Rhythmic control method of a worm robot based on ...

Rhythmic Control Method of a Worm Robot Based on Neural CPG Xingjian Wang1, 2, 3, *, Qing Zhang1, Yixin Zhang1, Shaoping Wang1, 3 2.

1. School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, China State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou 310027, China 3. Beijing Advanced Innovation Center for Big Data-based Precision Medicine, Beijing 100083, China * Corresponding author: [email protected]

Abstract—In this study, a motion control method is designed for software bionic robot based on peristaltic mechanism and central pattern generator (CPG). The earthworm, as a representative animal of Annelida, is chosen as the prototype of bionics. By making biological analysis of red earthworm and taking a lot of observations of the creep in the soil, the deformation mode and peristaltic mode of the robot are determined, then a continuous flexible deformation worm robot is designed and made which consists of a variable parallelogram array based on Similar Design Principle. The robot is made up of six modular telescoping units, and we call the unit “a segment”, which is the same as that of earthworms. The robot is controlled by CPG, which is specially designed according to the rhythmic motion of invertebrate; the differences between CPG and normal control were compared, and the simulation showed that CPG is more suitable for such rhythm control. By referring to relevant document literature and experiments, the intensity and rigidity of connecting rod in different positions in each telescopic unit are determined, and the key structures such as quadrilateral node connecting piece, driving motor base and bidirectional retracting wheel are designed. And one-dimensional shrinkage and expansion was achieved by one motor, too. The robot will be miniaturized, which will be widely used in special operations, medical fields and micro-pipe testing. Keywords—CPG, worm, bionic robot, rhythmic motion, software robot

make a hydrostatic robot. This robot used the deformation of SMA for the robot body’s arch and movement [1]. In 2006, EA Avila et al. invented an Inchworm-like Robot that arched and flexed during walking. The team realized its motion with a multi-joint motor but only one-dimensional motion [2]. In 2012, A. D. Horchler et al. designed the first worm-deformation robot based on a mesh that was controlled by only one motor. It achieved shrinkage at the overall robot level through the cam structure and sophisticated mechanical design, but it lacked in control of the motion [3]. In 2015, they designed a mesh-like peristaltic bionic robot which is divided into a plurality of joint modules. Each module is driven by a motor, and the contraction and expansion of each module are realized by positive and negative rotation of the motor. The onedimensional motility of the robot was realized through the combination of rhythm control and joint module movement [4, 5]. This paper refers to the CMM-worm robot by Andrew. D. Horchler’s team [4,5]. And we made a change in its structure and designed a modular worm robot, which improved the service life, made the installation easier, and enhanced the interchangeability between components. Then we used the CPG as its controller, and the simulation showed that CPG is suitable for such rhythm control. Finally, through the experiment, the CPG controller was tested and verified. II. SYSTEM OVERVIEW

I. INTRODUCTION In the nature, footless animals have all kinds of strange movement. Earthworms and other annelids possess the multidegree of freedom of movement, which is able to function in different medium such as various types of soil and surface by the regular expansion of their bodies. It can be observed that it is the fiber distribution of the animal’s muscle that makes its body deform freely. Meanwhile, there are many tiny microstructures on its surface, and pairs of setae on it can increase the friction during exercise, which has attracted the attention of researchers. Since 2000, with the development of mechatronics and MEMS, biomimetic peristaltic robots have drawn the attention of researchers. In 2000, R. Vaidyanathan et al. use SMA to This work was supported by the National Natural Science Foundation of China (51675019, 51620105010, 51575019), Open Foundation of the State Key Laboratory of Fluid Power and Mechatronic Systems (GZKF-201710) and the Fundamental Research Funds for the Central Universities (YWF-17-BJ-Y-105)

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Worm robots are based on the deformable principle of the rhombus. The deformation of the rhombus is only one degree of freedom but can be deformed in two directions. By using this feature, it is possible to realize the movement form of a part of worm, which is similar to earthworm’s movement [4]. The robot consists of six modular extensible units, which is similar to earthworms. We refer these units as “segments”, and we used our specially designed Central Pattern Generators (CPGs) for invertebrates’ rhythmic moving control. In our robot, each segment is controlled by a separate actuator. Through the cooperation of six segments, the robot can move with contracting like worms. Encoder on the motor is as a feedback sensor. the drive mechanisms are composed of the 24V direct-current motor and the 0.8mm nylon wires. The controller employs the microprocessor:STM32F103ZET6. In addition, it also includes a motor driving unit and power management unit. The power uses 3600mAh rechargeable lithium battery so that the robot can move portably. By using

L

b a

transverse section node nylon wire nylon tube regular hexagon

one block

Fig. 1.

Fig. 3.

Schematic diagram of the worm robot structure

Fig. 4. Fig. 2.

Longitudinal Axis

Prototype of worm robot.

Earthworm movement form

Bluetooth and the mobile APP, the robot can be monitored for independent motioning and remote controlling. The robot’s parts are designed by SolidWorks, and shaped by 3D printing technology, in order to complete the prototype rapid iteration experiment. Printed materials include PLA and SLA. In addition, the parts include some components which can be purchased online. We use CPGs as a control model. Here is the final design of the machine in Fig.1. III. BIOLOGICAL ANALYSIS AND SYSTEM DESIGN A. Biological Mechanism Analysis Through the observation and study of the earthworm movement form, we found that the earthworm's movement form is very simple that rhythmic movement by simple muscle contraction. Through the body's telescopic movement, earthworms transmit a traveling wave which is toward the rear of movement, while the body's setae are fixing on the ground. So, the body can creep forward by the friction. In Fig.2, Some segments are shrinking and the others are relaxing. By this movement, the earthworm’s movement is toward to the lift and the wave movement is toward right. B. Design of System Hardware Based on [4, 5], which used a planar pair as a rhombus node and used a nylon wire as a transmission medium in each node, we make the following modifications to the node: In the node’s design, we use ammeter bolts and nuts as the node axis, which makes the shaft more smooth and easier for maintenance

Robot connected node explosion map

and replacement. On the other hand, we use the V-shapedbearing as the rotating mechanisms in the winding place. As a result, the dry friction of the wire is less and the friction force decreases during the movement, which not only increases the service life of the wire but also improves the efficiency of transmission. In Fig.3, the worm robot structure principle is shown, each section is crossed as a hexagon by nylon wires, and them are connected as a rhombus by nylon tube. When the rhombuses deform, the length of a side in hexagon is longer or shorter, and the robot can deform as a worm. The explosion of the designed node structure is shown in Fig.4: In Fig.4, A node includes an ammeter bolt, a nut, a bearing, a hat for bearing, and two rotating mechanisms. It is the smallest motion mechanism in this robot. In the power mechanism, we use a DC motor, of which rated voltage is 24V, power is 12W and rated speed is 130r / min. And we use a 715-line Hall encoder as a sensor for speed feedback and position feedback. Using L298N chip as a motor drive module, we can drive two motors, each one can withstand 3A peak current to meet the needs of the system. Then we use a STM32F103ZET6 as a processor, of which hardware has six encoder mode timers so that it can be friendly connected to encoders. It can detect the speed and position, without frequent interruption of the main program and cutting down the operation. In terms of power supply, a 24V 3600mAh lithium battery with a maximum current of 6A is used. Using LM2596-5 and AMS1117-3.3 as a DC-DC module, 3.3V power supplies to the

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Fig. 5.

The overall system structure

STM32 and the encoder. 5V power supplies to the L298N motor drive module. The overall system structure is shown in Fig. 5.

Fig. 6.

CPG neuron structure diagram

Fig. 7.

The first gait state output graph

IV. NEURAL CPG MODEL AND SIMULATION A. Mathematical Model of Neural CPG CPG is a self-oscillating neural network model based on differential equations. Through the mutual coupling between neurons, a stable rhythmic motional signal is generated, and the signal is used as a control instruction to control the robot. The basic mathematical model of a HOPF oscillator is as follows [6]: ­ xi =-2ʌfyi +ı ( ȝ-xi 2 -yi 2 ) xi ° ® § §ʌ · §ʌ · · 2 2 ° yi =2ʌfxi +ı ( ȝ-xi -yi ) yi +¦ Ȝ ¨ sin ¨ -șij ¸ y j -cos ¨ -șij ¸ x j ¸ ¹ ©2 ¹ ¹ © ©2 ¯

(1)

where xi , yi are state variables that excites neurons and inhibits neurons, f is the oscillation frequency of the oscillator, ı is the oscillator's convergence strength, ȝ is the amplitude of the oscillator, Ȝ is the coupling strength factor of the oscillator phase difference, șij is the phase difference between the i neuron and the j neuron, șij =ij j − iji . And

șij +ș ji =0 . B. Rhythmic Output Simulation of CPG For the worm robot we studied, the rhythm signal is simple. Assuming a motor corresponds to the output of a neuron, the action of each neuron is only related to the last neuron and the next neuron, that is, the phase difference is only related to two adjacent neurons. The head and tail neurons are also coupled together, therefore, it forms a ring structure which is shown in Fig.6: For the above model, the HOPF oscillator model can be simplified as follows [7]: ­ xi =- 2ʌfyi +ı ( ȝ-xi 2 -yi 2 ) xi °° § sin ( și ) xi-1 +cos ( și ) yi −1 · ® 2 2 ¸¸ ° y i =2ʌfxi +ı ( ȝ-xi -yi ) yi +¦ Ȝ ¨¨ sin ș x +cos ș y − ( ) ( ) i+1 i+1 i+1 i +1 ¹ © ¯°

(2)

where și+1 is the phase difference between i and i + 1 , și+1=iji +1 − iji . For i = 1, 2 ,⋅⋅⋅, 6 . Let ȝ =4, f =1, ı =20. When

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each neuron and coupled neurons have the same phase difference, system state variables xi steady-state output is as shown in Fig.7: It is clear that the output signals are sine waves which have the same phase difference with the next one. In order to make the sine waves generated by CPG shaping into the control signals which we need, the output of each neuron is defined as follows:

dxi-1 dx ­ < 0&& > 0 °1 dt dt ° dx dx ° i+1 > 0&& < 0 Z i = ® -1 (3) dt dt ° °0 ° ¯ The segment is elongated when Z i is equal to 1, and is shortened when it is equal to -1, remaining stationary when equal to 0, in order to achieve the output of the control signal. The first control signals are as shown in Fig.8: In Fig.8, the outputs are same as others, and when the Z i is equal to 1, the Z i-1 is equal to -1. So, the corresponding control strategy can be seen in Fig.9:

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Fig. 11.

Fig. 8.

The first gait control signal output

Fig. 9.

The first gait control strategy graph

Fig. 12.

The second gait control strategy graph

The first gait inverted state variable output graph nd

neuron, the 2 neuron and the 5th neuron, and the 3rd neuron and the 6th neuron have the same states of excitement at this time. Therefore, the output signals are same. From the same output relationship Z i , we can see that the corresponding control strategy of the output signals is as shown in Fig.11: This control strategy excites both neurons at the same time, completing the exercise once every three excitements, so the robot's speed of movement will be doubled. Multiplying the phase difference matrix of Fig.7 by -1 so that the phase difference is reversed, the robot's reverse motion can be achieved. Controller status variable output as shown in Fig.12: According to the same mapping rule, it can be known that the phase of the control signal is opposite after the output phases are opposite, that is, the robot's reverse motion can be realized. Fig. 10.

The second gait state output graph

In Fig.9, the blue in the picture above indicates that the section is in an extended state, and the red indicates that the section is in a contracted state. Excited only one neuron at a time, each excite 6 times to complete a cycle of exercise. Through the rhythmic movement in the figure above, the robot can transmit a traveling wave backwards and make the robot move forward. That is, CPG can be used as a robot controller. When modifying the phase difference parameter in the HOPF model, the output can be changed as shown in Fig.10. In Fig.10, x1 and x4 , x2 and x5 , x3 and x6 have exactly the same curves. Which indicates that the 1st neuron and the 4th

V. EVALUATION OF CONTROLLER On the basis of the above theory and design, the experiment of the prototype is carried out, as shown in Fig. 13. The minimum diameter of the worm robot’s shrinking is 18.6 cm, while the maximum diameter of 32.8cm. According to the measurement, under the unconstrained environment, if taking the first control scheme, the worm speed of the robot on the tiled floor will reach 46cm/min; if going with second control scheme, the worm robot speed on the tiled floor will reach 80cm/min. Measurement of correlation between the angle of the rotation of the motor and the elongation of each section is

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VI. CONCLUSION

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6 Fig. 13.

Physical movement decomposition diagram

In this study, a CPG-based controller is designed according to the rhythmic motion of invertebrate. The relative position and absolute position of each section are recorded by encoder. A closed loop feedback is carried out to prevent the motor from blocking when it moves. And the feedback quantity is used to judge the environment. In this way, the gait can be controlled. The worm robot, which is produced in this paper, manages to realize the movement form of worm, and the speed of motion on the flat pavement can attain 46cm/min. Through the reappearance of biological movement, this article has given a new cognition of the peristaltic active robot. The advantages of worm robot are mainly focused on its body which is easily deformed and has small demand for sports places. In the future, we can do research in areas such as detection, pipeline detection and other fields by continuous research on worm robot. We are going to miniaturize the robot, which will be widely used in special operations, medical fields and micro-pipe testing. REFERENCES [1] Vaidyanathan, Ravi, H. J. Chiel, and R. D. Quinn. "A hydrostatic robot [2] [3]

Fig. 14.

Elongation - angle relationship diagram

[4] [5] [6] [7] [8]

[9] Fig. 15.

Elongation - Diameter diagram

carried out. Fig. 14 shows that the elongation of each section can walk for the distance of 42mm, and the specified single frequency is 1.1Hz, that is to say, it completes a contraction at each 0.9s. For the first gait, the cycle time is 5.4s, and the theoretical speed is 46.7cm/min. It can be seen that the loss of the robot in motion transmission is small. The second gait theory is 93.4cm/min, but it can only reach 80cm/min actually because it cannot be avoided to make the robot shrink a bit of distance in motion. Measurement of correlation between diameter and elongation is carried out. Fig. 15 illustrates that there is a negative correlation between diameter and elongation.

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for marine applications." Robotics & Autonomous Systems 30.1– 2(2000):103-113 Avila, Enrique Alarcon, A. M. Melendez, and M. R. Falfan. "An Inchworm-Like Robot Prototype for Robust Exploration." Electronics, Robotics and Automotive Mechanics Conference IEEE, 2006:91-96. Daltorio, K. A., et al. "Efficient worm-like locomotion: slip and control of soft-bodied peristaltic robots. " Bioinspiration & Biomimetics8.3(2013):035003. Horchler, Andrew D., et al. "Worm-Like Robotic Locomotion with a Compliant Modular Mesh." International Conference on Biomimetic and Biohybrid Systems Springer-Verlag New York, Inc. 2015:26-37. Horchler, Andrew D., et al. "Peristaltic Locomotion of a Modular MeshBased Worm Robot: Precision, Compliance, and Friction." 2.4(2016):135-145. K. Seo, S. J. Chung, and J. J. E. Slotine, “CPG-based control of a turtlelike underwater vehicle,” Auton. Robots, vol. 28, pp. 247–269, 2010. Zhou, Chunlin, and K. H. Low. "Design and Locomotion Control of a Biomimetic Underwater Vehicle With Fin Propulsion." IEEE/ASME Transactions on Mechatronics 17.1(2012):25-35. Kimura, Hiroshi, Y. Fukuoka, and A. H. Cohen. "Adaptive Dynamic Walking of a Quadruped Robot on Natural Ground Based on Biological Concepts." International Journal of Robotics Research 26.5(2003):475490. Kimura, H., and Y. Fukuoka. "Biologically inspired adaptive dynamic walking in outdoor environment using a self-contained quadruped robot: 'Tekken2'." Ieee/rsj International Conference on Intelligent Robots and Systems IEEE, 2004:986-991 vol.1. Kimura, H., et al. "Three-dimensional adaptive dynamic walking of a quadruped - rolling motion feedback to CPGs controlling pitching motion." IEEE International Conference on Robotics and Automation, 2002. Proceedings. ICRA IEEE, 2002:2228-2233. Qiang, Lu, et al. "Effects on hypothalamus when CPG is fed back to basal ganglia based on KIV model." Cognitive Neurodynamics9.1(2015):85. Williams, Thelma L., and T. Mcmillen. "Strategies for swimming: explorations of the behaviour of a neuro-musculo-mechanical model of the lamprey." Biology Open 4.3(2015):253-8. Gonzalez-Gomez, J., E. Aguayo, and E. Boemo. Locomotion of a Modular Worm-like Robot Using a FPGA-based Embedded MicroBlaze Soft-processor. Climbing and Walking Robots. Springer Berlin Heidelberg, 2005:869-878. Chang, Carolina, and P. Gaudiano. "Biomimetic Robotics." Robotics & Autonomous Systems 30.1–2(2000):1-2.

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