1. INTRODUCTION

Legged robots can move on various terrain because they have legs and utilize their several degrees of freedom. They are controlled by planning their motion based on a strict model of a robot and an environment. However, planning their motion based on a strict model for various environments is quite complex, and inefficient to move various terrains at high speed.

To overcome this problem, Central Pattern Generators (CPGs) can be used. The mechanism of the CPG is related to rhythmical movements such as walking and swimming [1,2]. The CPG, an animal motion generation method, enables the motion of legged robots on various terrain using only one algorithm because of a pull-in phenomenon.

Because of the above advantages, CPGs have been used in robots in several studies. Kimura et al. implemented the CPG on a real robot. The robot “Patrush” can walk [3] and “Tekken4” can turn [4] on rough terrain. The turning motion is realized by controlling the hip yaw joint. However, the vibrations of the robot body are large because falling phenomenon in the roll direction occurred.

In the case of teleoperation of a legged robot, an operator controls a robot while watching the images from a camera mounted on the robot. Therefore, the image vibration should be small for the operator to understand the surroundings of the robot. In the experiment conducted by Kimura et al. [4], the robot experiences vibration in the roll direction. Figure 1^a shows the graph of the posture of the main body (the roll and pitch direction) when turning on a flat ground [4]. According to the body roll angle (thick black line) in the graph, the robot vibrates, and it is finally overturned.

Figure 1

Tekken body angle in turning on flat land [4^a].

In the method proposed by Kimura et al., the camera image will vibrate so that teleoperation will be difficult. According to the study conducted by Tsubaki et al. [5], if the frequency of the image vibration is the same, a larger amplitude makes the operator uncomfortable. Therefore, in teleoperation, the image vibration should be small. Figure 2^b illustrates a graph showing the relation between the subjective evaluation and the rotation angle for motion sickness [6]. Vibration in the roll direction is most likely to cause motion sickness at any speed of rotation.

Figure 2

Subjective evaluation value of motion sickness with respect to speed of rotation when rotation relative to yaw, pitch, and roll axis is given in video [6^b].

The vibration of the robot body causes discomfort to the operator. There are many researches of robots installed CPG [7–9] without considering suppression of roll direction vibration. On the other hand, we found a research about suppression of quadruped robot body vibration [10]. However, the research did not consider of vibration during turning. Therefore, the purpose of this study is to suppress roll vibration in a legged robot during turning. To suppress roll vibration, we proposed a turning method using the asymmetric amplification of the CPG output waveform. In this study, we verified the effectiveness of the proposed method comparing with the previous method [4], that uses the yaw hip joint for turning, by carrying out an experiment using a dynamic simulator.

2. WALKING ON FLAT GROUND USING CPG

2.1. Nonlinear First-order Simultaneous Differential Equations Constituting CPG

The basic formula of the CPG is a nonlinear first-order simultaneous differential equation shown in Equations (1)–(3) [3].

(1)τu˙i=− ui−βvi+∑j=1nwijyj+u0+Feedi

(2)τ′v˙i=− vi+yi

(3)yi=max(0,ui)

u_i, v_i, and y_i are the value, fatigue state, and output of the i-th neuron, respectively, u₀ is the steady input that generates oscillation, Feed_i is the feedback such as the joint angle, β is the fatigue state factor, τ and τ′ are the time constants of u_i and v_i, respectively, and w_ij is the connection factor that determines the influence of the other neurons. A pair of CPGs was mounted on each joint, and four equations were formed corresponding to each leg. This method is based on the biped walking program [11] of the CPG where the connection factor is defined as follows:

• w₁ - Between the extensor and flexor of the same joint.

• w₂ - Between the right and left of the same extensor and flexor.

• w₃ - Between the knee and hip joints of the extensor.

• w₄ - Between the knee and hip joints of the flexor.

• w₅ - Others.

Figure 3 shows the proposed CPG configuration. We generated a waveform for walking by multiplying the different amplification gain by the output value of the CPGs of each joint. The walking waveform is given by Equation (4).

(4)θjoint=Kjoint(yE−yF)

θ_joint is the target angle of the joint, K_joint is the amplification gain at the joint, y_E and y_F are the CPG output values of the extensor and flexor, respectively.

Figure 3

Proposed CPG configuration.

2.2. Robot for Experiment

A robot, which is used in the experiment, is shown in Figure 4. We developed the robot using an open-source dynamic simulator, named “Gazebo”. The CPG parameters are listed in Table 1.

Figure 4

A robot in simulator.

Parameter	Value	Parameter	Value
u0	3.0	w1	−2.0
β	2.5	w2	−1.0
τ	0.10	w3	−0.50
τ′	0.080	w4	−0.30
		w5	0

Table 1

CPG parameters

3. TURNING MOVEMENT

4. VERIFICATION EXPERIMENT

4.2. Results and Discussion

Figures 5 and 6 show the graph of the robot posture when turning in orbit shown as Figure 7. The peak-to-peak value of the roll angle in the conventional method is −0.2 to 0.15 [rad] and that in the proposed method is −0.1 to 0.1 [rad].

Figure 5

Robot body roll angle.

Figure 6

Robot body pitch angle.

Figure 7

Orbit of robot turning.

In this study, we compared the conventional and proposed methods. As shown in Figure 5, the vibration in the roll direction could be suppressed. By comparing the maximum peak-to-peak value of both methods, we observed that the proposed method is able to suppress 43.7% vibration in the roll direction. Moreover, the proposed method suppressed 7.4% vibration in the pitch direction compared with the conventional method. We consider that the reason is the suppression of vibration around the falling axis. Moreover, motion sickness can be reduced because the vibration in the roll direction can be suppressed.

5. CONCLUSIONS AND FUTURE WORK

The purpose of this study is to suppress roll vibration in the turning motion of a legged robot. We suggest a turning method that changes the amplification factor of the joint angle between the left and right legs to suppress the robot body vibration. We verified the effectiveness of the proposed method using a dynamic simulator compared with the conventional method. As a result, we observed that the proposed method can suppress 43.7% vibration in the roll direction and 7.4% in the pitch direction. The proposed method will reduce the motion sickness caused by the image vibration during teleoperation. In the future, we will realize walking of legged robots on rough terrain by installing CPG feedback.

CONFLICTS OF INTEREST

The authors declare they have no conflicts of interest.

Authors Introduction

Mr. Makoto Kitani

He received Master of Engineering degree from Nagoya Institute of Technology in 2019. His research interests include autonomous control system, system integration and teleoperation system for legged rescue robots.

Mr. Ryo Asami

He received Master of Engineering degree from Nagoya Institute of Technology in 2018. His research interests include virtual reality, system integration and teleoperation system for crawler-type rescue robots.

Dr. Noritaka Sato

He received Doctor of Engineering degree from The University of Electro-Communications in 2009. He was a Program-Specific Assistant Professor of Kyoto University in 2009–2011, and is an Assistant Professor of Nagoya Institute of Technology since 2011. His research interests include human robot interaction for rescue robots, rehabilitation-assist robots and industrial robots. He is a member of the IEEE, RSJ and SICE.

Prof. Yoshifumi Morita

He is a Professor in the Department of Electrical and Mechanical Engineering at Nagoya Institute of Technology. He received the PhD degree from Nagoya Institute of Technology in 1998. His current research interests are rehabilitation support robot/device and robot teaching.

Dr. Tomofumi Fujiwara

He received his B.S., M.S., and PhD degrees in Engineering from Okayama University, Japan, in 2010, 2012, and 2016, respectively. From 2014 to 2015, he was a guest researcher at Technical University of Munich, Germany. From 2016 to 2019, he worked as a Program-Specific Assistant Professor (ImPACT) at Kyoto University, Japan. His research interests include rescue robots, interface systems for snake robots and legged robots, real-time 3D laser scanners, and stereoscopic presentation of 3D point clouds. He is a member of the Robotics Society of Japan (RSJ).

Dr. Takahiro Endo

He received the PhD (Dr. Eng.) degree from the Tokyo Institute of Technology, Japan, in 2006. Since April 2015, he has been with the Department of Mechanical Engineering and Science, Kyoto University, Kyoto, Japan, where he is currently an Associate Professor. His research interests include haptic interfaces, robotics, and the control of infinite dimensional systems.

Prof. Fumitoshi Matsuno

He received the Dr. Eng. from Osaka University in 1986. In 1986, he joined the Department of Control Engineering, Osaka University. Since 2009, he has been a Professor in the Department of Mechanical Engineering and Science, Kyoto University. His current research interests lie in robotics, swarm intelligence, control of distributed parameter system and nonlinear system, and rescue support system in disaster. He is a Fellow member of the SICE, the JSME, the RSJ and a member of the IEEE among other organizations.