International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 11, Pages 1759-1779

Brain-like functor control machine for general humanoid biodynamics

Vladimir Ivancevic and Nicholas Beagley

Land Operation Division, Defence Science and Technology Organisation, Department of Defence, P.O. Box 1500, Edinburgh 5111, SA, Australia

Received 7 June 2004; Revised 27 February 2005

Copyright © 2005 Vladimir Ivancevic and Nicholas Beagley. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A novel, brain-like, hierarchical (affine-neuro-fuzzy-topological) control for biomechanically realistic humanoid-robot biodynamics (HB), formulated previously in [15, 16], is proposed in the form of a tensor-invariant, “meta-cybernetic” functor machine. It represents a physiologically inspired, three-level, nonlinear feedback controller of muscular-like joint actuators. On the spinal level, nominal joint-trajectory tracking is formulated as an affine Hamiltonian control system, resembling the spinal (autogenetic-reflex) “motor servo.” On the cerebellar level, a feedback-control map is proposed in the form of self-organized, oscillatory, neurodynamical system, resembling the associative interaction of excitatory granule cells and inhibitory Purkinje cells. On the cortical level, a topological “hyper-joystick” command space is formulated with a fuzzy-logic feedback-control map defined on it, resembling the regulation of locomotor conditioned reflexes. Finally, both the cerebellar and the cortical control systems are extended to provide translational force control for moving 6-degree-of-freedom chains of inverse kinematics.