- Email: [email protected]
Biomimetic Motion Control System Based on a CPG for an Amphibious Multi-Link Mobile Robot
Journal of Bionic Engineering Suppl. (2008) 91–97
Biomimetic Motion Control System Based on a CPG for an Amphibious Multi-Link Mobile Robot Takayuki Matsuo, Takeshi Yokoyama, Daishi Ueno, Kasuo Ishii Kyushu Institute of Technology, Fukuoka 808-0196, Japan
Abstract Robots and robotics technologies are expected to provide new tools for inspection and manipulation, especially in extreme environments that are dangerous for human beings to access directly, such as underwater environments, volcanic areas, or nuclear power plants. Robots designed for such extreme environments should be sufficiently robust and strong to cope with disturbance and breakdowns. We focus on the movement of animals to realize robust robot systems. One approach is to mimic the nervous systems of animals. The central pattern generator of a nervous system has been shown to control motion patterns, such as walking, respiration and flapping. In this paper, a robot motion control system using a central pattern generator is proposed and applied to an amphibious multi-link mobile robot. Keywords: central pattern generator, Matsuoka model, biomimetic control system, amphibious multi-link mobile robot Copyright © 2008, Jilin University. Published by Elsevier Limited and Science Press. All rights reserved.
1 Introduction Robots and robotics technologies are expected to provide new tools for inspection and manipulation, especially in extreme environments that are dangerous for human beings to access directly, such as underwater environments, volcanic areas, and nuclear power plants. Robots designed for such extreme environments should be robust and reliable, have the ability to compensate for breakdowns using other parts, be adaptable to the environment, and have reasonable maintenance costs. In this research, we find a solution for a robust robot system by considering the natural world; animals adapt well to environmental changes over both short and long time periods by evolution and natural selection. Here, we investigate the motion of snakes and eels, which can move over land and under water by wriggling their bodies. Their motion mechanisms have already been studied by Hirose[1,2] and Azuma[3]. A snake’s body is covered with special scales that have low friction in the tangential direction and high friction in the normal direction. This feature enables thrust to be produced from a wriggle motion. An eel swims under water by Corresponding author: Takayuki Matsuo E-mail: [email protected]
generating an impellent force from a hydrodynamic force. There is a phase difference along the body and the amplitude of wriggling increases along the line of the body. It has been shown that motion patterns such as walking, respiration and flapping are controlled by the Central Pattern Generator (CPG) in the nervous systems of animals. To analyze such motions, various numerical models of the CPG have been proposed, such as the Matsuoka model[4,5], Terman-Wang model[6], Wilson-Cowan model[7]. The CPG consists of many neural oscillators, and rhythm patterns are generated on each oscillator as they affect each other. In this research, we introduce the Matsuoka model as the neuron model of the CPG. We also realize phase differences and bias by adjusting parameters and the periodical signals from the CPG are used for the target joint angles of a robot. We develop an amphibious multi-link mobile robot that can move on ground and under water for the purpose of evaluation. A biomimetic robot motion control system using a CPG is investigated and applied to the amphibious multi-link mobile robot.
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2 Amphibious multi link mobile robot In our previous work[8], we developed the MultiLink Mobile Robot (MLMR), shown in Fig. 1, as a test bed for the evaluation of a motion control system using a CPG. We realized a wriggle motion for forward and turning motions using periodical output signals of the CPG control system. However, the MLMR was not developed for evaluation of hybrid-dynamics systems in which the dynamics of a robot transfer from one mode to another. Hybrid-dynamics systems are an interesting application of the CPG[9,10] and thus we developed MLMR II (see Fig. 2) as a new test bed for motion control and adaptation in two different environments that require different dynamics: land and underwater environments. Table 1 gives the specifications of MLMR II.
In this paper, we evaluate the basic performance of MLMR II, and the CPG-based biomimetic control system is applied to MLMR II. 2.1 Mechanism MLMR II, which has eight links (cylinders) and seven joints, moves both on ground and under water. Therefore, waterproofness is an important design consideration. The robot comprises eight cylinders that are joined such that each cylinder can rotate around a yaw axis via DC motors and a gearbox as shown in Fig. 3. O-rings are employed on the shaft of each joint and the cylinder lids to ensure the waterproofness of the robot. The pressure capacity Pk = 0.156 MPa of each cylinder is calculated using Eq. (1). Therefore, the maximum operation depth of the robot is approximately 15 m, which is sufficient for an experimental pool test.
Pk
Fig. 1 Overview of MLMR.
4 2 ª S n2 1 § t · º § t · §r· E« 4 2 ¨ ¸ ¨ ¸ » ¨ ¸ , (1) ¬« n (n 1) © l ¹ 12(1 Q ) © r ¹ ¼» © r ¹
where, Pk is the elastic buckling stress, E is Young’s modules (3060 MPa), n is the buckling mode (2), is Poisson’s ratio (0.23), t is the thickness of the cylinder (3.0 × 103 m), r is the radius of the cylinder (5.0 × 102 m) and l is the length of the cylinder (17.5 × 102 m). Hydrodynamic forces produced by fins and the body produces thrust forces under water and passive wheels are used on ground (Fig. 4).
Fig. 2 Overview of MLMR II. Table 1 Specifications of MLMR II Specifications Length (m) Weight (kg)
2.2 12.8
Details
Number of joints
7
Operation depth (m)
15.6
MPU
PIC18F542
Communication
Actuator
RS485 Current sensor (LTS 6-NP) Potentiometer DC motor (05D-SU TUKASA)
Motor driver
TA8440H
Sensors
Fig. 3 Internal architecture of a cylinder.
2.2 Electrical system and communication MLMR II consists of two kinds of cylinders: a cylinder for the head (head module) and seven cylinders for the body (motor modules). A motor module has a motor to control the joint angle and a circuit board. The
Matsuo et al.: Biomimetic Motion Control System Based on a CPG for an Amphibious Multi-Link Mobile Robot
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3 Basic motion performance of MLMR II
Fig. 4 Front view of a cylinder.
circuit has a microprocessor unit (MPU, PIC18F452), a potentiometer to measure the joint angle, an RS485 transceiver (MAX1487) for communication and a current sensor to measure joint torque. To protect the MPU from the noise of the motor, the MPU ground is isolated from the actuator ground by photo couplers. A block diagram of the circuit is shown in Fig. 5. The MPU calculates the target trajectory using the neuron potential of the CPG, controls the motor using a PID control manages sensor information (e.g., current and angle data) and communicates with circuits of other modules using the RS485. The head module is the interface device between the robot and the host PC, and it transfers the target behavior to other modules. The token-passing method[11] is used for communication. The head module sends a token from the head to the tail and controls dataflow. If a target module receives the token, the module sends its measured data such as joint angle, current, and neuron potential data; other modules read and store the data for CPG calculation. The output of the neural oscillator is used as the target joint angle. The token flows between modules once every 6.25 ms and thus each module has a chance to output its data every 50 ms.
A sinusoidal target angle is given to MLMR II to investigate its basic performance under water and on ground by measuring the position of each joint using a motion capture system. The weight and buoyancy are adjusted so that MLMR II swims on the water surface. Markers are placed on the joints of MLMR II and the motion capture system tracks each marker and calculates the position and velocity of each link. In the motion of real snake, the body is controlled so that it follows the front joint with a certain phase difference so as to keep the same trail. The joint angle of MLMR II is controlled to have a certain phase difference using Eq. (2). y
A sin(2ft I ) B
Here, the parameters A, f, B, are the amplitude of the sinusoidal wave, frequency, bias and phase difference, respectively. The robot can move forward and backward by changing and rotate by adjusting B. Fig. 6a shows the measured position of the head module in the cases of forward motion on ground (solid line) and under water (dotted line) when parameters are set as A = 45, f = 0.25 Hz, = 45, and B = 0. When B is set to 15, the robot turns right as shown in Fig. 6b, and it turns left when B is set to 15 as shown in Fig. 6c. We can see that the robot can move forward in both environments using sinusoidal wriggling and it does this approximately three times faster on the ground than under water. The robot moves about 2.5 m under water and 7 m on the ground in a
(a) Forward motion
Fig. 5 Block diagram of the circuit.
(2)
(b) Right turn motion
Fig. 6 Motion capture data for different motion underwater and on ground.
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Fig. 7 Output of a neural oscillator. (b) Left turn motion
Fig. 6 Continued.
period of 30 s in the forward motion. For a turning motion, the robot returns to the starting position in five cycles on ground and almost half circle under water. One reason for this result is the effect of the large drag force under water.
4 Biomimetic motion control 4.1 Matsuoka model The Matsuoka model is expressed in Eqs. (3) to (5),
W v vi
vi yi ,
(3)
n
W u ui ui E vi ¦ wij yi u0 f i ,
(4)
j 1
yi
max(0, ui ) .
The neural oscillator wave in the Matsuoka model can entrain external oscillatory input using sensor input f. The neural oscillator wave is able to entrain a wave that matches the resonance frequency. Williamson[13], Bailey[14], Ijspeert[15] and Inoue[16] developed a robot control system that is able to adapt to changes in the environment and its own dynamics using senor input f. Additionally, the wave in the Matsuoka model is able to change amplitude and bias by adjusting u0. We adjusted u0 and realized motions such as forward, right turn and left turn. These motions were then analyzed using a motion capture system.
(5)
where ui is the membrane potential of the i-th neuron, vi represents the degree of adaptation, u0 is the external input with a constant rate, fi is the feedback signal from a sensory input, , u, v are parameters that specify the time constant for the adaptation, wij is the neuron weighting, and n is the number of neurons. A neural oscillator is able to generate periodical signals by combining neurons with mutually inhibitory connections. Fig. 7 shows the output of a neural oscillator. We developed a neural-oscillator-based controller for biped walking, and the simulation results of biped walking showed that the parameters and weights of the controller are capable of being optimized using a genetic algorithms approach[12].
4.2 Application of the CPG network to motion control A set of neural oscillators is assigned to each of our robot’s seven joints. The CPG for MLMR II is shown in Fig. 8. A neural oscillator consists of an Extensor Neuron (EN) and a Flexor Neuron (FN). ENs are connected to FNs of the neighboring neural oscillator, and FNs are connected to ENs of the neighboring neural oscillator.
Fig. 8 CPG network for biomimetic motion control.
Matsuo et al.: Biomimetic Motion Control System Based on a CPG for an Amphibious Multi-Link Mobile Robot
The network architecture is designed as a closed loop to generate periodically successive signals with a certain phase. After CPG simulations, we employed sets of CPG parameters for generating waves with a certain phase difference. Table 2 gives the parameters for forward motion and Fig. 9 shows the output of each neural oscillator. We determined the parameters through trial and error using Matlab software. If u0 of each oscillator was correctly adjusted, the CPG can output a wave with increasing amplitude as shown Fig. 10. u0 parameters are set as u0_e = u0_f = 0.45, 0.5, 0.55, 0.6, 0.65, 0.7, and 0.75 for the head oscillator. Other parameters are the same as are listed in Table 2. MLMR II can change direction with a change in parameter u0, which shifts the neutral position. If parameters are set as in Table 3, the robot turns and moves toward the right. Fig. 11 shows the output of the CPG network for a right turn motion. Alternatively,
95
if parameters are set as in Table 4, the robot turns and moves toward the left. Fig. 12 shows the output of the CPG network for a left turn motion. We analyzed the motion of our robot using a motion capture system for both underwater and on ground environments. Fig. 13 shows motion capture data for forward motion on the ground and under water. Parameter settings are those given in Table 2. Fig. 14a shows motion capture data for a right turn motion when parameters are those listed in Table 3. Fig. 14b shows motion capture data for a right turn motion when parameters are those listed in Table 4. Table 3 Parameters of the CPG network for right turn motion u wef
0.44 1.5
v wfe
0.54 1.5
W1
1 0.3
W2
0
u0_e
1.02
u0_f
1.95
Table 2 Parameters of the CPG network for forward motion u wef
0.44 1.5
v wfe
0.54 1.5
W1
1 0.3
W2
0
u0_e
0.75
u0_f
0.75
Fig. 11 Output of the CPG network for right turn motion. Table 4 Parameters of the CPG network for left turn motion
Fig. 9 Output of the CPG network for forward motion.
Fig. 10 Wave with increasing amplitude produced using the CPG.
u wef
0.44 1.5
v wfe
0.54 1.5
W1
1 0.3
W2
0
u0_e
0.95
u0_f
1.02
Fig. 12 Wave with increasing amplitude produced using the CPG.
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motion control was carried out both on the ground and under water by adjusting CPG parameters. Additionally, the motions of the robot were analyzed using a motion capture system. In future work, we will include a sensor feedback in the biomimetic motion control system and carry out dynamics simulations.
Acknowledgement
Fig. 13 Motion capture data for forward motion on ground and under water using CPG waves for target joint angles.
This work was supported by the 21st Century Center of Excellence Program, “World of Brain Computing Interwoven out of Animals and Robots (Pl: T. Yamakawa)” (center#J19) granted to the Kyushu Institute of Technology by the Ministry of Education, Culture, Sports, Science and Technology of Japan.
References [1]
Hirose S. Bionic Machine Engineering, Kougyo Chosakai, Tokyo, 1987. (in Japanese)
[2]
Mori M, Yamada H, Hirose S. Design and development of active cord mechanism “ACM-R3” and its 3-dimentional locomotion control. Journal of RSJ, 2005, 23, 886–897. (in Japanese)
[3]
Azuma A. The Subject-book of Animal’s Motion, Asakura, Tokyo, 1997.
[4]
Matsuoka K. Sustained oscillations generated by mutually inhibiting neurons with adaptation. Biological Cybernetics, 1985, 52, 367–376.
(a) With parameters of Table 3
(b) With parameters of Table 4
[5]
in the neural rhythm generators. Biological Cybernetics,
Fig. 14 Motion capture data for right turn motion with different parameters.
The robot is able to travel further on ground than under water in the same time frame for forward motion, as shown in Fig. 13. Under water, the robot was able to move through a distance of about 2.0 m whereas it moved about 5.5 m on ground. For right turn motion, the robot completes a circle on ground but is unable to do so under water in the same time frame. Turning radii are 1.6 m on ground and 1.2 m under water. The results are the same for left turn motion.
5 Conclusions MLMR II that has seven joints and moves on ground and under water was developed. A biomimetic motion control system using a CPG was developed and implemented. The system was applied to MLMR II, and
Matsuoka K. Mechanisms of frequency and pattern control 1987, 56, 345–353.
[6]
Terman D, Wang D L. Global competition and local cooperation in a network of neural oscillators. Physica D, 1995, 81, 148–176.
[7]
Wilson H R, Cowan J D. Excitatory and inhibitory Interactions in localized populations of model neurons. Biophysical Journal, 1972, 12, 1–24.
[8]
Matsuo T, Yokoyama T, Ishii K. Development of neural oscillator based motion control system and applied to snake-like robot. IEEE/RSJ International Conference on Intelligent Robots and Systems, San Diego, USA, 2007, 3697–3702.
[9]
Matsuoka K, Ohyama N, Watanabe A, Ooshima M. A giant swing robot using a neural oscillator. Brain-Inspired IT II, Proceedings of the 2nd International Conference on Braininspired Information Technology, Hibikino, Japan, 2006, 153–156.
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ogy, USA, 1999.
oscillator. Brain-Inspired IT III, Proceedings of the 3rd In-
[14] Bailey S A. Biomimetic Control with a Feedback Coupled
ternational Conference on Brain-Inspired Information
Nonlinear Oscillator: Insect Experiments, Design Tools, and
Technology, Hibikino, Japan, 2007, 218–221. [11] Fukunaga K. Computer Communication and Network (5th ed), Kyoritsu Shuppan, Tokyo, 2002. (in Japanese) [12] Inada H, Ishii K. Behavior generation of bipedal robot using central pattern generator (CPG), 1st report: CPG parameters
Hexapedal Robot Adaptation Results, PhD thesis, Stanford University, USA, 2004. [15] Ijspeert A J, Crespi A, Ryczko D, Cabelguen J M. From swimming to walking with a salamander robot driven by a spinal cord model. Science, 2007, 315, 1416–1420.
searching method by genetic algorithm. Proceedings of
[16] Inoue K, Ma S, Jin C. Neural oscillator network-based con-
IEEE/RSJ Intelligent Robots and System, 2003, 3, 2179–
troller for meandering locomotion of snake-like robot. Pro-
2184.
ceedings of 2004 IEEE International Conference on Robot-
[13] Williamson M M. Robot Arm Control Exploiting Natural Dynamics, PhD thesis, Massachusetts Institute of Technol-
ics and Automation, New Orleans, USA, 2004, 5064–5069.
Biomimetic Motion Control System Based on a CPG for an Amphibious Multi-Link Mobile Robot Takayuki Matsuo, Takeshi Yokoyama, Daishi Ueno, Kasuo Ishii Kyushu Institute of Technology, Fukuoka 808-0196, Japan
Abstract Robots and robotics technologies are expected to provide new tools for inspection and manipulation, especially in extreme environments that are dangerous for human beings to access directly, such as underwater environments, volcanic areas, or nuclear power plants. Robots designed for such extreme environments should be sufficiently robust and strong to cope with disturbance and breakdowns. We focus on the movement of animals to realize robust robot systems. One approach is to mimic the nervous systems of animals. The central pattern generator of a nervous system has been shown to control motion patterns, such as walking, respiration and flapping. In this paper, a robot motion control system using a central pattern generator is proposed and applied to an amphibious multi-link mobile robot. Keywords: central pattern generator, Matsuoka model, biomimetic control system, amphibious multi-link mobile robot Copyright © 2008, Jilin University. Published by Elsevier Limited and Science Press. All rights reserved.
1 Introduction Robots and robotics technologies are expected to provide new tools for inspection and manipulation, especially in extreme environments that are dangerous for human beings to access directly, such as underwater environments, volcanic areas, and nuclear power plants. Robots designed for such extreme environments should be robust and reliable, have the ability to compensate for breakdowns using other parts, be adaptable to the environment, and have reasonable maintenance costs. In this research, we find a solution for a robust robot system by considering the natural world; animals adapt well to environmental changes over both short and long time periods by evolution and natural selection. Here, we investigate the motion of snakes and eels, which can move over land and under water by wriggling their bodies. Their motion mechanisms have already been studied by Hirose[1,2] and Azuma[3]. A snake’s body is covered with special scales that have low friction in the tangential direction and high friction in the normal direction. This feature enables thrust to be produced from a wriggle motion. An eel swims under water by Corresponding author: Takayuki Matsuo E-mail: [email protected]
generating an impellent force from a hydrodynamic force. There is a phase difference along the body and the amplitude of wriggling increases along the line of the body. It has been shown that motion patterns such as walking, respiration and flapping are controlled by the Central Pattern Generator (CPG) in the nervous systems of animals. To analyze such motions, various numerical models of the CPG have been proposed, such as the Matsuoka model[4,5], Terman-Wang model[6], Wilson-Cowan model[7]. The CPG consists of many neural oscillators, and rhythm patterns are generated on each oscillator as they affect each other. In this research, we introduce the Matsuoka model as the neuron model of the CPG. We also realize phase differences and bias by adjusting parameters and the periodical signals from the CPG are used for the target joint angles of a robot. We develop an amphibious multi-link mobile robot that can move on ground and under water for the purpose of evaluation. A biomimetic robot motion control system using a CPG is investigated and applied to the amphibious multi-link mobile robot.
Journal of Bionic Engineering (2008) Suppl.
92
2 Amphibious multi link mobile robot In our previous work[8], we developed the MultiLink Mobile Robot (MLMR), shown in Fig. 1, as a test bed for the evaluation of a motion control system using a CPG. We realized a wriggle motion for forward and turning motions using periodical output signals of the CPG control system. However, the MLMR was not developed for evaluation of hybrid-dynamics systems in which the dynamics of a robot transfer from one mode to another. Hybrid-dynamics systems are an interesting application of the CPG[9,10] and thus we developed MLMR II (see Fig. 2) as a new test bed for motion control and adaptation in two different environments that require different dynamics: land and underwater environments. Table 1 gives the specifications of MLMR II.
In this paper, we evaluate the basic performance of MLMR II, and the CPG-based biomimetic control system is applied to MLMR II. 2.1 Mechanism MLMR II, which has eight links (cylinders) and seven joints, moves both on ground and under water. Therefore, waterproofness is an important design consideration. The robot comprises eight cylinders that are joined such that each cylinder can rotate around a yaw axis via DC motors and a gearbox as shown in Fig. 3. O-rings are employed on the shaft of each joint and the cylinder lids to ensure the waterproofness of the robot. The pressure capacity Pk = 0.156 MPa of each cylinder is calculated using Eq. (1). Therefore, the maximum operation depth of the robot is approximately 15 m, which is sufficient for an experimental pool test.
Pk
Fig. 1 Overview of MLMR.
4 2 ª S n2 1 § t · º § t · §r· E« 4 2 ¨ ¸ ¨ ¸ » ¨ ¸ , (1) ¬« n (n 1) © l ¹ 12(1 Q ) © r ¹ ¼» © r ¹
where, Pk is the elastic buckling stress, E is Young’s modules (3060 MPa), n is the buckling mode (2), is Poisson’s ratio (0.23), t is the thickness of the cylinder (3.0 × 103 m), r is the radius of the cylinder (5.0 × 102 m) and l is the length of the cylinder (17.5 × 102 m). Hydrodynamic forces produced by fins and the body produces thrust forces under water and passive wheels are used on ground (Fig. 4).
Fig. 2 Overview of MLMR II. Table 1 Specifications of MLMR II Specifications Length (m) Weight (kg)
2.2 12.8
Details
Number of joints
7
Operation depth (m)
15.6
MPU
PIC18F542
Communication
Actuator
RS485 Current sensor (LTS 6-NP) Potentiometer DC motor (05D-SU TUKASA)
Motor driver
TA8440H
Sensors
Fig. 3 Internal architecture of a cylinder.
2.2 Electrical system and communication MLMR II consists of two kinds of cylinders: a cylinder for the head (head module) and seven cylinders for the body (motor modules). A motor module has a motor to control the joint angle and a circuit board. The
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93
3 Basic motion performance of MLMR II
Fig. 4 Front view of a cylinder.
circuit has a microprocessor unit (MPU, PIC18F452), a potentiometer to measure the joint angle, an RS485 transceiver (MAX1487) for communication and a current sensor to measure joint torque. To protect the MPU from the noise of the motor, the MPU ground is isolated from the actuator ground by photo couplers. A block diagram of the circuit is shown in Fig. 5. The MPU calculates the target trajectory using the neuron potential of the CPG, controls the motor using a PID control manages sensor information (e.g., current and angle data) and communicates with circuits of other modules using the RS485. The head module is the interface device between the robot and the host PC, and it transfers the target behavior to other modules. The token-passing method[11] is used for communication. The head module sends a token from the head to the tail and controls dataflow. If a target module receives the token, the module sends its measured data such as joint angle, current, and neuron potential data; other modules read and store the data for CPG calculation. The output of the neural oscillator is used as the target joint angle. The token flows between modules once every 6.25 ms and thus each module has a chance to output its data every 50 ms.
A sinusoidal target angle is given to MLMR II to investigate its basic performance under water and on ground by measuring the position of each joint using a motion capture system. The weight and buoyancy are adjusted so that MLMR II swims on the water surface. Markers are placed on the joints of MLMR II and the motion capture system tracks each marker and calculates the position and velocity of each link. In the motion of real snake, the body is controlled so that it follows the front joint with a certain phase difference so as to keep the same trail. The joint angle of MLMR II is controlled to have a certain phase difference using Eq. (2). y
A sin(2ft I ) B
Here, the parameters A, f, B, are the amplitude of the sinusoidal wave, frequency, bias and phase difference, respectively. The robot can move forward and backward by changing and rotate by adjusting B. Fig. 6a shows the measured position of the head module in the cases of forward motion on ground (solid line) and under water (dotted line) when parameters are set as A = 45, f = 0.25 Hz, = 45, and B = 0. When B is set to 15, the robot turns right as shown in Fig. 6b, and it turns left when B is set to 15 as shown in Fig. 6c. We can see that the robot can move forward in both environments using sinusoidal wriggling and it does this approximately three times faster on the ground than under water. The robot moves about 2.5 m under water and 7 m on the ground in a
(a) Forward motion
Fig. 5 Block diagram of the circuit.
(2)
(b) Right turn motion
Fig. 6 Motion capture data for different motion underwater and on ground.
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Fig. 7 Output of a neural oscillator. (b) Left turn motion
Fig. 6 Continued.
period of 30 s in the forward motion. For a turning motion, the robot returns to the starting position in five cycles on ground and almost half circle under water. One reason for this result is the effect of the large drag force under water.
4 Biomimetic motion control 4.1 Matsuoka model The Matsuoka model is expressed in Eqs. (3) to (5),
W v vi
vi yi ,
(3)
n
W u ui ui E vi ¦ wij yi u0 f i ,
(4)
j 1
yi
max(0, ui ) .
The neural oscillator wave in the Matsuoka model can entrain external oscillatory input using sensor input f. The neural oscillator wave is able to entrain a wave that matches the resonance frequency. Williamson[13], Bailey[14], Ijspeert[15] and Inoue[16] developed a robot control system that is able to adapt to changes in the environment and its own dynamics using senor input f. Additionally, the wave in the Matsuoka model is able to change amplitude and bias by adjusting u0. We adjusted u0 and realized motions such as forward, right turn and left turn. These motions were then analyzed using a motion capture system.
(5)
where ui is the membrane potential of the i-th neuron, vi represents the degree of adaptation, u0 is the external input with a constant rate, fi is the feedback signal from a sensory input, , u, v are parameters that specify the time constant for the adaptation, wij is the neuron weighting, and n is the number of neurons. A neural oscillator is able to generate periodical signals by combining neurons with mutually inhibitory connections. Fig. 7 shows the output of a neural oscillator. We developed a neural-oscillator-based controller for biped walking, and the simulation results of biped walking showed that the parameters and weights of the controller are capable of being optimized using a genetic algorithms approach[12].
4.2 Application of the CPG network to motion control A set of neural oscillators is assigned to each of our robot’s seven joints. The CPG for MLMR II is shown in Fig. 8. A neural oscillator consists of an Extensor Neuron (EN) and a Flexor Neuron (FN). ENs are connected to FNs of the neighboring neural oscillator, and FNs are connected to ENs of the neighboring neural oscillator.
Fig. 8 CPG network for biomimetic motion control.
Matsuo et al.: Biomimetic Motion Control System Based on a CPG for an Amphibious Multi-Link Mobile Robot
The network architecture is designed as a closed loop to generate periodically successive signals with a certain phase. After CPG simulations, we employed sets of CPG parameters for generating waves with a certain phase difference. Table 2 gives the parameters for forward motion and Fig. 9 shows the output of each neural oscillator. We determined the parameters through trial and error using Matlab software. If u0 of each oscillator was correctly adjusted, the CPG can output a wave with increasing amplitude as shown Fig. 10. u0 parameters are set as u0_e = u0_f = 0.45, 0.5, 0.55, 0.6, 0.65, 0.7, and 0.75 for the head oscillator. Other parameters are the same as are listed in Table 2. MLMR II can change direction with a change in parameter u0, which shifts the neutral position. If parameters are set as in Table 3, the robot turns and moves toward the right. Fig. 11 shows the output of the CPG network for a right turn motion. Alternatively,
95
if parameters are set as in Table 4, the robot turns and moves toward the left. Fig. 12 shows the output of the CPG network for a left turn motion. We analyzed the motion of our robot using a motion capture system for both underwater and on ground environments. Fig. 13 shows motion capture data for forward motion on the ground and under water. Parameter settings are those given in Table 2. Fig. 14a shows motion capture data for a right turn motion when parameters are those listed in Table 3. Fig. 14b shows motion capture data for a right turn motion when parameters are those listed in Table 4. Table 3 Parameters of the CPG network for right turn motion u wef
0.44 1.5
v wfe
0.54 1.5
W1
1 0.3
W2
0
u0_e
1.02
u0_f
1.95
Table 2 Parameters of the CPG network for forward motion u wef
0.44 1.5
v wfe
0.54 1.5
W1
1 0.3
W2
0
u0_e
0.75
u0_f
0.75
Fig. 11 Output of the CPG network for right turn motion. Table 4 Parameters of the CPG network for left turn motion
Fig. 9 Output of the CPG network for forward motion.
Fig. 10 Wave with increasing amplitude produced using the CPG.
u wef
0.44 1.5
v wfe
0.54 1.5
W1
1 0.3
W2
0
u0_e
0.95
u0_f
1.02
Fig. 12 Wave with increasing amplitude produced using the CPG.
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motion control was carried out both on the ground and under water by adjusting CPG parameters. Additionally, the motions of the robot were analyzed using a motion capture system. In future work, we will include a sensor feedback in the biomimetic motion control system and carry out dynamics simulations.
Acknowledgement
Fig. 13 Motion capture data for forward motion on ground and under water using CPG waves for target joint angles.
This work was supported by the 21st Century Center of Excellence Program, “World of Brain Computing Interwoven out of Animals and Robots (Pl: T. Yamakawa)” (center#J19) granted to the Kyushu Institute of Technology by the Ministry of Education, Culture, Sports, Science and Technology of Japan.
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