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Instantaneous kinematic phase reflects neuromechanical response to lateral perturbations of running cockroaches

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Abstract

Instantaneous kinematic phase calculation allows the development of reduced-order oscillator models useful in generating hypotheses of neuromechanical control. When perturbed, changes in instantaneous kinematic phase and frequency of rhythmic movements can provide details of movement and evidence for neural feedback to a system-level neural oscillator with a time resolution not possible with traditional approaches. We elicited an escape response in cockroaches (Blaberus discoidalis) that ran onto a movable cart accelerated laterally with respect to the animals’ motion causing a perturbation. The specific impulse imposed on animals (0.50 \(\pm \) 0.04 m s\(^{-1}\); mean, SD) was nearly twice their forward speed (0.25 \(\pm \) 0.06 m s\(^{-1})\). Instantaneous residual phase computed from kinematic phase remained constant for 110 ms after the onset of perturbation, but then decreased representing a decrease in stride frequency. Results from direct muscle action potential recordings supported kinematic phase results in showing that recovery begins with self-stabilizing mechanical feedback followed by neural feedback to an abstracted neural oscillator or central pattern generator. Trials fell into two classes of forward velocity changes, while exhibiting statistically indistinguishable frequency changes. Animals pulled away from the side with front and hind legs of the tripod in stance recovered heading within 300 ms, whereas animals that only had a middle leg of the tripod resisting the pull did not recover within this period. Animals with eight or more legs might be more robust to lateral perturbations than hexapods.

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Notes

  1. When the series all have the same amplitude this is precisely the circular average (Fisher 1993) of their phase angles.

Abbreviations

Axes:

Y-axis is positive along the line of platform translation. Also called lateral axis. Z-axis is perpendicular to the Y-axis, positive vertical of the platform. X-axis is perpendicular to both the Y- and Z-axes, and positive in the direction of cockroach locomotion. Also called the forward axis

Vx:

Component of cockroach velocity in trackway direction

Vy:

Component of cockroach velocity across trackway

COM:

Center of mass

CPG:

Central pattern generator

EMG:

Electromyography

IBI:

Inter-burst interval. The time between two bursts of muscle action potentials in an electromyography

ISI:

Inter-spike interval

LLS:

Lateral leg spring model

MAP:

Muscle action potential

PCA:

Principal component analysis

LLS:

Lateral leg spring model

AEP:

Anterior extreme position. The transition from swing to stance.

PEP:

Posterior extreme position. The transition from stance to swing.

SLIP:

Spring loaded inverted pendulum model

\(\varPhi \) :

Phase threshold between classes (one class has \(\varPhi -\pi <\phi _{0} < \varPhi \), the other \(\varPhi < \phi _{0} < \varPhi + \pi \))

\(\phi _{0}\) :

Predictor phase

\(\phi , \theta \) :

Phases

\(\omega \) :

Derivative of phase with respect to time, i.e. instantaneous frequency

\(\Delta \phi \) :

Residual phase

\(x, v\) :

Position, velocity time series used to create complex phase time series

\(z \) :

Complex phase time series \(\langle .\rangle \) mean value; \(\langle w(t)\rangle \) is the expectation of the variable \(w(t)\)

\(t_{1\text{ pre}}\) :

Starting time window pre-perturbation

\(t_{2\text{ pre}}\) :

Ending time window pre-perturbation

\(t_{\text{ step}}\) :

Step duration

\(t_{\text{ on}}\) :

Onset of perturbation

\(t_{1\text{ post}}\) :

Starting time window post-perturbation

\(t_{2\text{ post}}\) :

Ending time window post-perturbation

std:

Standard deviation operator; std[\(w(t)\)] is the standard deviation of the variable \(w(t)\)

exp:

(Complex) exponential function

arg:

Complex argument (i.e., polar angle) function

C\(_{0}\) :

Class 0, one of the two phase classes (in red)

C\(_{1}\) :

Class 1, one of the two phase classes (in blue)

Vx\(_{0}\) :

Mean of cockroach velocity in trackway direction for C\(_{0}\)

Vx\(_{1}\) :

Mean of cockroach velocity in trackway direction for C\(_{1}\)

L\(_{1}\) norm:

Sum of absolute differences

L\(_{2}\) norm:

Square root of sum of squared differences, same as root mean square (RMS) up to a scale

\(N\) :

Parameter governing the number of bootstrap trials used for testing classification significance; \(N^{2}\) trials for H\(_{1}\) and H\(_{0(\mathrm{a})}\) are compared with a nested bootstrap of \(N\) trials of \(N\) nested trials each.

\(n\) :

Number of trials provided by an individual animal

H\(_{1}\) :

Statistical hypothesis that classes the C\(_{0}\) and C\(_{1}\) obtained from \(\phi _{ 0}\) and \(\varPhi \) describe animals that behave differently.

H\(_{0(\mathrm{a})}\) :

Statistical hypothesis that trial classes C\(_{0}\) and C\(_{1}\) are selected at random from the same distribution of animal motions.

H\(_{0(\mathrm{b}) }\) :

Statistical hypothesis that trial classes C\(_{0}\) and C\(_{1}\) are selected to be most dissimilar classes that can be obtained based on a choice of \(\varPhi \), while still being selected at random from the same distribution of animal motions.

\(\chi ^{2}\) :

Statistical distribution and associated test

References

  • Ahn AN, Full RJ (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(3):379–389

    PubMed  CAS  Google Scholar 

  • Ahn AN, Meijer K, Full RJ (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(17), 3370–3382. ISSN 0022-0949. doi:10.1242/jeb.02392

    Google Scholar 

  • Altendorfer R, Koditschek DE, Holmes P (2004) Stability analysis of legged locomotion models by symmetry-factored return maps. Int J Rob Res. 23(10–11):979–999

    Article  Google Scholar 

  • Altendorfer R, Moore N, Komsuolu H, Buehler M, Brown HB, McMordie D, Saranli U, Full RJ, Koditschek DE (2001) Rhex: a biologically inspired hexapod runner. Auton Rob 11(3):207–213. ISSN 1573-7527. doi:10.1023/A:1012426720699

    Google Scholar 

  • Bachmann RJ, Boria FJ, Vaidyanathan R, Ifju PG, Quinn RD (2009) A biologically inspired micro-vehicle capable of aerial and terrestrial locomotion. Mech Mach Theory 44(3):513–526. ISSN 0094-114X doi:10.1016/j.mechmachtheory.2008.08.008

    Google Scholar 

  • Bender JA, Pollack AJ, Ritzmann RE (2010) Neural activity in the central complex of the insect brain is linked to locomotor changes. Curr Biol 20:921–926

    Article  PubMed  CAS  Google Scholar 

  • Büschges A (2005) Sensory control and organization of neural networks mediating coordination of multisegmental organs for locomotion. J Neurophysiol 93:1127–1135. doi:10.1152/jn.00615.2004

    Article  PubMed  Google Scholar 

  • Büschges A, Scholz H, El-Manira A (2011) New moves in motor control. Curr Biol 21:R513–R524. doi:10.1016/j.cub.2011.05.029

    Article  PubMed  Google Scholar 

  • Carbonell C (1947) The thoracic muscles of the cockroach Periplaneta americana (L.). Smith Misc Coll 107:1–23

    Google Scholar 

  • Cruse H, Knauth A (1989) Coupling mechanisms between the contralateral legs of a walking insect (Carausius morosus). J Exp Biol 144:199–213

    Google Scholar 

  • Cruse H, Schwarze W (1988) Mechanisms of coupling between the ipsilateral legs of a walking insect (Carausius morosus). J Exp Biol 138:455–469

    Google Scholar 

  • Cruse H, Durr V, Schmitz J (2007) Insect walking is based on a decentralized architecture revealing a simple and robust controller. Philos Trans R Soc A 365(1850):221–250

    Article  Google Scholar 

  • Cruse H, Kinderman T, Schumm M, Dean J, Schmitz J (1998) Walknet—a biologically inspired network to control six-legged walking. Neural Netw. 11(7–8):1435–1447

    Article  PubMed  Google Scholar 

  • Delcomyn F (1980) Neural basis of rhythmic behavior in animals. Science 210(4469):492–498. doi:10.1126/science.7423199

    Article  PubMed  CAS  Google Scholar 

  • Dudek DM, Full RJ (2007) An isolated insect leg’s passive recovery from dorso-ventral perturbations. J Exp Biol 210:3209–3217. doi:10.1242/jeb.008367

    Article  PubMed  Google Scholar 

  • Duysens J, Clarac, Cruse H (2000) Load-regulating mechanisms in gait and posture: comparative aspects. Physiol Rev 80(1):83–133. ISSN 0031-9333. http://physrev.physiology.org/cgi/content/abstract/80/1/83

  • Fisher NI (1993) Statistical analysis of circular data. Cambridge University Press, Cambridge. ISBN 0-521-35018-2

  • Floquet G (1883) Sur les Equations différentielles linéaires à coefficients périodiques. Ann Sci Ecole Norm Sup 2:12

    Google Scholar 

  • 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. doi:10.3389/fncir.2010.00125

  • 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. doi:10.1242/jeb.067488

    Article  PubMed  Google Scholar 

  • Full RJ, Tu MS (1990) Mechanics of 6-legged runners. J Exp Biol 148:129–146. ISSN 0022-0949

    Google Scholar 

  • Full RJ, Blickhan R, Ting LH (1991) Leg design in hexapedal runners. J Exp Biol 158:369–390. ISSN 0022-0949

    Google Scholar 

  • Full RJ, Stokes DR, Ahn A, Josephson RK (1998) Energy absorption during running by leg muscles in a cockroach. J Exp Biol 201: 997–1012

    Google Scholar 

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

    Google Scholar 

  • Ghigliazza RM, Altendorfer R, Holmes P, Koditschek DE (2005) A simply stabilized running model. SIAM Rev 47(3):519–549

    Article  Google Scholar 

  • Grillner S (1972) The role of muscle stiffness in meeting the changing postural and locomotor requirements for force development by the ankle extensors. Acta Physiol Scand 86:92–108

    Article  PubMed  CAS  Google Scholar 

  • Grillner S (1985) Neurobiological bases of rhythmic motor acts in vertebrates. Science 228:143–149

    Article  PubMed  CAS  Google Scholar 

  • Grillner S, Wallén P (2002) Cellular bases of a vertebrate locomotor system—steering, intersegmental and segmental co-ordination and sensory control. Brain Res Rev 40(1–3):92–106

    Article  PubMed  Google Scholar 

  • Guckenheimer J, Holmes P (1983) Nonlinear oscillations, dynamical systems, and bifurcations of vector fields. Springer, Berlin

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

    Article  Google Scholar 

  • Holtje M, Hustert R (2003) Rapid mechano-sensory pathways code leg impact and elicit very rapid reflexes in insects. J Exp Biol 206(16):2715–2724. ISSN 0022-0949. doi:10.1242/jeb.00492

    Google Scholar 

  • Ijspeert AJ (2008) Central pattern generators for locomotion control in animals and robots: a review. Neural Netw. 21(4):642–653. ISSN 0893-6080. doi:10.1016/j.neunet.2008.03.014

    Google Scholar 

  • Jaric S, Latash ML (2000) The equilibrium-point hypothesis is still doing fine. Hum Mov Sci 19(6):933–938

    Article  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 

  • Jindrich DL, Full RJ (2002) Dynamic stabilization of rapid hexapedal locomotion. J Exp Biol 205(18):2803–2823. ISSN 0022-0949

    Google Scholar 

  • Kalman RE (1960) A new approach to linear filtering and prediction problems. J Basic Eng 82:35–45

    Article  Google Scholar 

  • Kim S, Clark JE, Cutkosky MR (2006) iSprawl: design and tuning for high-speed autonomous open-loop running. Int J Robot Res 25(9):903–912. ISSN 0278-3649. doi:10.1177/0278364906069150

    Google Scholar 

  • Klavins E, Komsuoglu H, Full RJ, Koditschek DE (2002) The role of reflexes versus central pattern generators in dynamical legged locomotion. In: Ayers J, Davis J, Rudolph A (eds) Neurotechnology for biomimetic robots. MIT Press, Cambridge, pp 351–382

    Google Scholar 

  • Kralemann B, Cimponerlu L, Rosenblum M, Pikovsky A, Mrowka R (2007) Uncovering interaction of coupled oscillators from data. Phys Rev E 76(5):055201. ISSN: 1539-3655. doi:10.1103/PhysRevE.76.055201

    Google Scholar 

  • Kram R, Wong B, Full RJ (1997) Three-dimensional kinematics and limb kinetic energy of running cockroaches. J Exp Biol 200(13):1919–1929. ISSN 0022-0949

    Google Scholar 

  • Kubow TM, Full RJ (1999) The role of the mechanical system in control: a hypothesis of self-stabilization in hexapedal runners. Phil Trans R Soc B 354(1385):849–861. ISSN 0962-8436

    Google Scholar 

  • Kukillaya RP, Holmes PJ (2007) A hexapedal jointed-leg model for insect locomotion in the horizontal plane. Biol Cybern 97(5–6): 379–395. ISSN 0340-1200. doi:10.1007/s00422-007-0180-2

    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. doi:10.1016/j.jtbi.2009.07.036

    Article  PubMed  Google Scholar 

  • Kukillaya R, Proctor J, Holmes P (2009) Neuromechanical models for insect locomotion: stability, maneuverability, and proprioceptive feedback. Chaos 19(2). ISSN 1054-1500. doi:10.1063/1.3141306

  • MacKay-Lyons M (2002) Central pattern generation of locomotion: a review of the evidence. Phys Ther 82(1):69–83. ISSN 0031-9023. http://www.ptjournal.org/cgi/content/abstract/82/1/69

    Google Scholar 

  • Maes LD, Herbin M, Hackert R, Bels VL, Abourachid A (2008) Steady locomotion in dogs: temporal and associated spatial coordination patterns and the effect of speed. J Exp Biol 211:138–149. doi:10.1242/jeb.008243

    Article  PubMed  Google Scholar 

  • Marder E, Bucher D, Schulz D, Taylor A (2005) Invertebrate central pattern generator moves along. Curr Biol 15:685–699

    Article  Google Scholar 

  • Mazo M, Tabuada P (2009) Input-to-state stability of self-triggered control systems. In: Conference on decision and control, 48th IEEE, pp 928–933

  • Noah JA, Quimby L, Frazier SF, Zill SN (2004) Walking on a peg leg: extensor muscle activities and sensory feedback after distal leg denervation in cockroaches. J Comp Physiol A 190:217–231. ISSN 0340-7594. doi:10.1007/s00359-003-0488-x

    Google Scholar 

  • Pearson KG (1993) Common principles of motor control in vertebrates and invertebrates. Ann Rev Neurosci 16:265–297

    Article  PubMed  CAS  Google Scholar 

  • Pearson KG (1995) Proprioceptive regulation of locomotion. Curr Opin Neurobiol 5:786–791

    Article  PubMed  CAS  Google Scholar 

  • Pearson KG (2004) Generating the walking gait: role of sensory feedback. Prog Brain Res 143:123–129

    Article  PubMed  Google Scholar 

  • Pearson KG, Iles JF (1971) Innervation of coxal depressor muscles in cockroach, Periplaneta americana. J Exp Biol 54(1):215–232

    PubMed  CAS  Google Scholar 

  • Pearson KG, Collins DF (1993) Reversal of the influence of group Ib afferents from plantaris on activity in medial gastrocnemius-muscle during locomotor-activity. J Neurophysiol 70(3):1009–1017. ISSN 0022-3077

    Google Scholar 

  • Politis DN (1995) A primer on bootstrap methods in statistics. Technical report 95-19. Purdue University. http://www.stat.purdue.edu/research/technical_reports/pdfs/1995/tr95-19.pdf

  • Politis DN (1998) Computer-intensive methods in statistical analysis. IEEE Signal Proc Mag 15(1):39–55. ISSN 1053-5888. doi:10.1109/79.647042

    Google Scholar 

  • Prochazka A, Gillard D, Bennett DJ (1997a) Implications of positive feedback in the control of movement. J Neurophysiol 77(6):3237–3251. ISSN 0022-3077

    Google Scholar 

  • Prochazka A, Gillard, D, Bennett DJ (1997b) Positive force feedback control of muscles. J Neurophysiol 77(6):3226–3236. ISSN 0022-3077

    Google Scholar 

  • Proctor J, Holmes PJ (2008) Steering by transient destabilization in piecewise-holonomic models of legged locomotion. Regul Chaotic Dyn 13(4):267–282. doi:10.1134/S1560354708040047

    Article  Google Scholar 

  • Proctor J, Holmes PJ (2010) Reflexes and preflexes: on the role of sensory feedback on rhythmic patterns in insect locomotion. Biol Cybern 102:513–531. doi:10.1007/s00422-010-0383-9

    Article  PubMed  CAS  Google Scholar 

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

    Article  PubMed  CAS  Google Scholar 

  • Pullin AO, Kohut NJ, Zarrouk D, Fearing RS (2012) Dynamic turning of 13 cm robot comparing tail and differential drive. In: IEEE international conference on robotics and automation, May

  • Quinn RD, Ritzmann RE (1998) Construction of a hexapod robot with cockroach kinematics benefits both robotics and biology. Connect Sci 10(3–4):239–254. ISSN 0954-0091. doi:10.1080/095400998116422

    Google Scholar 

  • Rauch HE, Tung F, Striebel CT (1965) Maximum likelihood estimates of linear dynamic systems. AIAA J 3(8):1445–1450. ISSN 0001-1452

    Google Scholar 

  • Revzen S (2009) Neuromechanical control architectures of arthropod locomotion. PhD Thesis. University of California, Berkeley

  • Revzen S, Guckenheimer JM (2008) Estimating the phase of synchronized oscillators. Phys Rev E 78(5):051907. ISSN 1539-3755. doi:10.1103/PhysRevE.78.051907

    Google Scholar 

  • Revzen S, Koditschek DE, Full RJ (2008) Towards testable neuromechanical control architectures for running. In: Sternad D (ed) Progress in motor control—a multidisciplinary perspective, pp 25–56. Springer, New York doi:10.1007/978-0-387-77064-2-3

  • Ridgel AL, Ritzmann RE (2005) Effects of neck and circumoesophageal connective lesions on posture and locomotion in the cockroach. J Comp Physiol A 191(6):559–573

    Article  Google Scholar 

  • Ridgel A, Frazier F, Zill SN (2001) Dynamic responses of tibial campaniform sensilla studied by substrate displacement in freely moving cockroaches. J Comp Physiol A 187(5):405–420. doi:10.1007/s003590100213

    Article  PubMed  CAS  Google Scholar 

  • Ritzmann RE, Büschges A (2007) Adaptive motor behavior in insects. Curr Opin Neurobiol 17(6):629–636. ISSN 0959-4388. doi:10.1016/j.conb.2008.01.001

    Google Scholar 

  • Schilling M, Cruse H, Arena P (2007) Hexapod walking: an expansion to walknet dealing with leg amputations and force oscillations. Biol Cybern 96(3):323–340. ISSN 0340-1200. doi:10.1007/s00422-006-0117-1

    Google Scholar 

  • Schmitt J, Holmes P (2000a) 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 (2000b) Mechanical models for insect locomotion: dynamics and stability in the horizontal plane II. Application. Biol Cybern 83(6):517–527

    Article  PubMed  CAS  Google Scholar 

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

    Article  Google Scholar 

  • Schmitt J, Holmes P (2003) Mechanical models for insect locomotion: active muscles and energy losses. Biol Cybern 89(1): 43–55. ISSN 0340-1200. doi:10.1007/s00422-003-0404-z

    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 

  • Seyfarth A, Geyer H, Herr H (2003) Swing-leg retraction: a simple control model for stable running. J Exp Biol 206(15):2547–2555

    Article  PubMed  Google Scholar 

  • Spagna JC, Goldman DI, Lin P-C, Koditschek DE, Full RJ (2007) Distributed mechanical feedback in arthropods and robots simplifies control of rapid running on challenging terrain. Bioinspir Biomim 2(1): 9–18. ISSN 1748-3182. doi:10.1088/1748-3182/2/1/002

    Google Scholar 

  • Spenko MJ, Haynes GC, Saunders JA, Cutkosky MR, Rizzi AA, Full RJ, Koditschek DE (2008) Biologically inspired climbing with a hexapedal robot. J Field Robot 25(4–5):223–242. ISSN 1556-4959. doi:10.1002/rob.20238

    Google Scholar 

  • Spence AJ, Revzen S, Seipel J, Mullens C, Full RJ (2010) Insects running on elastic surfaces. J Exp Biol 213:1907–1920. ISSN 0022-0949. doi:10.1242/jeb.042515

    Google Scholar 

  • Sponberg S, Full RJ (2008) Neuromechanical response of musculo-skeletal structures in cockroaches during rapid running on rough terrain. J Exp Biol 211(3):433–446. ISSN 0022-0949. doi:10.1242/jeb.012385

    Google Scholar 

  • Sponberg S, Libby T, Mullens C, Full RJ (2011a) Shifts in a single muscle’s control potential of body dynamics. Phil Trans R Soc B 366:1606–1620. doi:10.1098/rstb.2010.0368

    Article  PubMed  Google Scholar 

  • Sponberg S, Spence A, Mullens C, Full RJ (2011b) A single muscle’s multifunctional control potential of body dynamics for postural control and running. Philos Trans R Soc B 366:1592–1605. doi:10.1098/rstb.2010.0367

    Article  Google Scholar 

  • Tabuada P (2007) Event-triggered real-time scheduling of stabilizing control tasks. IEEE Trans Autom Control 52(9):1680–1685. ISSN 0018-9286. doi: 10.1109/TAC.2007.904277

    Google Scholar 

  • Ting LH, Blickhan R, Full RJ (1994) Dynamic and static stability in hexapedal runners. J Exp Biol 197:251–269. ISSN 0022-0949

    Google Scholar 

  • Watson JT, Ritzmann RE (1998a) Leg kinematics and muscle activity during treadmill running in the cockroach, Blaberus discoidalis: I. Slow running. J Comp Physiol A 182(1):11–22. ISSN 0340-7594. doi:10.1007/s003590050153

  • Watson JT, Ritzmann RE (1998b) Leg kinematics and muscle activity during treadmill running in the cockroach, Blaberus discoidalis: II. Fast running. J Comp Physiol A 182(1):23–33. ISSN 0340–7594. doi:10.1007/s003590050154

  • Watson JT, Ritzmann RE, Pollack AJ (2002a) Control of climbing behavior in the cockroach, Blaberus discoidalis. II. Motor activities associated with joint movement. J Comp Physiol A 188(1):55–69. ISSN 0340-7594. doi:10.1007/s00359-002-0278-x

    Google Scholar 

  • Watson JT, Ritzmann RE, Zill SN, Pollack AJ (2002b) Control of obstacle climbing in the cockroach, Blaberus discoidalis. I. Kinematics. J Comp Physiol A 188(1):39–53. ISSN 0340-7594. doi:10.1007/s00359-002-0277-y

    Google Scholar 

  • Webb B (2002) Robots in invertebrate neuroscience. Nature 417(6886):359–363. ISSN 0028-0836

    Google Scholar 

  • Wilson DM (1961) The central nervous control of flight in a locust. J Exp Biol 38:471–490

    Google Scholar 

  • Zehr EP, Stein RB (1999) What functions do reflexes serve during human locomotion? Prog Neurobiol 58(2):185–205. ISSN 0301–0082

    Google Scholar 

  • Zill SN, Moran DT, Varela, FG (1981) The exoskeleton and insect proprioception. 2. Reflex effects of tibial campaniform sensilla in the american cockroach, Periplaneta americana. J Exp Biol 94:43–55. ISSN 0022-0949

  • Zill SN, Schmitz J, Büschges A (2004) Load sensing and control of posture and locomotion. Arthropod Struct Dev 33(3):273–286. ISSN 1467-8039. doi: 10.1016/j.asd.2004.05.005

  • Zill SN Keller BR, Duke ER (2009) Sensory signals of unloading in one leg follow stance onset in another leg: transfer of load and emergent coordination in cockroach walking. J Neurophysiol 101(5):2297–2304. ISSN 0022-3077. doi:10.1152/jn.00056.2009

    Google Scholar 

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Acknowledgments

We would like to thank Teressa Alexander for laboratory assistance in collecting EMG data. This work was funded by NSF Frontiers for Integrative Biology Research (FIBR) Grant No. 0425878-Neuromechanical Systems Biology to RJF. SB and JMM were partially supported by NSF Graduate Research Fellowships and an NSF IGERT Traineeship to JMM.

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Revzen, S., Burden, S.A., Moore, T.Y. et al. Instantaneous kinematic phase reflects neuromechanical response to lateral perturbations of running cockroaches. Biol Cybern 107, 179–200 (2013). https://doi.org/10.1007/s00422-012-0545-z

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