Self-organized control of bipedal locomotion by neural oscillators in unpredictable environment

Andersson O, Grillner S (1983) Peripheral control of the cat's step cycle. II Entrainment of the central pattern generators for locomotion by sinusoidal hip movements during “fictive locomotion”. Acta Physiol Scand 118:229–239

Arshavsky YI, Gelfand IM, Orlovsky GN (1984) Cerebellum and rhythmical movements. Springer, Berlin Heidelberg New York

Bässler U (1986) On the definition of central pattern generator and its sensory control. Biol Cybern 54:65–69

Beuter A, Flashner H, Arabyan A (1986) Phase plane modeling of leg motion. Biol Cybern 53:273–284

Brown TG (1914) On the nature of the fundamental activity of the nervous centeres. J Physiol 48:18–46

Doya K, Yoshizawa S (1989) Adaptive neural oscillator using continuous-time back-propagation learning. Neural Networks 2:375–385

Friesen WO, Stent GS (1977) Generation of a locomotory rhythm by a neural network with recurrent cyclic inhibition. Biol Cybern 28:27–40

Grillner S (1975) Locomotion in vertebrates: central mechanisms and reflex interaction. Physiol Rev 55:247–304

Grillner S (1981) Control of locomotion in bipeds, tetrapods and fish. In: Brooks VB (ed) Handbook of physiology, Sect 1: The nervous system vol II: motor control. Waverly Press, Maryland, pp 1179–1236

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

Haken H (1983) Synergetics — An introduction, 3rd edn. Springer, Berlin Heidelberg New York

Haken H, Kelso JAS, Bunz H (1985) A theoretical model of phase transitions in human hand movements. Biol Cybern 51:347–356

Ito M (1984) The cerebellum and neural control. Raven Press, New York

Kato I (1983) Biped walking robot — its history and problems. J Robot Soc Jpn 1–3:4–6 (in Japanese)

Kato R, Mori M (1984) Control method of biped locomotion giving asymptotic stability of trajectory. Automatica 20–4:405–414

Kawahara K, Mori S (1982) A two compartment model of the stepping generator: Analysis of the roles of a stage-setter and a rhythm generator. Biol Cybern 43:225–230

Kawato M, Furukawa K, Suzuki R (1987) A hierarchical neural-network model for control and learning of voluntary movement. Biol Cybern 57:169–185

Kelso JAS (1984) Phase transitions and critical behavior in human bimanual coordination. Am J Physiol: Reg Integ Comp 15:R1000-R1004

Kleinfeld D, Sompolinsky H (1988) Associative neural network model for the generation of temporal patterns — theory and application to central pattern generators. Biophys J 54:1039–1051

Matsuoka K (1985) Sustained oscillations generated by mutually inhibiting neurons with adaptation. Biol Cybern 52:367–376

Matsuoka K (1987) Mechanisms of frequency and pattern control in the neural rhythm generators. Biol Cybern 56:345–353

McGeer T (1989) Powered flight, child's play, silly wheels and walking machines. Proceedings of the IEEE International Conference on Robotics and Automation. 1989, pp 1592–1598

Miller S, Scott PD (1977) The spinal locomotor generator. Exp Brain Res 30:387–403

Mochon S, McMahon TA (1980) Ballistic walking. J Biomech 13:49–57

Mori S (1987) Integration of posture and locomotion in acute decerebrate cats and in awake, freely moving cats. Prog Neurobiol 28:161–195

Murray MP (1967) Gait as a total pattern of movement. Am J Phys Med 46:290–333

Nicolis G, Prigogine I (1977) Self-organization in nonequilibrium systems. Wiley, New York

Nilsson J, Thorstensson A, Halbertsma J (1985) Changes in leg movements and muscle activity with speed of locomotion and mode of progression in humans. Acta Physiol Scand 123:457–475

Pandy M, Berme N (1988) A numerical method for simulating the dynamics of human walking. J Biomech 21–12:1043–1051

Pearlmutter BA (1989) Learning state space trajectories in recurrent neural networks. Neural Comput 1:263–269

Pearson KG (1987) Central pattern generation: a concept under scrutiny. In: Advances in physiological research. Plenum Press, New York, pp 167–185

Raibert MH (1984) Hopping in legged systems — modeling and simulation for the two-dimensional one-legged case. IEEE Transactions on systems, man, and cybernetics SMC-14–3:451–463

Schöner G, Kelso JAS (1988) Dynamic pattern generation in behavioral and neural systems. Science 239:1513–1520

Schöner G, Jiang WY, Kelso JAS (1990) A synergetic theory of quadrupedal gaits and gait transitions. J Theor Biol 142:359–391

Selverston AI (ed) (1985) Model neural networks and behavior. Plenum Press, New York

Shik ML, Severin FV, Orlovsky GN (1966) Control of walking and running by means of electrical stimulation of the mid-brain. Biophysics 11:756–765

Thelen H (1988) Dynamical approaches to the development of behavior. In: Kelso JAS, Mandell AJ, Shlesinger MF (eds) Dynamic patterns in complex systems, World Scientific, Singapore, pp 348–369

Williams RJ, Zipser D (1989) A learning algorithm for continually running fully recurrent neural networks. Neural Comput 1:270–280

Yuasa H, Ito M (1990) Coordination of many oscillators and generation of locomotory patterns. Biol Cybern 63:177–184