Journal of Robotics, Networking and Artificial Life
Vol. 5(3); December (2018), pp. 161–164
DOI: 10.2991/jrnal.2018.5.3.4; ISSN 2405-9021 print; 2352-6386 online
https://www.atlantis-press.com/journals/jrnal

Research Article

A Four-legged Robot’s Soft Feet Structural Design andWalking Gait Generated from Inverse Kinematics
Amornphun Phunopas1,*, Eiji Hayashi2
Department of Production Engineering, King Mongkut’s University of Technology North Bangkok, Bang Sue, Bangkok 10800, Thailand
Computer Science and Systems Engineering, Kyushu Institute of Technology, Iizuka, Fukuoka 820-0067, Japan1
2

ARTICLE INFOABSTRACT

Article History

The conventional wheel is famous in the industrial mobile robot because it is simple to build and easy to control and to maneuver.
On the other hand, the legged robot is complicated to control but has a high performance in locomotion like highly evolved
legged-creatures. This research describes the four-legged robot design platform with the soft feet, which are made by siliconematerial forming. The robot’s feet are implanted by the strain gauge sensor. The robot can percept the external force sensitively
when its feet touch something. The research demonstrates the forward kinematics and inverse kinematics of a four-legged robot
with three joints for each. The result has validated the kinematic equations by implementing them on the real dog-like pet robot.
The robot walked with a pure walking gait and showed a sensing signal from the soft foot and ground contact.

Received 25 July 2018
Accepted 12 November 2018
Keywords
Soft material robot
robot’s foot sensing
statics balance condition© 2018 The Authors. Published by Atlantis Press SARL.
This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

1. INTRODUCTION
The legged robot consumes more energy than wheel type robot.
The equation of motion of the legged robot is also complicated.
However, the legged robot has good maneuverability and mobility similar to revolute vertebrate animals with legs. The robot canperform mimicking from animal’s movement using a mathematical model or a trained behavior. The smooth floor is a primary
test that the robot can repeat its movement pattern when it walks
with stable balance control condition. Moreover, the robot hasto adapt its movement simultaneously on the stepping terrain ormulti-levels. In the high-level cognition in fast movement, thehuman has the experiences to plan its motion before moving forexample in a hurdle race. Elsewhere, the human can sometimes
focus on the smartphone while he is walking without paying
attention to everyday walking path. However, it is possible to
make an accident. For those views basically, the robot has to beable to sense when the feet contact the ground in every direction.
For the animal, the body is covered by skin which has a nerve cellto sense the impact force. The reviewed works use various methods regarding the sensors of the robot’s perception. The humanoid robot foot has an effective contact area of perception. Thus,
the sensor is a flexible force sensor array with the spatial rectangle
in Wu et al. [1]. The robot transfers weight to its foot while it iswalking under a dynamic equilibrium criterion or zero moment
point (ZMP). Next, a curvature sensor module can be embedded
into the soft-bodied robots in Ozel et al. [2]. The sensor type isan electro-mechanical sensor that is fabricated and merged intoa soft robot. For an application, a soft robotic grove has a soft
* Corresponding author. Email: amornphun.p@eng.kmutnb.ac.thfiber-reinforced actuator to sense the human hand movement as
a human interface device in Polygerinos et al. [3]. Another sensor
is a strain gauge, which is a skin-like, ultra-thin sensor. It canbe bent and used for prosthetic devices in Sencadas et al. [4].
There is a research about soft robotic fingertips that is a similar
idea to its use as a robot foot soft tip. The soft robotic fingertip
has a metal bar as a bone, a body, and a skin layer. The receptors
are strain gauges and PVDF films. The body is made of liquidsilicone rubber in Hosoda et al. [5]. The soft robot is a series
elastic actuator that interfaces with an environment. To control
the soft robot is designed with impedance-controlled compliant
actuators in Calanca and Fiorini [6]. For previous work of thisresearch in Phunopas and Suwichien [7], the robot has a plastics material for robot foot. This paper presents to test the robot
walking pattern with a defined static balanced condition and thesensing signals from the robot foot.

2. THE ROBOT STRUCTURES
The robot has four legs that have the same module for each leg.
It has three joints for shoulder, wing and, knee. It has 12 joints.
The robot size is approximately a small pet in 1 cubic-feet volume.
The robot weight is about 2 kg including mini PC and battery. Therobot body frame is made from ABS plastic as in Figure 1.

2.1. Robot’s Soft Foot Design
The robot feet are made from soft material which is implanted astrain gauge sensor inside to sense the impact force as in Figure 2.

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x+yq 1 = acos 	  − a (4)
 sign( A + B) ( A + B)2 + ( A − B)2  −2a a +1 2q 2 = acos 

4a12a22 − 4(a12 + C 2 )(a22 − C 2 )  (5)
2(a12 + C 2 ) z − a2 sin(q 2 ) − d0 q 3 = acos  (6)a3sin(q 2 )A = a3 cos(q 2 )cos (q 3 ) + a2 cos(q 2 ) + a1 (7)	 B = a3sin(q 3 ) (8)Figure 1 | (Left) A robot leg configuration. (Right) The robot structurewith four legsC=

(x 2 + y 2 + (z − d0 )2 − a12 + a22 − a32 ) (9)2(z − d0 )B − A

 A + B 	 a = a tan (10)where A, B, and C are derived coefficients.
The sequence of the robot walking gait and static balance configuration is generated in the walking gait pattern.

4. WALKING GAIT PATTERN

Figure 2 | The robot foot material is the end-effector of the robot leg or
the soft tip

From the sensor placement, it can sense on the vertical axial load
because of its weight pressing and distribute in various directions
along the axial load. However, it does not sense the torsional andbending load. A strain gauge sensor has an amplifier circuit which
sends the analog signal to the analog to digital converter.

The walking gait possibly has many patterns under the condition of a smooth floor with the ZMP area as a stability criterion.
Commonly, ZMP is used for dynamical walking, but in this case, itis to initiate some conditions to make the robot walk continuouslywith no falling head over heels or stumbling as in Figure 3. The
robot configurations are posed by kinematic equations to keep all
feet’s tip or the end-effector of the robot’s legs on the same planar
floor. The center of gravity is approximately in the ZMP area on thefloor plane. The robot’s body plane orientates itself around the XYZaxes, as shown in Figure 4.
The normal vector is created to define the robot’s body plane inEqs. (11–12). In Eq. (13), there are three rotations, roll, pitch, andyaw, for the X, Y, and Z axes respectively.

3. KINEMATICSThe summary of forward and inverse kinematics is used to control
the robot posture. The equation is individually applied to each leg.
First is the forward kinematics in Eqs. (1–3):
x = −a3 cosq 1cosq 2cosq 3 + a3sinq 1sinq 3 − a2cosq 1cosq 2 − a1cosq 1 (1)y = a3sinq 2cosq 3 + a2sinq 2 + d0(2)z = −a3 sinq 1cosq 2cosq 3 − a3cosq 1sinq 3 − a2sinq 1cosq 2 − a1sinq 1 (3)where a1, a2, a3 and d0 are link’s length parameters.
Second is inverse kinematics in Eqs. (4–6) that is the solved equations
from Eqs. (1–3) using the Harmonic Addition Theorem. The singularity condition is that q2 equals to 0° in case of dividing by zero in Eq. (6).

Figure 3 | The robot’s body plane can change its planar slope when­changing each leg’s height on the smooth floor

A. Phunopas and E. Hayashi / Journal of Robotics, Networking and Artificial Life 5(3) 161–164

 = ai+ bj + ck
 (11)	    N = a2 + b2 + c 2 (12)		    NR(roll, pitch, yaw ) = Rx (roll)R y (pitch)Rz (yaw ) (13)where a is the position of the normal vector on the X-axis, b is theposition of the normal vector on the Y-axis, and c is the position ofthe normal vector on the Z-axis.
The normal vector is perpendicular to the robot’s body plane. Thepoint of the normal vector represents the tilt plane and the transfer
CG position. The robot walks by lifting its legs one-by-one. Therefore,
when the other three legs are on the floor, the CG will transfer theZMP area to the floor area contacted by the three feet. The normalvector will move along the diagonal axis 1 from point P2 to P4 andalong diagonal axis 2 from point P1 to P3, as shown in Figure 5.

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the software that support the robot system. The computer sends
a command to the robot by writing the motor’s trajectory. The
strain gauge sensor amplifier is the differential bridge operational
amplifier circuit with gain adjustment. The output analog voltage
is 0–3.5 V, which is compatible to the analog input of the general
microcontroller.

5. RESULTThe first experiment showed the signal from a robot foot in Figure 7
when it contacted the floor in the axial load. Similarly, the four legs
have the same result because it has the same structure.
In the second experiment, the robot walks applying the designed
walking gait. The walking gait is generated from kinematic equations. For every walking step, one leg paces and the remaining threelegs are on the floor, as in Tables 1 and 2.

4.1. Control System
The robot has a strain gauge sensor inside each foot, which has
the job of detecting the floor contact. The control system integrates
the information on the angle of every joint and the end-effector
positions. It can compute the robot configurations under the ZMP
method when the robot’s feet contact the floor. Respectively to thewalking-gait pattern, the robot walks in a sequence, sensing thefloor contact simultaneously. Figure 6 shows the hardware andFigure 6 | The soft tip foot of each leg can sense the floor contact signal.
Moreover, the computer reads the signals of the floor-contact detection

Figure 4 | The defined normal vector of the robot’s body plane has threeorientations: roll, pitch, and yaw

Figure 7 | A soft robot foot contacted the floor. The analog voltage signal
is measured by oscilloscope
Table 1 | One pace of the front left leg and the relative joint angles (°) of all legstFigure 5 | From the top view, the point of the normal vector moves in theunit circle of the normal vector area

0123

Front left leg

Rear right leg Front right leg

Rear left leg

q1q2q3q1q2q3q1q2q3q1q2q3

20
20
18
18−5−5−5−655
55
70
79−20
−19−19−20−5−5−5−5−55−64−64−55−20−20−20−20

5555−55
−55
−55
−55

20
20
20
20

555555555555

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164

Table 2 | One pace of the front left leg and the relative foot tip XZ-positions (mm) of all legs
Front left leg

Rear right leg

Front right leg

Rear left legxzxzxzxz−103.57−103.57−87.86−76.01−103.07−103.07−102.65−103.07−103.57−103.57−103.57−103.57−103.07−93.07−93.07−103.07−103.57−103.57−103.57−103.57−103.07−103.07−103.07−103.07−103.57−103.57−103.57−103.57−103.07−103.07−103.07−103.07t012
3

6. DISCUSSION

REFERENCES

The soft material is made of silicone. A hardness level is a maximum number, but it is still too soft to take the robot weight.
Consequently, the soft robot foot is immoderately deformed its
shape. The strain gauge sensor is very fragile and easy to be broken.
Due to the robot moves dynamically, CG, inertia and external force
affect the system. The walking stability constraint is very complicated to maintain its balance when the robot walks.

[1] B. Wu, Z. Wang, J. Luo, Z. Wu, Perception of effective contact area
distribution for humanoid robot foot, Measurement 46 (2013),
2093–2098.
[2] S. Ozel, N.A. Keskin, D. Khea, C.D. Onal, A precise embedded
curvature sensor module for soft-bodied robots, Sens. Actuators A236 (2015), 349–356.
[3] P. Polygerinos, Z. Wang, K.C. Galloway, R.J. Wood, C.J. Walsh,
Soft robotic glove for combined assistance and at-home rehabilitation, Robot. Auton. Syst. 73 (2015), 135–143.
[4] V. Sencadas, R. Mutlu, G. Alici, Large area and ultra-thin compliant strain sensors for prosthetic devices, Sens. Actuators A 266(2017), 56–64.
[5] K. Hosoda, Y. Tada, M. Asada, Anthropomorphic robotic softfingertip with randomly distributed receptors, Robot. Auton.
Syst. 54 (2006), 104–109.
[6] A. Calanca, P. Fiorini, Impedance control of series elastic actuators based on well-defined force dynamics, Robot. Auton. Syst. 96(2017), 81–92.
[7] A. Phunopas, N. Suwichien, Kinematic Analysis and Trajectoryof a Dog-like Robot, The 8th TSME International Conference on
Mechanical Engineering, 2017, pp. 454–464.

7. CONCLUSION
The robot can walk and sense the floor contact from the soft footusing the implanted strain gauge sensor. The foot tip position andtrajectory can independently be designed depending on the solved
kinematic equations coherently. However, the walking gait in thefixed pattern is very difficult to define the stability state. It had
better apply the control law or soft computation for robot control.

ACKNOWLEDGMENT
King Mongkut’s University of Technology North Bangkok andKyushu Institute of Technology have supported this research.

Authors Introduction
Dr. Amornphun Phunopas
He graduated Doctor course
at Department of Mechanical
Information Science and Technology
in Kyushu Institute of Technology.
He is a lecturer in the Departmentof Production Engineering at King
Mongkut’s University of Technology
North Bangkok.

Dr. Eiji Hayashi
He graduated Doctor course atDivision of Science and Engineeringin Waseda University. He is a Professor
in the Faculty of Computer Scienceand Systems Engineering in Kyushu
Institute of Technology.