Biological Cybernetics

, Volume 107, Issue 2, pp 179–200 | Cite as

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

  • Shai Revzen
  • Samuel A. Burden
  • Talia Y. Moore
  • Jean-Michel Mongeau
  • Robert J. FullEmail author
Original Paper


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.


Biomechanics Phase Neuromechanical control Neural clock Locomotion Cockroach Perturbation 



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


Component of cockroach velocity in trackway direction


Component of cockroach velocity across trackway


Center of mass


Central pattern generator




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


Inter-spike interval


Lateral leg spring model


Muscle action potential


Principal component analysis


Lateral leg spring model


Anterior extreme position. The transition from swing to stance.


Posterior extreme position. The transition from stance to swing.


Spring loaded inverted pendulum model

List of symbols

\(\varPhi \)

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

\(\phi _{0}\)

Predictor phase

\(\phi , \theta \)


\(\omega \)

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


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


(Complex) exponential function


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


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


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


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


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


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.


Number of trials provided by an individual animal


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


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



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.


  1. 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):379–389PubMedGoogle Scholar
  2. 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
  3. 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):979–999CrossRefGoogle Scholar
  4. 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
  5. 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
  6. Bender JA, Pollack AJ, Ritzmann RE (2010) Neural activity in the central complex of the insect brain is linked to locomotor changes. Curr Biol 20:921–926PubMedCrossRefGoogle Scholar
  7. 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 PubMedCrossRefGoogle Scholar
  8. 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 PubMedCrossRefGoogle Scholar
  9. Carbonell C (1947) The thoracic muscles of the cockroach Periplaneta americana (L.). Smith Misc Coll 107:1–23Google Scholar
  10. Cruse H, Knauth A (1989) Coupling mechanisms between the contralateral legs of a walking insect (Carausius morosus). J Exp Biol 144:199–213Google Scholar
  11. Cruse H, Schwarze W (1988) Mechanisms of coupling between the ipsilateral legs of a walking insect (Carausius morosus). J Exp Biol 138:455–469Google Scholar
  12. 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):221–250CrossRefGoogle Scholar
  13. 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):1435–1447PubMedCrossRefGoogle Scholar
  14. Delcomyn F (1980) Neural basis of rhythmic behavior in animals. Science 210(4469):492–498. doi: 10.1126/science.7423199 PubMedCrossRefGoogle Scholar
  15. 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 PubMedCrossRefGoogle Scholar
  16. Duysens J, Clarac, Cruse H (2000) Load-regulating mechanisms in gait and posture: comparative aspects. Physiol Rev 80(1):83–133. ISSN 0031-9333.
  17. Fisher NI (1993) Statistical analysis of circular data. Cambridge University Press, Cambridge. ISBN 0-521-35018-2Google Scholar
  18. Floquet G (1883) Sur les Equations différentielles linéaires à coefficients périodiques. Ann Sci Ecole Norm Sup 2:12Google Scholar
  19. 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
  20. 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 PubMedCrossRefGoogle Scholar
  21. Full RJ, Tu MS (1990) Mechanics of 6-legged runners. J Exp Biol 148:129–146. ISSN 0022-0949Google Scholar
  22. Full RJ, Blickhan R, Ting LH (1991) Leg design in hexapedal runners. J Exp Biol 158:369–390. ISSN 0022-0949Google Scholar
  23. Full RJ, Stokes DR, Ahn A, Josephson RK (1998) Energy absorption during running by leg muscles in a cockroach. J Exp Biol 201: 997–1012Google Scholar
  24. Full RJ, Koditschek DE (1999) Templates and anchors: neuromechanical hypotheses of legged locomotion on land. J Exp Biol 202: 3325–3332Google Scholar
  25. Ghigliazza RM, Altendorfer R, Holmes P, Koditschek DE (2005) A simply stabilized running model. SIAM Rev 47(3):519–549CrossRefGoogle Scholar
  26. 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 86:92–108PubMedCrossRefGoogle Scholar
  27. Grillner S (1985) Neurobiological bases of rhythmic motor acts in vertebrates. Science 228:143–149PubMedCrossRefGoogle Scholar
  28. 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):92–106PubMedCrossRefGoogle Scholar
  29. Guckenheimer J, Holmes P (1983) Nonlinear oscillations, dynamical systems, and bifurcations of vector fields. Springer, BerlinGoogle Scholar
  30. Holmes P, Full RJ, Koditschek D, Guckenheimer J (2006) Dynamics of legged locomotion: models, analyses, and challenges. SIAM Rev 48(2):207–304CrossRefGoogle Scholar
  31. 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
  32. 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
  33. Jaric S, Latash ML (2000) The equilibrium-point hypothesis is still doing fine. Hum Mov Sci 19(6):933–938CrossRefGoogle Scholar
  34. Jindrich DL, Full RJ (1999) Many-legged maneuverability: dynamics of turning in hexapods. J Exp Biol 202(12):1603–1623PubMedGoogle Scholar
  35. Jindrich DL, Full RJ (2002) Dynamic stabilization of rapid hexapedal locomotion. J Exp Biol 205(18):2803–2823. ISSN 0022-0949Google Scholar
  36. Kalman RE (1960) A new approach to linear filtering and prediction problems. J Basic Eng 82:35–45CrossRefGoogle Scholar
  37. 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
  38. 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 351–382Google Scholar
  39. 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
  40. 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 0022-0949Google Scholar
  41. 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 0962-8436Google Scholar
  42. 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
  43. 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 PubMedCrossRefGoogle Scholar
  44. 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
  45. MacKay-Lyons M (2002) Central pattern generation of locomotion: a review of the evidence. Phys Ther 82(1):69–83. ISSN 0031-9023. Google Scholar
  46. 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 PubMedCrossRefGoogle Scholar
  47. Marder E, Bucher D, Schulz D, Taylor A (2005) Invertebrate central pattern generator moves along. Curr Biol 15:685–699CrossRefGoogle Scholar
  48. Mazo M, Tabuada P (2009) Input-to-state stability of self-triggered control systems. In: Conference on decision and control, 48th IEEE, pp 928–933Google Scholar
  49. 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
  50. Pearson KG (1993) Common principles of motor control in vertebrates and invertebrates. Ann Rev Neurosci 16:265–297PubMedCrossRefGoogle Scholar
  51. Pearson KG (1995) Proprioceptive regulation of locomotion. Curr Opin Neurobiol 5:786–791PubMedCrossRefGoogle Scholar
  52. Pearson KG (2004) Generating the walking gait: role of sensory feedback. Prog Brain Res 143:123–129PubMedCrossRefGoogle Scholar
  53. Pearson KG, Iles JF (1971) Innervation of coxal depressor muscles in cockroach, Periplaneta americana. J Exp Biol 54(1):215–232PubMedGoogle Scholar
  54. 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 0022-3077Google Scholar
  55. Politis DN (1995) A primer on bootstrap methods in statistics. Technical report 95-19. Purdue University.
  56. 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
  57. Prochazka A, Gillard D, Bennett DJ (1997a) Implications of positive feedback in the control of movement. J Neurophysiol 77(6):3237–3251. ISSN 0022-3077Google Scholar
  58. Prochazka A, Gillard, D, Bennett DJ (1997b) Positive force feedback control of muscles. J Neurophysiol 77(6):3226–3236. ISSN 0022-3077Google Scholar
  59. 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 CrossRefGoogle Scholar
  60. 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 PubMedCrossRefGoogle Scholar
  61. 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 368:5087–5104PubMedCrossRefGoogle Scholar
  62. 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, MayGoogle Scholar
  63. 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
  64. Rauch HE, Tung F, Striebel CT (1965) Maximum likelihood estimates of linear dynamic systems. AIAA J 3(8):1445–1450. ISSN 0001-1452Google Scholar
  65. Revzen S (2009) Neuromechanical control architectures of arthropod locomotion. PhD Thesis. University of California, BerkeleyGoogle Scholar
  66. 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
  67. 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
  68. 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):559–573CrossRefGoogle Scholar
  69. 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 PubMedCrossRefGoogle Scholar
  70. 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
  71. 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
  72. Schmitt J, Holmes P (2000a) Mechanical models for insect locomotion: dynamics and stability in the horizontal plane I. Theory. Biol Cybern 83(6):501–515PubMedCrossRefGoogle Scholar
  73. Schmitt J, Holmes P (2000b) Mechanical models for insect locomotion: dynamics and stability in the horizontal plane II. Application. Biol Cybern 83(6):517–527PubMedCrossRefGoogle Scholar
  74. Schmitt J, Holmes P (2001) Mechanical models for insect locomotion: stability and parameter studies. Physica D 156(1–2):139–168CrossRefGoogle Scholar
  75. 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
  76. 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):343–353PubMedCrossRefGoogle Scholar
  77. Seyfarth A, Geyer H, Herr H (2003) Swing-leg retraction: a simple control model for stable running. J Exp Biol 206(15):2547–2555PubMedCrossRefGoogle Scholar
  78. 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
  79. 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
  80. 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
  81. 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
  82. 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 PubMedCrossRefGoogle Scholar
  83. 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 CrossRefGoogle Scholar
  84. 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
  85. Ting LH, Blickhan R, Full RJ (1994) Dynamic and static stability in hexapedal runners. J Exp Biol 197:251–269. ISSN 0022-0949Google Scholar
  86. 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
  87. 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
  88. 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
  89. 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
  90. Webb B (2002) Robots in invertebrate neuroscience. Nature 417(6886):359–363. ISSN 0028-0836Google Scholar
  91. Wilson DM (1961) The central nervous control of flight in a locust. J Exp Biol 38:471–490Google Scholar
  92. Zehr EP, Stein RB (1999) What functions do reflexes serve during human locomotion? Prog Neurobiol 58(2):185–205. ISSN 0301–0082Google Scholar
  93. 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 0022-0949Google Scholar
  94. 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
  95. 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

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Shai Revzen
    • 1
  • Samuel A. Burden
    • 2
  • Talia Y. Moore
    • 1
  • Jean-Michel Mongeau
    • 3
  • Robert J. Full
    • 1
    Email author
  1. 1.Department of Integrative BiologyUniversity of CaliforniaBerkeleyUSA
  2. 2.Department of Electrical Engineering and Computer SciencesUniversity of CaliforniaBerkeleyUSA
  3. 3.Biophysics Graduate GroupUniversity of CaliforniaBerkeleyUSA

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