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Lateral undulation of the flexible spine of sprawling posture vertebrates

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Abstract

Sprawling posture vertebrates have a flexible spine that bends the trunk primarily in the horizontal plane during locomotion. By coordinating cyclical lateral trunk flexion and limb movements, these animals are very mobile and show extraordinary maneuverability. The dynamic and static stability displayed in complex and changing environments are highly correlated with such lateral bending patterns. The axial dynamics of their compliant body can also be critical for achieving energy-efficient locomotion at high velocities. In this paper, lateral undulation is used to characterize the bending pattern. The production of ground reaction forces (GRFs) and the related center of mass (COM) dynamics during locomotion are the fundamental mechanisms to be considered. Mainly based on research on geckos, which show unrestricted movement in three-dimensional space, we review current knowledge on the trunk flexibility and waveforms of lateral trunk movement. We investigate locomotion dynamics and mechanisms underlying the lateral undulation pattern. This paper also provides insights into the roles of this pattern in obtaining flexible and efficient walking, running, and climbing. Finally, we discuss the potential application of lateral undulation patterns to bio-inspired robotics.

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Abbreviations

GRFs:

Ground reaction forces

COM:

Center of mass

SLIP:

Spring loaded inverted pendulum

LLS:

Lateral leg spring

References

  • Aerts P, Van DR, Van EL, Duchêne V (2000) Spatio-temporal gait characteristics of the hind-limb cycles during voluntary bipedal and quadrupedal walking in bonobos (Pan paniscus). Am J Physical Anthropol 111(4):503

    Article  CAS  Google Scholar 

  • Altendorfer R, Moore N, Komsuoglu H, Buehler M, Brown JR, Mcmordie D, Saranli U, Full RJ, Koditschek DE (2001) RHex: a biologically inspired hexapod runner. Auton Robot 11(3):207–213

    Article  Google Scholar 

  • Ashley-Ross MA (1994a) Hindlimb kinematics during terrestrial locomotion in a salamander (Dicamptodon tenebrosus). J Exp Biol 193(1):255–283

    PubMed  CAS  Google Scholar 

  • Ashley-Ross MA (1994b) Metamorphic and speed effects on hindlimb kinematics during terrestrial locomotion in the salamander Dicamptodon tenebrosus. J Exp Biol 193(1):285

    PubMed  CAS  Google Scholar 

  • Autumn K (2002) Mechanisms of adhesion in geckos. Integr Comp Biol 42(6):1081–1090

    Article  PubMed  Google Scholar 

  • Autumn K, Buehler M, Cutkosky M et al (2005) Robotics in scansorial environments. Proc SPIE 5804:291–302

    Article  Google Scholar 

  • Autumn K, Hsieh ST, Dudek DM et al (2006) Dynamics of geckos running vertically. J Exp Biol 209(2):260–272

    Article  PubMed  CAS  Google Scholar 

  • Avery RA, Mueller CF, Smith JA, Bond DJ (1987) The movement patterns of lacertid lizards: speed, gait and pauses in Lacerta vivipara. J Zool 211(1):47–63

    Article  Google Scholar 

  • Azizi E, Horton JM (2004) Patterns of axial and appendicular movements during aquatic walking in the salamander Siren lacertina. Zoology 107(2): 111–120

  • Barclay OR (1946) The mechanics of amphibian locomotion. J Exp Biol 23(2):177–203

    PubMed  CAS  Google Scholar 

  • Bennett WO, Simons RS, Brainerd EL (2001) Twisting and bending: the functional role of salamander lateral hypaxial musculature during locomotion. J Exp Biol 204(11):1979–1989

    PubMed  CAS  Google Scholar 

  • Bertram JEA, Gutmann A (2009) Motions of the running horse and cheetah revisited: fundamental mechanics of the transverse and rotary gallop. J R Soc Interface 6(35):549–559

    Article  PubMed  Google Scholar 

  • Blickhan R (1989) The spring-mass model for running and hopping. J Biomech 22(11–12):1217

    Article  PubMed  CAS  Google Scholar 

  • Blickhan R, Full RJ (1993) Similarity in multilegged locomotion: bouncing like a monopode. J Comp Physiol A 173(5):509–517

    Article  Google Scholar 

  • Breithaupt R, Dahnke J, Zahedi K, Hertzberg J, Pasemann F (2002) Robo-Salamander-an approach for the benefit of both robotics and biology. In: 5th International Conference on Climbing and Walking Robots, pp 55–62

  • Cabelguen J, Ijspeert A, Lamarque S, Ryczko D (2010) Axial dynamics during locomotion in vertebrates: lesson from the salamander. Prog Brain Res 187:149–162

    Article  PubMed  Google Scholar 

  • Carrier D (1990) Activity of the hypaxial muscles during walking in the lizard Iguana iguana. J Exp Biol 152(1):453–470

    PubMed  CAS  Google Scholar 

  • Cavagna GA, Heglund NC, Taylor CR (1977) Mechanical work in terrestrial locomotion: two basic mechanisms for minimizing energy expenditure. Am J Physiol 233(5):243–261

    Google Scholar 

  • Chen JJ, Peattie AM, Autumn K, Full RJ (2006) Differential leg function in a sprawling posture quadrupedal trotter. J Exp Biol 209(2):249–259

    Article  PubMed  CAS  Google Scholar 

  • Clark JE, Goldman DI, Chen TS, Full RJ, Koditschek D (2006) Toward a dynamic vertical climbing robot. In Belgium, Brussels: International Conference On Climbing And Walking Robots (CLAWAR), Sep 2006

  • Clark JE, Goldman DI, Pei-Chun L, Lynch G, Chen TS, Komsuoglu H, Full RJ, Koditschek D (2007) Design of a bio-inspired dynamical vertical climbing robot. In Atlanta, USA: Proceedings of Robotics: Science and Systems, June 2007

  • Cohen AH (1988) Evolution of the vertebrate central pattern generator for locomotion. In: Cohen AH, Rossignol S, Grillner S (eds) Neural control of rhythmic movements in vertebrates. Wiley Inter-Science, New York, pp 129–166

    Google Scholar 

  • Crespi A, Karakasiliotis K, Guignard A, Ijspeert AJ (2013) Salamandra robotica II: an amphibious robot to study salamander-like swimming and walking gaits. IEEE T Robot 29(2):308–320

    Article  Google Scholar 

  • Daan S, Belterman T (1968) Lateral bending in locomotion of some lower tetrapods. Proc Koninklijke Nederlandse Akademie van Wetenschappen Series C 71(3):245–266

    Google Scholar 

  • Dai ZD, Ji AH (2011) Biomechanical base for bioinspiration of gecko locomotion. Harbin Institute of Technology Press, Harbin

    Google Scholar 

  • Dai ZD, Yu M, Ji AH, Guo C, Zhang H (2005) Study on tribological characteristics of animals’ driving pads and their bionic design. Chin Mech Eng 16(16):1454–1457

    Google Scholar 

  • De A, Lynch G, Johnson A, Koditschek D (2011) Motor selection using task specifications and thermal limits. In: IEEE International Conference on Technologies for Robot Applications, 2011

  • Deban SM, Schilling N (2009) Activity of trunk muscles during aquatic and terrestrial locomotion in Ambystoma maculatum. J Exp Biol 212(18):2949–2959

    Article  PubMed  Google Scholar 

  • Delvolvé I, Bem T, Cabelguen JM (1997) Epaxial and limb muscle activity during swimming and terrestrial stepping in the adult newt, Pleurodeles waltl. J Neurophysiol 78(2):638–650

    Article  PubMed  Google Scholar 

  • Dickinson MH, Farley CT, Full RJ, Koehl MA, Kram R, Lehman S (2000) How animals move: an integrative view. Science 288(5463):100–106

    Article  PubMed  CAS  Google Scholar 

  • Edwards JL (1977) The evolution of terrestrial locomotion. In: Hetch M, Goody P, Hetch B (eds) Major patterns in vertebrate evolution. Plenum, New York, pp 553–576

    Chapter  Google Scholar 

  • English AW (1980) The functions of the lumbar spine during stepping in the cat. J Morphol 165(1):55–66

    Article  PubMed  Google Scholar 

  • Farley CT, Ko TC (1997) Mechanics of locomotion in lizards. J Exp Biol 200(16):2177–2188

    PubMed  CAS  Google Scholar 

  • Frolich LM, Biewener AA (1992) Kinematic and electromyographic analysis of the functional role of the body axis during terrestrial and aquatic locomotion in the salamander Ambystoma tigrinum. J Exp Biol 162(1):107–130

    Google Scholar 

  • Full RJ, Koditschek D (1999) Templates and anchors: neuromechanical hypotheses of legged locomotion on land. J Exp Biol 202(23):3325–3332

    PubMed  CAS  Google Scholar 

  • Full RJ, Tu MS (1991) Mechanics of a rapid running insect: two-, four- and six-legged locomotion. J Exp Biol 156(3):215

    PubMed  CAS  Google Scholar 

  • Full RJ, Blickhan R, Ting LH (1991) Leg design in hexapedal runners. J Exp Biol 158(1):369–390

    PubMed  CAS  Google Scholar 

  • Full RJ, Kubow T, Schmitt J, Holmes P, Koditschek D (2002) Quantifying dynamic stability and maneuverability in legged locomotion. Integr Comp Biol 42(1):149–157

    Article  PubMed  Google Scholar 

  • Gál JM (1993a) Mammalian spinal biomechanics. I. Static and dynamic mechanical properties of intact intervertebral joints. J Exp Biol 174(1):247–280

    PubMed  Google Scholar 

  • Gál JM (1993b) Mammalian spinal biomechanics. II. Intervertebral lesion experiments and mechanisms of bending resistance. J Exp Biol 174:S 3–4): 281

    Google Scholar 

  • Gambaryan PP (1974) How mammals run: anatomical adaptations. Wiley, New York

    Google Scholar 

  • Goldman DI, Chen TS, Dudek DM, Full RJ (2006) Dynamics of rapid vertical climbing in a cockroach reveals a template. J Exp Biol 209(15):2990–3000

    Article  PubMed  Google Scholar 

  • Hildebrand M (1985) Walking and running. In: Hildebrand M, Bramble DL, Liem KF, Wake DB (eds) Functional vertebrate morphology. Harvard University Press, Cambridge, pp 38–57

    Chapter  Google Scholar 

  • Hill WO (1953) Primates: comparative anatomy and taxonomy. Edinburgh University Press, Edinburgh

    Google Scholar 

  • Ijspeert AJ (2001) A connectionist central pattern generator for the aquatic and terrestrial gaits of a simulated salamander. Biol Cybern 84(5):331–348

    Article  PubMed  CAS  Google Scholar 

  • Ijspeert AJ (2014) Biorobotics: using robots to emulate and investigate agile locomotion. Science 346(6206):196–203

    Article  PubMed  CAS  Google Scholar 

  • Ijspeert AJ, Crespi A, Ryczko D, Cabelguen JM (2007) From swimming to walking with a salamander robot driven by a spinal cord model. Science 315(5817):1416–1420

    Article  PubMed  CAS  Google Scholar 

  • Jenkins FA, Camazine SM (1977) Hip structure and locomotion in ambulatory and cursorial carnivores. J Zool 181(3):351–370

    Article  Google Scholar 

  • Ji AH, Han LB, Dai ZD (2011) Adhesive contact in animal: morphology, mechanism and bio-inspired application. J Bionic Eng 8(4):345–356

    Article  Google Scholar 

  • Ji AH, Lei YF, Wang ZY, Dong BZ, Yao N, Dai ZD (2014) Balancing strategy to lateral impact in a rat Rattus norvegicus. J Bionic Eng 59:1249–1257

    Google Scholar 

  • Jindrich DL, Full RJ (1999) Many-legged maneuverability: dynamics of turning in hexapods. J Exp Biol 202(12):1603–1623

    PubMed  Google Scholar 

  • Jusufi A, Goldman DI, Revzen S, RJ Full (2008) Active tails enhance arboreal acrobatics in geckos. P Natl Acad Sci USA 105(11):4215–4219

    Article  Google Scholar 

  • Karakasiliotis K (2013) Legged locomotion with spinal undulations. PhD thesis, Lausanne: Swiss federal Institute of Technology in Lausanne

  • Karakasiliotis K, Ijspeert AJ (2009) Analysis of the terrestrial locomotion of a salamander robot. In: 2009 IEEE/RSJ International Conference on Intelligent Robots and Systems

  • Karakasiliotis K, Schilling N, Cabelguen J, Ijspeert AJ (2013) Where are we in understanding salamander locomotion: biological and robotic perspectives on kinematics. Biol Cybern 107(5):529–544

    Article  PubMed  Google Scholar 

  • Karakasiliotis K, Thandiackal R, Melo K, Horvat T, Mahabadi NK, Tsitkov S, Cabelguen JM, Ijspeert AJ (2016) From cineradiography to biorobots: an approach for designing robots to emulate and study animal locomotion. J R Soc Interface 13(119):20151089

    Article  PubMed  PubMed Central  Google Scholar 

  • Kim S, Asbeck AT, Cutkosky MR, Provancher WR (2015) SpinybotII: climbing hard walls with compliant microspines. In: Seattle, WA: Proceedings, IEEE, ICAR, PP 601–605

  • Knuesel J, Ijspeert AJ (2011) Effects of muscle dynamics and proprioceptive feedback on the kinematics and CPG activity of salamander stepping. Bmc Neurosci 12(1):1–2

    Article  CAS  Google Scholar 

  • Knuesel H, Geyer H, Seyfarth A (2005) Influence of swing leg movement on running stability. Hum Movement Sci 24(4):532–543

    Article  Google Scholar 

  • Krause C, Fischer MS (2013) Biodynamics of climbing: effects of substrate orientation on the locomotion of a highly arboreal lizard (Chamaeleo calyptratus). J Exp Biol 216(8):1448–1457

    Article  PubMed  Google Scholar 

  • Kukillaya RP, Holmes P (2009) A model for insect locomotion in the horizontal plane: Feedforward activation of fast muscles, stability, and robustness. J Theor Biol 261(2):210–226

    Article  PubMed  Google Scholar 

  • Lamarque S, Ryczko D, Didier H, Cabelguen JM (2009) Dynamics of the axial locomotor network in intact, freely moving salamanders. In: 31st International Symposium GRSNC: Breathe, walk and chew—the neural challenge: Abstr. 22

  • Libby T, Moore TY, Chang-Siu E, Li D, Cohen DJ, Jusufi A, Full RJ (2012) Tail-assisted pitch control in lizards, robots and dinosaurs. Nature 481(7380):181–184

    Article  PubMed  CAS  Google Scholar 

  • Lynch GA, Rome L, Koditschek D (2011) Sprawl angle in simplified models of vertical climbing: Implications for robots and roaches. Appl Bionics Biomech 8(3–4):441–452

    Article  Google Scholar 

  • Manoonpong P (2007) Neural preprocessing and control of reactive walking machines: towards versatile artificial perception-action systems: cognitive Technologies, Springer

  • Manoonpong P, Parlitz U, Wörgötter F (2013) Neural control and adaptive neural forward models for insect-like, energy-efficient, and adaptable locomotion of walking machines. Front Neural Circuit 7(3):12

    Google Scholar 

  • Martinez MM, Full RJ, Koehl M (1998) Underwater punting by an intertidal crab: a novel gait revealed by the kinematics of pedestrian locomotion in air versus water. J Exp Biol 201(18):2609–2623

    PubMed  Google Scholar 

  • Nam W, Seo T, Kim B, Jeon D, Choi K, Kim J (2009) Kinematic analysis and experimental verification on the locomotion of gecko. J Bionic Eng 6(3):246–254

    Article  Google Scholar 

  • Nyakatura JA, Fischer MS (2010) Functional morphology and three-dimensional kinematics of the thoraco-lumbar region of the spine of the two-toed sloth. J Exp Biol 213(24):4278–4290

    Article  PubMed  Google Scholar 

  • Ritter D (1992) Lateral bending during lizard locomotion. J Exp Biol 173(1):1–10

    Google Scholar 

  • Ritter D (1995) Epaxial muscle function during locomotion in a lizard (Varanus salvator) and the proposal of a key innovation in the vertebrate axial musculoskeletal system. J Exp Biol 198(12):2477–2490

    PubMed  CAS  Google Scholar 

  • Ritter D (1996) Axial muscle function during lizard locomotion. J Exp Biol 199(11):2499–2510

    PubMed  CAS  Google Scholar 

  • Roos PJ (1964) Lateral bending in newt locomotion. Proc Kon Ned Akad Wet (C) 67:223–232

    Google Scholar 

  • Rubin CT, Lanyon LE (1982) Limb mechanics as a function of speed and gait: a study of functional strains in the radius and tibia of horse and dog. J Exp Biol 101(3):187–211

    PubMed  CAS  Google Scholar 

  • Schilling N, Carrier DR (2009) Function of the epaxial muscles during trotting. J Exp Biol 212(7):1053–1063

    Article  PubMed  Google Scholar 

  • Schilling N, Hackert R (2006) Sagittal spine movements of small therian mammals during asymmetrical gaits. J Exp Biol 209(19):3925–3939

    Article  PubMed  Google Scholar 

  • Schmiedeler JP (2001) The mechanics of and robotic design for quadrupedal galloping. PhD thesis, Columbus: The Ohio State University

  • Schmitt J, Holmes P (2000) Mechanical models for insect locomotion: dynamics and stability in the horizontal plane I. Theory. Biol Cybern 83(6):501–515

    Article  PubMed  CAS  Google Scholar 

  • Schmitt J, Holmes P (2001) Mechanical models for insect locomotion: stability and parameter studies. Physica D Nonlinear Phenomena 156(1–2):139–168

    Article  Google Scholar 

  • Schmitt J, Garcia M, Razo RC, Holmes P, Full RJ (2002) Dynamics and stability of legged locomotion in the horizontal plane: a test case using insects. Biol Cybern 86(5):343–353

    Article  PubMed  CAS  Google Scholar 

  • Ting LH, Blickhan R, Full RJ (1994) Dynamic and static stability in hexapedal runners. J Exp Biol 197(6):251

    PubMed  CAS  Google Scholar 

  • Walker A (1969) The locomotion of the lorises, with special reference to the potto. Afr J Ecol 7(1):1–5

    Article  Google Scholar 

  • Walter RM, Carrier DR (2002) Scaling of rotational inertia in murine rodents and two species of lizard. J Exp Biol 205(14):2135–2141

    PubMed  Google Scholar 

  • Wang ZY, Gu WW, Wu Q, Ji AH, Dai ZD (2010) Morphology and reaction force of toes of geckos freely moving on ceilings and walls. Sci China Technol Sc 53(6):1688–1693

    Article  Google Scholar 

  • Wang ZY, Wang JT, Ji AH, Zhang YY, Dai ZD (2011) Behavior and dynamics of gecko’s locomotion: the effects of moving directions on a vertical surface. Chin Sci Bull 56(6):573–583

    Article  Google Scholar 

  • Wang ZY, Ji AH, Endlein T, Li W, Samuel D, Dai ZD (2014) Locomotor kinematics of the gecko (tokay gecko) upon challenge with various inclines. Chin Sci Bull 59(33):4568–4577

    Article  Google Scholar 

  • Wang W, Wu S, Zhu P, Liu R (2015a) Analysis on the dynamic climbing forces of a gecko inspired climbing robot based on GPL model. In Hamburg, Germany: 2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp 3314–3319

  • Wang ZY, Cai L, Li W, Ji AH, Wang WB, Dai ZD (2015b) Effect of slope degree on the lateral bending in Gekko gecko. J Bionic Eng 12(2):238–249

    Article  Google Scholar 

  • Wang ZY, Dai ZD, Ji AH, Ren L, Xing Q, Dai LM (2015c) Biomechanics of gecko locomotion: the patterns of reaction forces on inverted, vertical and horizontal substrates. Bioinspir Biomim 10(1):16019

    Article  Google Scholar 

  • Zaaf A, Van Damme R, Herrel A, Aerts P (2001) Spatio-temporal gait characteristics of level and vertical locomotion in a ground-dwelling and a climbing gecko. J Exp Biol 204(7):1233–1246

    PubMed  CAS  Google Scholar 

  • Zhang H (2010) Research on gecko’s moving behavior and developing gecko-like robot. PhD thesis, Nanjing: Nanjing University of Aeronautics and Astronautics

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Acknowledgements

The authors thank Dr. Guangming Chen from the University of Aeronautics and Astronautics for his constructive comments on this paper. This work was supported by the National Natural Science of Foundation of China (Grant No. 51375232, 51475230) and the Key Research and Development Plan of Jiangsu Province (Grant No. BE2017766). Poramate Manoonpong acknowledges funding by the Thousand Talents Program of China.

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Authors and Affiliations

  1. Institute of Bio-Inspired Structure and Surface Engineering, Nanjing University of Aeronautics and Astronautics, 29 Yudao Street, Nanjing, 210016, China

    Wei Wang, Aihong Ji, Poramate Manoonpong, Huan Shen, Jie Hu, Zhendong Dai & Zhiwei Yu

  2. College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, China

    Wei Wang & Huan Shen

  3. Embodied AI and Neurorobotics Lab, Centre for Biorobotics, Mærsk Mc-Kinney Møller Institute, University of Southern Denmark, Odense, Denmark

    Poramate Manoonpong

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  1. Wei Wang
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  2. Aihong Ji
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  3. Poramate Manoonpong
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  4. Huan Shen
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  5. Jie Hu
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  7. Zhiwei Yu
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Correspondence to Aihong Ji.

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Wang, W., Ji, A., Manoonpong, P. et al. Lateral undulation of the flexible spine of sprawling posture vertebrates. J Comp Physiol A 204, 707–719 (2018). https://doi.org/10.1007/s00359-018-1275-z

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