This work explores the representations and mathematical modeling of biologically-inspired robotic muscles called Cellular Actuator Arrays.These actuator arrays are made of many small interconnected actuation units which work together to provide force, displacement, robustness and other properties beyond the original actuator's capability.The arrays can also exhibit properties generally associated with biological muscle and can thus provide test bed for research into the interrelated nature of the nervous system and muscles, kinematics/dynamics experiments to understand balance and synergies, and building full-strength, safe muscles for prosthesis, rehabilitation, human force amplification, and humanoid robotics.This thesis focuses on the mathematical tools needed bridge the gap between the conceptual idea of the cellular actuator array and the engineering design processes needed to build physical robotic muscles.The work explores the representation and notation needed to express complex actuator array typologies, the mathematical modeling needed to represent the complex dynamics of the arrays, and properties to guide the selection of arrays for engineering purposes.The approach is designed to aid automation and simulation of actuator arrays and provide an intuitive base for future controls and physiology work.The work is validated through numerical results using MatLab's SimMechanics dynamic modeling system and with three physical actuator arrays built using solenoids and shape memory alloy actuators.
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