following advantages:
 Operability of the injury-related variable: theexternal/contact momentum can be bounded in a
desired safe zone;
 Effectiveness for the worst case: The human bodypart can escape from the clamping situation;
 Intercommunity: It is common to all (if any) related
control strategies; It does not require any prior information about themechanical properties of the environment (thehuman body parts);
 Also friendly to such environments as rigid obstacles,
by which contact takes and achieved.
The reminder of this paper is organized as follows.
Section II introduces the mathematical model of the
proposed control strategy. Section III presents the in-vivo
experiment obtaining the viscoelasticity of the human upper
arm, and the simulation results regarding the operational
space control to demonstrate the effectiveness of the
proposed momentum adjustment method. The conclusion is
discussed in Section IV.
II.

A. Introduction of the Momentum Controller
The dynamic model of an n-DOF manipulator isexpressed by(1)
M  θ  θ + C  θ, θ  θ + G  θ  = τ
where M  θ  , C  θ, θ  nndenotes the inertia and the

Coriolis/Centripetal matrices, G  θ  nthe gravity vector,

the vector of joint variables, and τ  n the net
θtorque for operating the manipulator.
The traditional computed torque control in theoperational space for an n-DOF manipulator employs theinverse dynamic model for transforming a given command
motion trajectory of the operational space into that of thejoint space and a PD or proportional-integral-derivative (PID)
controller with an adjustment loop to compensate the
Coriolis/Centripetal term C θ, θ θ and the gravity termn G  θ  considering the linearization of the dynamic model (1)[24] or directly combining the command motion. The motion
trajectory of the operational space is input into the controllerloop by using the inverse of the Jacobian matrix [25].
Ohnishi et al. [23] proposed a momentum controller forthe operational-space motion tracking task, which can avoid
the calculation of the inverse of the Jacobian matrix J . The
reference torque signal for the manipulator is set asτ ref where

xref , x 

m



d T
J M  xref dt
dt
x = Jθ

(2)(3)
denotes the reference operational

acceleration signal and the actual velocity in operational
space, and m is the degree of freedom of the operational
space.
The momentum controller is shown in Fig. 1. The
reference signal xref is converted first into an operationalspace momentum Mx ref , joint-space momentum Mθref , andthen torque τ ref in sequence, which can also be classified as

the computed torque control. The controller C  s  can besimilar to a conventional controllers such as the PD or PID
controller,(4)
xref  K pex  K d ex  xd
e x  xd  xwhere K p , K d 

SAFETY-ORIENTED CONTROL STRATEGY

m m

(5)

denotes the gain matrices for the PD

controller, xd , x 
the operational-space command
motion trajectory of the end effector and the actual one.
m

The momentum controller proposed in the study [23]deals with the Cartesian force control of the manipulator forboth the stability at the singularity and the applicability in the
dynamic state. In this study on the safety-oriented control
strategy based on the momentum injury criteria, we foundthat the momentum controller is more suitable forinterpreting its mechanism and functionality, so themomentum controller dealing with the Cartesian motion is
introduced here as an element of our proposed safetyoriented control strategy.

Figure 1. Momentum controller.

81

Since the conversion from the operational-space
momentum into the joint-space one requires the transpose of
the Jacobian matrix J T but not the inverse of it J 1 , thiscontrol strategy performs well under the situation that the
manipulator passes through the singularity point and isconvenient for the controller loop calculation. On the other
hand, the momentum controller provides a more intuitive
way of obtaining the reference torque signal for commanding
the manipulator. This study employs a momentum controller
for the convenience of handling momentum signals andcombining them with momentum injury criteria.

a momentum controller, the reference signals contain amomentum signal, which provides a more convenient way.
A second-order observer is proposed as

B. Compensator for the Momentum Controller
A compensator is necessary for eliminating the gravity
and Coriolis/centrifugal terms as well as maintaining thestability of the PD controller.
The kinetic energy of an n-DOF manipulator is

Figure 2. Proposed safety-oriented control strategy for the operationalspace task.

11 θ T Mθ  x T Mx
22xˆ   xˆ dt  x  0

(14)

Lˆext  Fˆext dt  MK1  xdt(15)xˆ  xref  K 2 x  K1  xdt

(6)
m m

denotes the kinetic energy, and M 
iswhere the inertia matrix in the operational space.
Corresponding to Lagrange's formula, the dynamics inthe joint space of the manipulator is
d


Mθ 

 τ  τ ref  τ ext  τ dis
dt
θ θ





m m

where K 2 , K1 are positive definite gain matrices, andx  x  xˆ . Equations (13) to (15) are shown in the top rightpart of Fig. 2.
The relation between the estimated external momentum
and the actual one is1(16)Lˆ  K  s 2 I  sK  K  L(7)where τ ext denotes the torque corresponding to the external
force, τ dis the disturbance torque, the potential energy.

extNote that  θ  G  θ  , and    θ  J T    x  .
Introducing the Jacobian matrix to connect the joint andoperational space,(8)Mθ  J T Mx
(2), (7) and (8) can be combined as
J T Mxref  J T Mx  dt  dtθθ  τ ext dt   τ dis dt

1

2

1

ext

if K1 and K 2 are the diagonal matrices.
The error dynamics of the estimated external momentumisLext  s  sI  K 2   s 2 I  sK 2  K1  Lext
1

(17)

where Lext  Lext  Lˆ ext . The momentum estimation error
converges to zero for a constant external momentum. For aconstant external force, Lext  Fext s 2 leads the estimation(9)

error to converge to K 2 K11Fext . This requires the gain matrix
K1 to be as large as enough.

A compensator C ff can be proposed to eliminate theeffect of the terms in the right hand side of (9),
 G  θ   τ dis(10)θWhich can be added to τ ref . Consequently, (9) becomes

D. Adjustment loop
Unlike the active stiffness control [9], the estimatedexternal momentum Lˆ ext can be compared with the

C ff  

Mxref  Mx  J T  τ ext dt

(13)

(11)

momentum injury criteria Lindex . If Lˆ ext exceeds Lindex , anadjustment loop will be triggered to adjust the command
motion trajectory via the mass matrix M as follows:Lˆext  Lindex
0，(18)
xadj  1 ˆˆ  M Lext dt， Lext  Lindex
Equations (4), (5) are modified as follows:(19)
xref  K pex  K d ex  xd  xadj

Corresponding to the study [23], the Jacobian matrix J
can be regarded as a constant matrix in some cases of slow
movements, and (11) becomes(12)
Mxref  Mx   Fext dt
The compensator is shown at the bottom of Fig. 2.

C. External Momentum Observer
To estimate the external momentum, that is, the integralof the external force, a traditional way is to estimate theexternal force by utilizing observers or comparing the
response torque from (1) with the reference torque signal
from the controller, and taking integral operator. However, inex  xd  xadj  x(20)From (18) and (19), it is seen that the momentum
variable manipulated in the adjustment loop provides a moreintuitive and essential transformation between the force and82

motion variables. The adjustment loop can eliminate theexternal force because the integral of the external force ismanipulated within the injury criterion only if the external
force decreases to zero. On the other hand, the proposed
method does not require the mechanical properties of theenvironment.
III.

SIMULATION
Figure 4. Aerial view of the experimental apparatus.
30

Contact force (N)A. Viscoelasticity of Human Upper Arm
The viscoelasticity of the human upper arm wasestimated by human experiments and input in the simulation
to complete the pHRI task. Our previous study [26] focusedon modeling the viscoelasticity of the soft tissue on humanhands, inherited from which a nonlinear 5-element
viscoelastic model (Fig. 3(a)) is taken into account formodeling the mechanical property of the human upper arm.
The in-vivo experimental design is shown in Fig. 4. The
impactor was moved by the manipulator at a velocity of 250
mm/s to contact the human upper arm and stopped if thecompression displacement reached 32 mm. The maximum
compression displacement was carefully determined inadvance by communicating with human subjects byincreasing the compression displacement gradually until theyfelt uncomfortable. In addition, the safety device uses a
release mechanism to ensure the safety of human subjects.
The support plant for the human upper arm is fixed on a slideand is attracted by two magnets, so the upper arm can avoid
contact if the contact force exceeds the attractive force (100N according to the study [7]) provided by magnets. The
experiment was conducted with the approval of the Ethics
Committee of the Department of Engineering, Nagoya
University.

Experimantal result iExperimantal result ii
Experimantal result iii
Simulation result

25
20
15
10
5
0
0

2

4

6

8

10

Time (s)1214Figure 5. Comparison between the experimental and simulation results.

where xc yields the compression displacement, vc contact
velocity, t p peak value time, Fc contact force, k i and ci
stiffness of spring and damping ratio of the damper, as
shown in Fig. 3(a).
Note that k i has a nonlinear relationship with thecompression displacement xc . A coefficient  i is introduced
to describe the nonlinearity:(23)
k1   1 xc2
k2   2 xc3(24)

k3   x

3
3 c

(25)
With (21)-(25), a set of viscoelastic parameters is
obtained by curve fitting, as shown in Table I, and by using
the block diagram of the nonlinear model shown in Fig. 3(b),the simulation result is obtained and shown in Fig. 5. Thisnonlinear model is intended to be used in human-robot
contact simulation as a substitute for the human upper arm,and note that it is not to be applied for controller design.
(a)

TABLE I.

(b)

Figure 3. Nonlinear 5-element viscoelastic model and its block diagram.

The mathematicalviscoelastic model isexpression

vct ,
xc  
 vct p ,of0  t  tpt  tpthe5-element

VISCOELASTIC PARAMETERS OF THE HUMAN UPPER ARM

Parameters

1

2

3

c2

c3

Valuea3.11×10-4

3.27×10-6

1.48×10-5

0.39340.0415

N/mm3

Unit

(21)

k
3

 it 
k1vct   ci vc 1  e ci ,
0  t  tp



i2


(22)
Fc  
kk3
 i t p   i t t p 


ci
ci
e
, t  tp
k1vct p   ci vc 1  e

i2




N/(mm/s)a. Experimental condition: 32 mm compression displacement and 250 mm/s contact velocity.

TABLE II.

STRUCTURE PARAMETERS OF THE 2-DOF MANIPULATOR

Parameters

l1

l2

m1

m2

g

Value

0.160

0.210

1.580

0.970

9.807

Unit

m

m

kg

kg

m/s2

B. Parameter Settings for Simulation
Using the Simulink ○R simulation platform, a simple 2DOF manipulator was established, as shown in Fig. 6(a). The
structure parameters of this 2-DOF manipulator are shown in
Table II. In such a case, a conventional PD controller with agravity compensator performs well in a non-external force
environment [27].
In addition, the viscoelastic model of the human upperarm mentioned in section III-A was established in thesimulation by a linear joint attached to two mass units. The
viscoelastic parameters were set as shown in Table I, and the
distance between the contact surface of the viscoelastic
model and the base of the manipulator is set as 250 mm, as
shown in Fig. 6(b).

of motion where the manipulator is located at a singularity
point. In the contact period, the x-direction tracking error
remains small and does not converge to zero caused by the
PD controller with no integral terms eliminating the steadystate error. Nevertheless, the observed external momentum is
fed to the reference signal Mx ref as an external momentum
compensator. The steady-state error is then eliminatedwithout changing the estimated external momentum, as
shown in Fig. 7(d).
TABLE III.

MOTION COMMAND FOR THE 2-DOF MANIPULATOR

Name

Motiona

Time period

Motion I(M-I)( 0, -370) to (30, -298)

0 to1 sStop

1 to 3 s

Motion II(M-II)(30, -298) to (150, 0)

3 to 7 s

Stop

7 to 10 s

Motion III(M-III)(150, 0) to (282.4, 0)

250 mm/s

Stop and end

to 20 sa. Unit: mm.

(a)

(b)

Figure 6. Simulation models of the 2-DOF manipulator and upper arm.

For the differential operator in (2), a pseudo-differential
operator or a high-pass filter is used,(26)s  gc s  gc  s 

where gc  2  is the cutoff frequency.

The mass matrix M is calculated as (27) when the
manipulator is near the singularity,
1
0 0   JM 1J T    det JM 1J T   ,
0 1  M (27)
det JM 1J T   
1 T 1det JM 1J T     JM J  ,In the simulation, K p , K d , K1 and K 2 are set as

1600I 2 , 80I 2 , 400I 2 and 40I 2 , respectively, g c as 100, 

as 0.0645 and Lindex as 10 10 . I 2 is a 2-by-2 identify
matrix.
The motion commands for the robot are listed in Table
III. M-I is used to test the performance at the singularity
point and keep away from it, M-II for testing theperformance in the non-contact case, and M-III for the
impacting.
T

C. Discussion
The results of the simulation without the compensator are
shown in Fig. 7(a), from which it can be seen that the
manipulator performs well in tracking the command signal in
the non-contact period (0 to 10.4 s), even at the initial phase

Comparing the external momentum values in Fig. 7(b)with those in Fig. 7(e), the adjustment loop affects both theestimated external momentum Lˆ ext and the actual one Lext ,which are suppressed within the injury criterion Lindex , andthe external force Fext rises as shown in Fig. 7(f) whenLˆ ext  Lindex . However, it quickly decreases to 0 for satisfyingLˆ  L . The adjustment loop shows a good performance
ext

index

for limiting the external momentum and eliminating thecontact force in the pHRI task. Moreover, the design of theadjustment loops uses only the mass matrix of themanipulator that can be effortlessly obtained by numericalcomputation and does not have to model the mechanicalproperties of the environment (such as the human body part).
It can be inferred that, if the human body part is clamped in
the working environment between the end effector of themanipulator and some obstacles (e.g., work table), it canescape from such clamping situations by directly moving theend effect against the contact direction to enlarge thedistance between the end effector and the obstacle.
IV.

CONCLUSION

This study proposes a novel safety-oriented control
strategy consisting of a conventional PD controller, an
external momentum observer-based compensator, and an
adjustment loop. The proposed control strategy can be
designed without the necessity of obtaining the mechanicalproperties of the environment and can combine the related
injury variable. It effectively ensures the safety in theclamping situation since the momentum variable
manipulated by the adjustment loop processes more intuitionand essence of transform between force and motion variables.
The proposed control strategy was verified bysimulations of the worst-case scenario in which a 2-DOF

adjustment loop successfully reshaped the predeterminedtrajectory motion command to bind the external momentum
within the injury criterion. Therefore, it is inferred that thehuman body part can escape from the clamping situation.

External momentum (kg*m/s)

25

4
2
0
-2
-4
-6

x dir.
y dir.

-8
-10
0

2

4

6

8

10

12

14

16

18

20

80
Actual (x dir.)Estimated (x dir.)

60
40
20
0
2

4

4

x dir.
y dir.

2
0
-2
-4
-6
-8

-10
6

8

10

10
5

6

8

10

12

14

16

18

0

20

2

4

6

12

14

16

18

20

10

12

14

16

18

20

(c) w/o adjustment loop
25

20
Actual (x dir.)Estimated (x dir.)

15
10
5
0

Actual (x dir.)

20
15
10
5
0

-5
0

2

4

6

8

10

12

14

16

Time (s)Time (s)(d) w/ adjustment loop

8Time (s)(b) w/o adjustment loop
External momentum (kg*m/s)

Tracking error (mm)(a) w/o momentum compensator

4

15Time (s)62Actual (x dir.)

20

0
0

Time (s)0External force (N)100

6External force (N)Tracking error (mm)manipulator was operated to accomplish an operationalspace task while the human soft tissue was clamped. The
results showed that the observer-based compensator
performed well in the trajectory tracking task, and the(e) w/ adjustment loop

18

20

0

2

4

6

8

10

12

14

16

18

20

Time (s)(f) w/ adjustment loop

Figure 7. Simulation results.

ACKNOWLEDGMENT
This study was financially supported by “Knowledge
Hub Aichi” research project: R7 and conducted through“Construction of Risk Assessment System for Service Robot
Applications: Establishment of a V&V Testing Method”.
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