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The effects of feedback on stability and maneuverability of a phase-reduced model for cockroach locomotion

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Abstract

In previous work, we built a neuromechanical model for insect locomotion in the horizontal plane, containing a central pattern generator, motoneurons, muscles actuating jointed legs, and rudimentary proprioceptive feedback. This was subsequently simplified to a set of 24 phase oscillators describing motoneuronal activation of agonist–antagonist muscle pairs, which facilitates analyses and enables simulations over multi-dimensional parameter spaces. Here we use the phase-reduced model to study dynamics and stability over the typical speed range of the cockroach Blaberus discoidalis, the effects of feedback on response to perturbations, strategies for turning, and a trade-off between stability and maneuverability. We also compare model behavior with experiments on lateral perturbations, changes in body mass and moment of inertia, and climbing dynamics, and we present a simple control strategy for steering using exteroceptive feedback.

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Figure courtesy of S. Revzen, S. Burden, T. Moore, J-M. Mongeau, and R. Full

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References

  • Ahn A, Full R (2002) A motor and a brake: two leg extensor muscles acting at the same joint manage energy differently in a running insect. J Exp Biol 205:379–389

    PubMed  CAS  Google Scholar 

  • Ahn A, Meijer K, Full R (2006) In situ muscle power differs without varying in vitro mechanical properties in two insect leg muscles innervated by the same motor neuron. J Exp Biol 209:3370–3382

    Article  PubMed  CAS  Google Scholar 

  • Altendorfer R, Moore N, Komsuoglu H, Buehler M, Brown HB Jr, McMordie D, Saranli U, Full R, Koditschek D (2001) RHex: a biologically inspired hexapod runner. Auton Robots 11:207–213

    Article  Google Scholar 

  • Brown I, Scott S, Loeb G (1995) Preflexes—-programmable high-gain zero-delay intrinsic responses of perturbed musculoskeletal systems. Soc Neurosci Abstr 21(562):9

    Google Scholar 

  • Couzin-Fuchs E, Kiemel T, Gal O, Holmes P, Ayali A (2015) Intersegmental coupling and recovery from perturbations in freely-running cockroaches. J Exp Biol 218:285–297

    Article  PubMed  PubMed Central  Google Scholar 

  • Cowan N, Lee J, Full R (2006) Task-level control of rapid wall following in the american cockroach. J Exp Biol 209:1617–1629

    Article  PubMed  CAS  Google Scholar 

  • David I, Holmes P, Ayali A (2016) Endogenous rhythm and pattern generating circuit interactions in cockroach motor centers. Biol Open 5:1229–1240

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  • Delcomyn F (1980) Neural basis of rhythmic behaviors in animals. Science 210:492–498

    Article  PubMed  CAS  Google Scholar 

  • Delcomyn F (2004) Insect walking and robotics. Annu Rev Entomol 149:51–70

    Article  CAS  Google Scholar 

  • Electronic Physics Auxiliary Publication Service E (2009) See document no. e-chaoeh-19-005992 for parameter values and code documentation. http://ftp.aip.org/epaps/chaos/E-CHAOEH-19-005992/. For more information on EPAPS, see http://www.aip.org/pubservs/epaps.html

  • Fuchs E, Holmes P, Kiemel T, Ayali A (2011) Intersegmental coordination of cockroach locomotion: adaptive control of centrally coupled pattern generator circuits. Front Neural Circuits 4:125

    PubMed  PubMed Central  Google Scholar 

  • Fuchs E, Holmes P, David I, Ayali A (2012) Proprioceptive feedback reinforces centrally-generated stepping patterns in the cockroach. J Exp Biol 215:1884–1891

    Article  PubMed  Google Scholar 

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

    PubMed  CAS  Google Scholar 

  • Full R, Tu M (1991) Mechanics of a rapid running insect: two-, four- and six-legged locomotion. J Exp Biol 156:215–231

    PubMed  CAS  Google Scholar 

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

    Article  PubMed  Google Scholar 

  • Ghigliazza R, Holmes P (2004a) A minimal model of a central pattern generator and motoneurons for insect locomotion. SIAM J Appl Dyn Syst 3(4):671–700

    Article  Google Scholar 

  • Ghigliazza R, Holmes P (2004b) Minimal models of bursting neurons: how multiple currents, conductances and timescales affect bifurcation diagrams. SIAM J Appl Dyn Syst 3(4):636–670

    Article  Google Scholar 

  • Goldman D, Chen T, Dudek D, Full R (2006) Dynamics of rapid vertical climbing in a cockroach reveals a template. J Exp Biol 209:2990–3000

    Article  PubMed  Google Scholar 

  • Guckenheimer J, Holmes P (2002) Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, 6th edn. Springer, Berlin

    Google Scholar 

  • Guckenheimer J, Johnson S (1995) Planar hybrid systems. In: Lecture notes in computer science No. 999, Springer, Berlin, pp 202–225

  • Hill A (1938) The heat of shortening and the dynamic constants of muscle. Proc R Soc Lond B 126:136–195

    Article  Google Scholar 

  • Holmes P, Full R, Koditschek D, Guckenheimer J (2006) The dynamics of legged locomotion: models, analyses and challenges. SIAM Rev 48(2):207–304

    Article  Google Scholar 

  • Hoover A, Burden S, Fu X, Sastry S, Fearing R (2010) Bio-inspired design and dynamic maneuverabiliity of a actuated six-legged robot. In: Proceedings of IEEE international conference on biomedical robotics and biomechatronics (BIOROB), pp 869–876

  • Jayaram K, Mongeau JM, McRae B, Full R (2010) High-speed horizontal to vertical transitions in running cockroaches reveals a principle of robustness. In: Society for Integrative and Comparative Biology. http://www.sicb.org/meetings/2010/schedule/ abstractdetails.php3?id=1109

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

    PubMed  Google Scholar 

  • Jindrich D, Full R (2002) Dynamic stabilization of rapid hexapedal locomotion. J Exp Biol 205:2803–2823

    PubMed  Google Scholar 

  • Kram R, Wong B, Full R (1997) Three-dimensional kinematics and limb kinetic energy of running cockroaches. J Exp Biol 200:1919–1929

    PubMed  CAS  Google Scholar 

  • Kubow T, Full R (1999) The role of the mechanical system in control: a hypothesis of self stabilization in hexapedal runners. Philos Trans R Soc Lond B 354:849–861

    Article  Google Scholar 

  • Kukillaya R, Holmes P (2007) A hexapedal jointed-leg model for insect locomotion in the horizontal plane. Biol Cybern 97:379–395

    Article  PubMed  Google Scholar 

  • Kukillaya R, 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 

  • Kukillaya R, Proctor J, Holmes P (2009) Neuro-mechanical models for insect locomotion: stability, maneuverability, and proprioceptive feedback. CHAOS Interdiscip J Nonlinear Sci 19(2):026107

    Article  CAS  Google Scholar 

  • Lee J, Sponberg S, Loh O, Lamperski A, Full R, Cowan N (2008) Templates and anchors for antenna-based wall following in cockroaches. IEEE Trans Robot 24(1):130–143

    Article  Google Scholar 

  • Mongeau JM, Alexander T, Full R (2012) Neuromechanical feedback during dynamic recovery after a lateral perturbation in rapid running cockroaches. In: Society for Integrative and Comparative Biology. http://www.sicb.org/meetings/2012/schedule/abstractdetails.php ?id=555

  • Moore T, Revzen S, Burden S, Full R (2010) Adding inertia and mass to test stability predictions in rapid running insects. In: Society for Integrative and Comparative Biology. http://www.sicb.org/meetings/2010/schedule/abstractdetails.php 3?id=1290

  • Pearson K (1972) Central programming and reflex control of walking in the cockroach. J Exp Biol 56:173–193

    Google Scholar 

  • Pearson K, Iles J (1970) Discharge patterns of coxal levator and depressor motoneurones in the cockroach Periplaneta americana. J Exp Biol 52:139–165

    PubMed  CAS  Google Scholar 

  • Pearson K, Iles J (1971) Innervation of the coxal depressor muscles in the cockroach Periplaneta americana. J Exp Biol 54:215–232

    PubMed  CAS  Google Scholar 

  • Pearson K, Iles J (1973) Nervous mechanisms underlying intersegmental co-ordination of leg movements during walking in the cockroach. J Exp Biol 58:725–744

    Google Scholar 

  • Proctor J, Holmes P (2008) Steering by transient destabilization in piecewise-holonomic models of legged locomotion. Regul Chaotic Dyn 13(4):267–282

    Article  Google Scholar 

  • Proctor J, Holmes P (2010) Reflexes and preflexes: on the role of sensory feedback on rhythmic patterns in legged locomotion. Biol Cybern 2:513–531

    Article  Google Scholar 

  • Proctor J, Kukillaya R, Holmes P (2010) A phase-reduced neuro-mechanical model for insect locomotion: feed-forward stability and proprioceptive feedback. Philos Trans R Soc A 368:5087–5104

    Article  CAS  Google Scholar 

  • Revzen S, Burden S, Moore T, Mongeau JM, Full R (2013) Instantaneous kinematic phase reflects neuromechanical response to lateral perturbations of running cockroaches. Biol Cybern 107:179–200

    Article  PubMed  Google Scholar 

  • Schmitt J, Bonnono S (2009) Dynamics and stability of lateral plane locomotion on inclines. J Theor Biol 261:598–609

    Article  PubMed  CAS  Google Scholar 

  • 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 (2003) Mechanical models for insect locomotion: active muscles and energy losses. Biol Cybern 89(1):43–55

    PubMed  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 

  • Sefati S, Neveln I, Roth E, Mitchell T, Snyder J, MacIver M, Fortune E, Cowan N (2013) Mutually opposing forces during locomotion can eliminate the tradeoff between maneuverability and stability. Proc Natl Acad Sci 110(47):18798–18803

    Article  PubMed  CAS  Google Scholar 

  • Seipel J, Holmes P, Full R (2004) Dynamics and stability of insect locomotion: a hexapedal model for horizontal plane motion. Biol Cybern 91(2):76–90

    Article  PubMed  Google Scholar 

  • Sponberg S, Full R (2008) Neuromechanical response of musculo-skeletal structures in cockroaches during rapid running on rough terrain. J Exp Biol 211:433–446

    Article  PubMed  CAS  Google Scholar 

  • Sponberg S, Spence A, Mullens C, Full R (2011) A single muscle’s multifunctional control potential of body dynamics for postural control and running. Philos Trans Roy Soc B 366:1592–1605

    Article  Google Scholar 

  • Ting L, Blickhan R, Full R (1994) Dynamic and static stability in hexapedal runners. J Exp Biol 197:251–269

    PubMed  CAS  Google Scholar 

  • Zill S, Moran D (1981a) The exoskeleton and insect proprioception I. Responses of tibial campaniform sensilla to external and muscle-generated force in the American cockroach Periplaneta americana. J Exp Biol 91:1–24

    Google Scholar 

  • Zill S, Moran D (1981b) The exoskeleton and insect proprioception III. Activity of tibial campaniform sensilla during walking in the American cockroach Periplaneta americana. J Exp Biol 94:57–75

    Google Scholar 

  • Zill S, Moran D, Varela F (1981) The exoskeleton and insect proprioception II. Reflex effects of tibial campaniform sensilla in the American cockroach Periplaneta americana. J Exp Biol 94:43–55

    Google Scholar 

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Acknowledgements

This work was partially supported by NSF EF-0425878 (Frontiers in Biological Research), NSF DMS-1430077 (CRCNS U.S.-German Collaboration) and Princeton’s J. Insley Blair Pyne Fund. We thank the anonymous reviewers for their useful suggestions and for helping us to correct several errors.

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Authors and Affiliations

  1. Institute for Disease Modeling, 3150, 139th Ave SE, Bellevue, WA, 98005, USA

    J. L. Proctor

  2. Department of Mechanical and Aerospace Engineering, Program in Applied and Computational Mathematics and Princeton Neuroscience Institute, Princeton University, Princeton, NJ, 08544, USA

    P. Holmes

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  1. J. L. Proctor
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  2. P. Holmes
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Correspondence to P. Holmes.

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Communicated by J. Leo van Hemmen.

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Proctor, J.L., Holmes, P. The effects of feedback on stability and maneuverability of a phase-reduced model for cockroach locomotion. Biol Cybern 112, 387–401 (2018). https://doi.org/10.1007/s00422-018-0762-1

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