0　Introduction

How to perceive the knowledge and control a snake-like robot to imitate the motion of snakes is a hot topic for researchers. The MNSM-based controller for a snake-like robot is developed to understand the rhythm of swimming motion, and uses its knowledge to represent the swimming strategies.

The remainder of this study is organized as follows: In Section 1, the related work is specified. Section 2 presents a MNSM-based controller for swimming motion of snake-like robots. A dynamic model of a snake-like robot is addressed in Section 3. In Section 4, the knowledge definition for swimming motion of snake-like robots is specified. In section 5, the swimming motion by MNSM-based controller is developed. The swimming motion speed regulated by MNSM-based controller is studied in Section 6. In Section 7, the phase modulation knowledge presentation is defined. Finally, the conclusion is discussed in Section 8.

则可证⊗ξ是三角模,且(⊗ξ,→ξ)是[0,1]上的伴随对,其中{L,G,π,0},且([0,1],⊗ξ,→ξ)是剩余格。

1　Related work

The lack of legs does not impede the locomotion of snakes. They use several different gaits to deal with particular environments. Unlike the gaits of legged animals, snakes use at least five unique modes of terrestrial locomotion. The typical gaits are serpentine locomotion, side-winding locomotion, concertina locomotion, and rectilinear locomotion[1].

In serpentine gait, waves of lateral bending are propagated along the body from head to tail. When the body contacts an object, it exerts force against it and deforms locally around it. When a snake pushes against multiple objects, the lateral force vectors counteract each other, generating a resultant vector that propels the snake forward[2].

① 周美彤.浅谈中国流行乐坛的“中国风”现象及意义[D].武汉:沈阳师范大学学报社会科学版165期,2011.

Different snake-like robots are developed to imitate the swimming motion in water[4-7].

Most swimming motions of snake-like robots could be controlled by kinematic planning, artificial neuron networks, etc[8-12]. In order to understand the mechanism and realize similar motion of snake-like robot, knowledge presentation should be adopted to present the motion, and generate corresponding control strategies. Typically, knowledge presentation is a high level neuron system activity. Neuroscientists have previously identified that the MNSM (mirror neuron system mechanism) appears to play a fundamental role in both action understanding and imitation[13-15].

Fig.1　Swimming snake

In humans, mirror neuron systems have been found in Broca’s area and the inferior parietal cortex of the brain[13]. Diagram of the brain, as shown in Fig.2, shows the locations of the frontal and parietal lobes of the cerebrum, viewed from the left. It contains the inferior frontal lobe, and the superior parietal lobe.

Fig.2　Diagram of the brain

随着物联网技术的推广以及智能电网概念的兴起，国内外都在智能用电建设方面开展了大量的理论研究与实际探索，并逐渐对智能电网概念在用电侧体现出的特征内涵和典型建设内容形成了共识；同时，国务院“三网融合”的开展对于促进信息和文化产业发展，提高国民经济和社会信息化水平，满足人民群众日益多样的生产、生活服务需求，拉动国内消费，形成新的经济增长点，因此智能小区的建设具有重要意义。

Fig.3　MNSM motion control for dual arm robots

The MNSM-based controller has been developed by Lu to perceive the rhythmic output of the UCI-CPG (unidirectional cyclic inhibition-central pattern generator) network-based swimming motion of the snake-like robot[19], as shown in Fig.4.

Fig.4　UCI-CPG control system of the snake-like robot

A MNSM-based controller for a snake-like robot is developed to understand the rhythm of swimming motion, and uses its knowledge to represent the swimming strategies.

正如休·廷克(Hugh Tinker)所指出的，新独立的缅甸政府对英国的态度主要由两个元素构成，对英国模式的推崇和对英帝国主义的怀疑。在缅甸领导人的同一篇讲话中，可以经常发现这两个交织在一起的元素。[29]吴努眼中所谓的“最友好的”“最坦诚的”缅英关系，在缅甸人满怀期望的援助诉求被英国冷遇、英帝国主义与国内叛乱藕断丝连之下，自然遭到打击，导致缅甸对英国的信任与期望降低。1953年缅方通知英国，1947年签署的英缅防卫协定在1954年1月4日终止，不再签署新的协定。美国学者卡拉汉(Callahan)认为，这主要是因为军方高层认为英国在支持叛乱的克伦族，没有向缅军提供足够的援助所致。[30]

2　MNSM-based controller for swimming motion of snake-like robots

A MNSM-based controller is developed, as shown in Fig.5, to present the knowledge in Cartesian space.

The dynamics of the MNSM-based controller is shown as follows.

When swimming in water, the waves become larger as they move down the snake’s body, and the thrust can be generated by pushing their body against the water, resulting in the observed slip[3].

(1)

Fig.5　MNSM-based controller of the snake-like robot

Here, Mx,i(r), My,i(r), Mr,i(r) are the neurons to generate a mirror network for a snake-like robot; Fr,i(r) is the knowledge function to present the dynamic of the swimming motion; Fx,i(r), Fy,i(r), are the high level knowledge function to perceive the rhythm and generate the corresponding information in XY plane.

3　Dynamic model of a snake-like robot

where, βi(r) is the joint angle of i-th joint; sign(*) is 1 or -1 to regulate the rotation direction of the joint; P is defined as 2×kn×π/N; i=1,…,N. The outputs of the joint patterns are shown in Fig.8.

Fig.6　Snake-like robot model

Table 1　Robot parameter

Links’number(N)9Links’lengthl(mm)200Links’massm(kg)1．833Max．jointtorqueT(N·m)10Totallengthl＿r(mm)1800

The snake-like robot model is composed of 9 links connected with 8 vertical joints. Each joint has one DOF (degree of freedom) which makes the robot realize swimming motion in horizontal plane. The parameters of the experiment system are shown in Table 1.

The body contacting force is set as {0,0, m{i}.g}, m{i} is the mass of i-th link, i=1,…,9. And the reaction force between robot and water is decomposed into x, y and z directions which will propel the robot swimming in the water.

4　Knowledge definition for swimming motion of snake-like robots

+i×P)

果然，推门而入的是一位陌生女人。楚墨点一壶铁观音，问她：“收银台那位，这里的老板？”女子说：“嗯啊。”楚墨问：“他的腿一直这样？”女子说：“嗯啊。”楚墨长舒一口气，我确信楚歌真的看错了。

y(r)=a×cos(b×(r+r0))

泉州属于亚热带海洋性季风气候，多年平均水资源总量达96.78亿m3。但泉州的水资源形势却不容乐观：一是多年人均水资源量仅为1 158 m3，是全国、全省平均水平的1/2和1/3。沿海片区更是严重缺水，石狮、晋江、惠安的人均水资源量仅有102～389 m3，属于绝对贫水区。二是时空降雨分布不均，雨季集中在4—9月份，且70%的水资源量分布在人口较少、经济水平较低的山区。三是蓄水工程偏少，拦蓄调节能力低，出境外流量大，多年平均外流水资源量达34.32亿m3，占全市水资源总量的35.5%。泉州实际可利用的水资源量十分有限，用水紧缺形势日趋明显。

(2)

Here, y(r) is the output of the rhythm (Knowledge); a and b are the constant parameters to regulate the rhythm; r is a variable, here r≥0; r0 is a constant value for the beginning stage, here r0=20000. In order to show that the knowledge is suitable for snake-like robot motion control, the parameters are b=2×kn×π/l_r, and a=λ×sin(kn×π/N)×l_r/(kn×π). An example is shown in Fig.7, where kn=1, π=3.1415926, N=9, l_r=1800, λ=0.4.

良好的通风不仅可以提高室内空气品质，还可以充分利用自然资源，达到节能效果。在南方的春秋季节，自然风可以达到减热的效果，从而尽可能地减少制冷设备的使用，如窗户设置。窗户的位置和窗户的大小都是室内空间设计中需要重点考虑的问题。按照当地的气候特点和风向特征，应合理设置窗户的位置和大小。

In order to control the whole shape of the snake-like robot to imitate the given curve, the rhythm pattern in joint angle space can be given as

βi(r)=sign(*)×a×b×sin(b×(r+r0)

Firstly, the snake-like robot realizes kinematical motion along the given curve formulated as

多进行舞台表演，对演员心理素质的培养以及整体能力的提升是非常有利的。例如，多参加各种晚会、歌唱比赛等活动，多上台进行实践，这样有助于提升声乐演唱中的舞台表演能力，以下两方面的训练是非常必要的。

(3)

The dynamic model of a snake-like robot[20] is developed with V-REP for the study of swimming motion, as shown in Fig.6.

Under a speed v_r=60mm, the variable r changes from 0mm to 120000mm. With given parameters, the snake-like robot can realize swimming motion, as shown in Fig.9. The size of swimming pool is 8m×2m×2m.

糖尿病周围神经病变诊断标准 出现上下肢麻木疼痛,有手套袜套样感,蚁行感,冰冷感,肌无力感,甚至肌肉萎缩,肢体废用,腱反射迟钝或消失,肌电图检查肢体感觉神经、运动神经传导速度减慢等异常。

实验结果显示低压缺氧环境中B组小鼠迅速出现焦躁不安、呼吸加快、喘呼吸、发绀，生存耐受时间为（0.73±0.07）分钟；常压缺氧环境中A组小鼠相对平静，喘呼吸和紫绀出现较晚，生存耐受时间为（10.93±2.07）分钟。两组耐受时间经t检验统计分析，差异具有统计学意义（P＜0.05），说明低压缺氧环境中小鼠耐受性低，生存短，常压缺氧环境中小鼠耐受时间较长。

Fig.7　Rhythm curve

Fig.8　Joint angle patterns

Fig.9　Experimental results

Fig.10　Motion trajectories in Cartesian space

The trajectories of robot head in XYZ plane are shown in Fig.10, and it moves towards a fixed direction.

5　Swimming motion by MNSM-based controller

A MNSM-based controller is developed, as shown in Fig.11, to represent the knowledge for swimming motion control of the snake-like robot.

Fig.11　MNSM-based control system for swimming motion

The dynamics of the MNSM-based controller is shown as

(4)

where C_d_to_r=π/180. The knowledge shown in Fig.12 is the rhythm in XY plane, the phase angle of the rhythm for i-th joint is the output of Mr,i(r).

Fig.12　Rhythm in Cartesian space

With an inhibitory connection from head to tail, a MNSM-based controller is developed to generate corresponding joint pattern. The dynamics of the joint patterns are shown as

花岗闪长斑岩SiO2含量为62.28%～65.78%；Na2O+K2O含量为5.5%～6.44%；里特曼指数σ为1.33～1.97，属钙碱性系列；Na2O/K2O在0.46～0.88之间，属I型花岗岩；A/CNK为1.35～1.45；固结指数SI在8.93～15.05之间，反映岩浆分异程度较高。经对成矿母岩花岗闪长斑岩进行黑云母、白云母K-Ar测年结果分别为120.6Ma和127.6Ma[14]。

βi(r)=

(5)

The outputs of the joint patterns by MNSM-based controller are shown in Fig.13. Here 1，2，…，8-th output of the networks controls the corresponding joints of the snake-like robot.

Fig.13　Joint angle patterns

The errors between the outputs of Fig.8 and Fig.13 are shown in Fig.14.

Based on the mechanism of mirror neuron system, different controllers are developed for the motion control or knowledge presentation for humanoid robots or robotic arms[16-18]. Lu presented typical applications of MNSM based method for motion control of dual robotic arms[18], as shown in Fig.3.

Fig.14　Errors between two outputs

Fig. 15　Absolute errors

The errors are rhythmic, it shows that the joint pattern by the MNSM-based controller is the same knowledge of the curve-based controller. The sums of the errors are shown in Fig.15. With the output of MNSM-based controller, the snake-like robot can reproduce swimming motion of given knowledge. The experimental results are shown in Fig.16.

Fig.16　Experimental results

The snake-like robot swims in water towards a fixed direction. The trajectories in XYZ plane are shown in Fig.17.

喝了酒的李老黑跟没喝酒的李老黑大不一样，简直就是判若两人，这是我那天的一大发现。不喝酒的李老黑天天绷着个黑脸，不怒自威，跟人说话从来不肯多浪费一个字。喝了酒的李老黑脸活泛了，话多了，支书的架子少了。那天李老黑的话实在太多了，如滔滔江水连绵不绝，压得我透不过气来。其实单李老黑话多倒没什么，我洗耳恭听就是了，问题是李老黑的话跟我喝下的酒紧密关联。李老黑说两句，就跟我喝一杯。再说两句，再喝一杯。到后来，我眼巴巴地盯着李老黑的嘴，心里一遍遍祷告它赶紧停下来。

Fig. 17　Motion trajectories in Cartesian space

6　Swimming motion speed regulated by MNSM-based controller

The swimming speed of the snake-like robot can be regulated by the variation speed v_r. The average speeds for different values of v_r (0,0.2,0.4,0.6,0.8,1.2) are shown in Fig.18 . The motion trajectories are shown in Fig.19.

7　Phase modulation knowledge presentation

The proposed MNSM-based controller presented the knowledge of serpenoid curve for each joint, and the new knowledge by phase modulation of Eq.(3) will also generate the corresponding knowledge through Eq.(5).

Fig.18　Average speeds of swimming motion

Fig. 19　Motion trajectories in Cartesian space

Through adding a bias to Eq.(3), a new knowledge to control the movement of the snake-like robot could be got as shown in

βi(r)=sign(*)×a×b×sin(b×(r+r0)

+i×P)+Biasi

(6)

where, Biasi is the bias value of i-th joint, and here all bias value is set as

(7)

where， t<t0 is one stage of swimming knowledge, and t≥t0 is another stage of swimming knowledge. When the knowledge Eq.(6) changes from the state of t<t0 to the state of t≥t0, it will control the snake-like robot to generate a turn motion during swimming, here t0 =20s. The knowledge of joint angle is shown in Fig.20. The trajectory of the robot is shown in Fig.21. The experimental result captured from the video is shown in Fig.22.

Fig.20　Joint angle rhythm of snake-like robot

Fig.21　Swimming trajectory

Fig.22　Experimental results

8　Conclusions

A MNSM-based controller has been proposed to realize knowledge presentation for swimming motion of a snake-like robot. The curve based motion knowledge can be decomposed as rhythm angle, rhythm coordinates in XY plane. By an inhibitory connection of the MNSM-based controller from head to tail, it can represent the curve-based knowledge for swimming motion of the snake-like robot. The experimental results have validated that the proposed MNSM-based controller can realize not only knowledge presentation of curve-based swimming motion of the snake-like robot, but also realize knowledge representation for swimming motion in different speeds and turn motion during swimming.

References

[ 1] Gray J. The mechanism of locomotion in snakes[J]. JournalofExperimentalBiology, 1946, 23(2):101-20

[ 2] Gray J. Undulatory propulsion[J]. JournalofCellScience, 1953, s3-94(28):551-578

[ 3] Jayne B C. Muscular mechanisms of snake locomotion: an electromyographic study of lateral undulation of the Florida banded water snake (Nerodia fasciata) and the yellow rat snake (Elaphe obsoleta)[J]. JournalofMorphology, 1988, 197 (2): 159-181

[ 4] Yamada H, Chigisaki S, Mori M, et al. Development of amphibious snake-like robot ACMR5[C]. In: Proceedings of the 36th International Symposium on Robotics, Tokyo, Japan,2005. 433-440

[ 5] Crespi A, Ijspeert A J. AmphiBot II: An amphibious snake robot that crawls and swims using a central pattern generator[C]. In: Proceedings of the 9th International Conference on Climbing and Walking Robots, Brussels, Belgium. 2006. 19-27

[ 6] Crespi A, Ijspeert A J. Artificial Life Models in Hardware[M]. Berlin: Springer， 2009. 35-64

[ 7] Westphal A, Rulkov N F, Ayers J, et al. Controlling a lamprey-based robot with an electronic nervous system[J]. SmartStructuresandSystems, 2011, 8(1): 39-52

[ 8] Takayama T, Hirose S. Amphibious 3D active cord mechanism “HE-LIX” with Helical swimming motion[C]. In: Proceedings of the 2002 IEEE/RSJ International Conference on Inteligent Robots and Systems, Lausanne, Switzerland, 2002, 775-780

[ 9] Ostrowski J, Burdick J. Gait kinematics for a serpentine robot[C]. In: Proceedings of the 1996 IEEE International Conference on Robotics and Automation, Mineapolis, USA, 1996. 1294-1299

[10] Matsuno F, Suenaga K. Control of redundant 3D snake robot based on kinematic model[C]. In: Proceedings of the 2003 IEEE International Conference on Robotics & Automation, Osaka, Japan, 2003. 2061-2066

[11] Prautsch P, Mita T. Control and analysis of the gait of snake robots[C]. In: Proceedings of the 1999 IEEE International Conference on Control Applications, Kohala Coast, USA, 1999. 502-507

[12] Ute J, Ono K. Fast and efficient locomotion of a snake robot based on self-excitation principle[C]. In: Proceedings of the 7th International Workshop on Advanced Motion Control, Maribor, Slovenia, 2002. 532-539

[13] Brass M, Heyes C. Imitation: is cognitive neuroscience solving the correspondence problem?[J]. TrendsinCognitiveSciences, 2005, 9(10):489-495

[14] Fadiga L, Fogassi L, Pavesi G, et al. Motor facilitation during action observation: a magnetic stimulation study[J]. JournalofNeurophysiology, 1995,73(6): 2608-2611

[15] Shikha A, Mohammad H A. Studying the behaviour of model of mirror neuron system in case of autism[J]. InternationalJournalofScienceandEngineering, 2012, 3(1):1-7

[16] Giorgio M, Giulio S, Lorenzo N, et al. Understanding mirror neurons-a bio-robotic approach[J]. InteractionStudies, 2006, 7(2): 97-23

[17] Fitzpatrick P, Metta G. Grounding vision through experimental manipulation[J]. PhilosophicalTransactions, 2003, 361(1811): 2165

[18] Lu Z, Silva F, Zhang L, et al. MNSM-Inspired method for the motion control of dual-arm robot[C]. In: Proceedings of the 2013 IEEE International Conference on Robotics and Biomimetics (ROBIO 2013), Shenzhen, China, 2013, 1341-1346

[19] Lu Z, Xie Y, Xu H, et al. Design of a MNSM-based controller for the swimming motion of a snake-like robot[C]. In: Proceedings of the 5th Annual IEEE International Conference on Cyber Technology in Automation,Control and Intelligent Systems, Shenyang, China, 2015. 2050-2055

[20] Lu Z, Li B. Dynamics simulation analysison serpentine swimming performance of a snake-like robot[J]. Robot, 2015, 37(6):748-753