Abstract
A system that controls the leg movement of an animal or a robot walking over irregular ground has to ensure stable support for the body and at the same time propel it forward. To do so, it has to react adaptively to unpredictable features of the environment. As part of our study of the underlying mechanisms, we present here a model for the control of the leg movement of a 6-legged walking system. The model is based on biological data obtained from the stick insect. It represents a combined treatment of realistic kinematics and biologically motivated, adaptive gait generation. The model extends a previous algorithmic model by substituting simple networks of artificial neurons for the algorithms previously used to control leg state and interleg coordination. Each system controlling an individual leg consists of three subnets. A hierarchically superior net contains two sensory and two ‘premotor’ units; it rhythmically suppresses the out-put of one or the other of the two subordinate nets. These are continuously active. They might be called the ‘swing module’ and the ‘stance module’ because they are responsible for controlling the swing (return stroke) and the stance (power stroke) movements, respectively. The swing module consists of three motor units and seven sensory units. It can produce appropriate return stroke movements for a broad range of initial and final positions, can cope with mechanical disturbances of the leg movement, and is able to react to an obstacle which hinders the normal performance of the swing movement. The complete model is able to walk at different speeds over irregular surfaces. The control system rapidly reestablishes a stable gait when the movement of the legs is disturbed.
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References
Bässler U (1977) Sensory control of leg movement in the stick insect Carausius morosus. Biol Cybern 25:61–72.
Bässler U (1983) Neural basis of elementary behavior in stick insects. Springer, Berlin Heidelberg New York.
Bässler U (1986) On the definition of central pattern generator and its sensory control. Biol Cybern 54:65–69.
Bässler U, Wegner U (1983) Motor output of the denervated thoracic ventral nerve cord in the stick insect Carausius morosus. J Exp Biol 105:127–145.
Beer RD, Gallagher JC (1992) Evolving dynamical neural networks for adaptive behaviour. Adapt Behav 1:91–122.
Beer RD, Chiel HJ, Sterling LS (1989) Heterogenous neural networks for adaptive behavior in dynamic environments. In: Touretzky DS (ed) Advances in neural information processing systems 1. Morgan Kaufmann, San Mateo, pp 577–585.
Beer RD, Chiel HJ, Quinn RD, Espenschied KS, Larsson P (1992) A distributed neural network architecture for hexapod robot locomotion. Neural Comput 4:356–365.
Berns K (1994) Steuerungsansätze auf der Basis neuronaler Netze für sechsbeinige Laufmaschinen. PhD thesis, University of Karlsruhe.
Berns K, Piekenbrock S, Dillmann R (1994) Learning control of a sixlegged walking machine. In: Jamashidi M, Ngyen Ch, Lumia R, Yuh J (eds) Proceedings of the 5th Intern Symp on Robotics and Manufacturing, Vol 5. ASME, New York, pp 29–34.
Brooks RA (1986): A robust layered control system for a mobile robot. IEEE J Rob Autom RA-2:14–23.
Brook RA (1989) A robot that walks: emergent behavior from a carefully evolved network. Neural Comput 1:253–262.
Brown TG (1911) The intrinsic factors in the act of progression in the mammal. Proc Lond Soc [Biol] 84:308–319.
Brunn DE, Dean J (1994) Intersegmental and local interneurones in the metathorax of the stick insect, Carausius morosus. J Neurophysiol 72:1208–1219.
Camhi JM (1994) Neuroethology. Sinauer, Sunderland.
Cruse H (1976) On the function of the legs in the free walking stick insect Carausius morosus. J Comp Physiol 112:235–262.
Cruse H (1979) The control of the anterior extreme position of the hindleg of a walking insect. Physiol Entomol 4:121–124.
Cruse H (1980) A quantitative model of walking incorporating central and peripheral influences. II. The connections between the different legs. Biol Cybern 37:137–144.
Cruse H (1983) The influence of load and leg amputation upon coordination in walking crustaceans: a model calculation. Biol Cybern 49:119–125.
Cruse H (1985) Which parameters control the leg movement of a walking insect? II. The start of the swing phase. J Exp Biol 116:357–362.
Cruse H (1990) What mechanisms coordinate leg movement in walking arthropods? Trends Neurosci 13:15–21.
Cruse H, Bartling Ch (1995) Movement of joint angles in the legs of a walking insect, Carausius morosus. J. Insect Physiol (in press).
Cruse H, Müller U (1986) Two coupling mechanisms which determine the coordination of ipsilateral legs in the walking crayfish. J Exp Biol 121:349–369.
Cruse H, Steinkühler U (1993) Solution of the direct and inverse kinematic problems by a common algorithm based on the mean of multiple computations. Biol Cybern 69:345–351.
Cruse H, Warnecke H (1992) Coordination of the legs of a slow-walking cat. Exp Brain Res 89:147–156.
Cruse H, Dean J, Heuer H, Schmidt RA (1990) Utilization of sensory information for motor control. In: Neumann, Prinz W (eds) Relationship between action and perception. Springer, Berlin Heidelberg New York, pp 43–79.
Cruse H, Müller-Wilm U, Dean J (1993) Artificial neural nets for a 6-legged walking system. In: Meyer JA, Roitblat HL, Wilson SW (eds) From animals to animals 2. MIT Press, Cambridge, Mass.
Dean J (1990) Coding proprioceptive information to control movement to a target: simulation with a simple neural network. Biol Cybern 63:115–120.
Dean J (1991a) Effect of load on leg movement and step coordination of the stick insect Carausius morosus. J Exp Biol 159:449–471.
Dean J (1991b) A model of leg coordination in the stick insect, Carausius morosus. I. A geometrical consideration of contralateral and ipsilateral coordination mechanisms between two adjacent legs. Biol Cybern 64:393–402.
Dean J (1991c) A model of leg coordination in the stick insect, Carausius morosus. II. Description of the kinematic model and simulation of normal step pattern. Biol Cybern. 64:403–411.
Dean J (1992a): A model of leg coordination in the stick insect, Carausius morosus. III. Responses to perturbations of normal coordination. Biol Cybern 66:335–343.
Dean J (1992b) A model of leg coordination in the stick insect, Carausius morosus. IV. Comparison of different forms of coordinating mechanisms. Biol Cybern 66:345–355.
Dean J, Wendler G (1983) Stick insect locomotion on a walking wheel: Interleg coordination of leg position. J Exp Biol 103:75–94.
Delcomyn F (1981) Insect locomotion on land. In: Herreid CF, Fourtner CR (eds) Locomotion and energetics in arthropods. Plenum, New York, pp 103–125.
Delcomyn F (1985) Factors regulating insect walking. Annu Rev Entomol 30:239–256.
Donner MD (1984) Control of walking. Local control systems and real time systems. PhD thesis, Carnegie-Mellon University, Pittsburgh.
Getting PA, Dekin MS (1985) Tritonia swimming: a model system for integration within rhythmic motor systems. In: Selverston AI (ed) Model neural networks and behavior. Plenum, New York, pp 3–20.
Graham D (1972) A behavioural analysis of the temporal organisation of walking movements in the 1st instar and adult stick insect. J Comp Physiol 81:23–52.
Grillner S, Wallen P, Brodin L, Lansner A (1991) Neural network generating locomotor behavior in lamprey: circuitry transmitters membrane properties and simulation. Annu Rev Neurosci 14:169–199.
Land MF (1972) Stepping movements made by jumping spider during turns mediated by lateral eyes. J Exp Biol 57:15–40.
Levin E (1990) A recurrent network: limitations and training. Neural Networks 3:641–650.
Maes P, Brooks RA (1990): Learning to coordinate behaviors. Proc Eighth Natl Conf AI (AAAI-90) pp 796–802.
Minski M (1985) The society of mind. Simon and Schuster, New York.
Müller U, Cruse H (1991) The contralateral coordination of walking legs in the crayfish Astacus leptodactylus. I. Experimental results. Biol Cybern. 64:429–436.
Müller-Wilm U, Dean J, Cruse H, Weidemann HJ, Eltze J, Pfeiffer F (1992) Kinematic model of a stick insect as an example of a 6-legged walking system. Adapt Behav 1:33–46.
Pearson KG (1972) Central programming and reflex control of walking in the cockroach. J Exp Biol 56:173–193.
Pearson KG (1981) Function of sensory input in insect motor systems. Can J Physiol Pharmacol 59:660–666.
Pearson KG, Iles FJ (1973) Nervous mechanisms underlying intersegmental co-ordination of leg movements during walking in the cockroach. J Exp Biol 58:725–744.
Pfeiffer F, Cruse H (1994) Bionik des Laufens — technische Umsetzung biologischen Wissens. Konstruktion 46:261–266.
Pfeiffer F, Weidemann HJ, Eltze J (1994) The TUM walking machine. In: Jamashidi M, Yuh J, Ngyen Ch, Lumia R (eds) Proceedings of the 5th Intern Symp on Robotics and Manufacturing, Vol 2. ASME, New York, pp 167–174.
Schmitz J (1993) Load-compensation reactions in the proximal leg joints of stick insects during standing and walking. J Exp Biol 183:15–33.
Schmitz J, Büschges A (1993) Pilocarpine induced rhythmicity in the thoracic nerve cord of the stick insect. In: Elsner N Heisenberg M (eds) Proceedings of the 21st Göttingen Neurobiology Conf. Thieme, Stuttgart, p 208.
Schmitz J, Haßfeld G (1989) The treading-on-tarsus reflex in stick insects: phase-dependence and modifications of the motor output during walking. J Exp Biol 143:373–388.
Wendler G (1964) Laufen und Stehen der Stabheuschrecke Carausius morosus: Sinnesborstenfelder in den Beingelenken als Glieder von Regelkreisen. Z Vergl Physiol 48:198–250.
Wendler G (1968) Ein Analogmodell der Beinbewegungen eines laufenden Insekts. In: Kybernetik 1968, Supplement to ‘elektronischen Anlagen’ 18:68–74. Oldenbourg, München.
Wilson DM (1966) Insect walking. Annu Rev Entomol 11:103–122.
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Cruse, H., Bartling, C., Cymbalyuk, G. et al. A modular artificial neural net for controlling a six-legged walking system. Biol. Cybern. 72, 421–430 (1995). https://doi.org/10.1007/BF00201417
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DOI: https://doi.org/10.1007/BF00201417