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.

Les actionneurs numériques sont composés d'une partie mobile pouvant se déplacer entre des positions discrètes précisément connues et répétables. Contrairement aux actionneurs analogiques classiques, le pilotage d'actionneurs numériques est réalisé très simplement à l'aide d'une commande impulsionnelle et en boucle ouverte. De ce fait, aucun capteur n'est nécessaire ce qui facilite leur intégration dans des systèmes hôtes. La qualité de fabrication de ces actionneurs est cependant primordiale car une éventuelle erreur ne peut pas être corrigée par la commande. Les travaux présentés porteront sur un réseau composé de 25 actionneurs numériques disposant chacun de quatre positions discrètes avec un plateau glissant. L'application visée est la réalisation d'un système de convoyage planaire dans laquelle les actionneurs permettent de déplacer un plateau selon les deux directions du plan. Les résultats de la simulation sont comparés avec les résultats expérimentaux. En suite, un réseau composé de quatre actionneurs numériques avec un plateau structuré est étudié. La conception du réseau d'actionneurs puis la stratégie de pilotage permettant de réaliser le déplacement du plateau structuré seront tout d'abord présentées. Un prototype de réseau d'actionneurs et des résultats expérimentaux de convoyage selon une direction sera ensuite détaillé et l'influence d'erreurs de fabrication sur le fonctionnement du réseau sera mise en évidence. / The open loop control is widely used by the digital systems to facilitate the integration in complex systems because no sensor is needed. The research is based on digital actuator which is composed of a mobile part and a fixed part. The actuator moves between the discrete positions. The discrete displacement consumes low energy, which is controlled by impulse only needed to switch the actuator between the discrete positions. However, the stroke of digital actuator is fixed at the manufacturing. So the digital actuators array is used to obtain variable strokes. A digital actuators array used here with a structured plate is applied as a 2D planar conveyance. Firstly, an actuators array composed of 25 elementary actuators with a flat plate is studied. The simulated results are compared with the experimental results. Then another actuators array composed of four elementary actuators with a structured plate is designed. The design and the plate displacement are firstly presented. Then the prototype of the conveyance is fabricated with laser cutting machine and 3D printer. The experiment is then tested in one direction to study the plate displacement. The open loop control is simple by using current impulse. The operation can be well functioned which is observed during the experiment. The experimental results are compared with the theoretical results.

Shape plays an important role in our everyday life to interpret information about the surroundings whether we are aware or not. Together with visual and auditory information, we are able to obtain and process information for different purposes. Output devices such as monitors and speakers convey visual and auditory information while input devices such as touch screen and microphones receive that information for human machine interaction. Such devices have become commonplace but there has yet to be a fitting input/output device utilizing our haptic perception. Digital Clay is a next generation Human Machine Interface (HMI) device for 2.5D shape input/output via an array of hydraulic actuators. This device potentially has wide applications in the areas of engineering, sciences, medicine, military, entertainment etc. The user can perceive the shape of a computer programmed model in a tangible and concrete manner which means an added realism with the addition of the sense of touch. Conversely, the user can also use Digital Clay as an input device to the computer, by shaping and molding desired shapes on the device, no longer limited to drawing models with a mouse on CAD software. Shape display has been achieved with the current 5x5 prototype at the Georgia Institute of Technology but this research seeks to expand its capability to include haptic feedback and consequently shaping mode. This thesis gives an overview of the current 5x5 prototype and implements 2 commonly used haptic control methods, the admittance control and the impedance control. For implementing the admittance control, actuator displacement and velocity controllers and a proportional integral observer (PIO) are designed. The model-based unknown input observer is a solution for force estimation without added sensors in the actuators. For implementing the impedance control, a novel pressure control technique is designed to provide pressure feedback to the actuators array along with accurate and reliable displacement measurement. Both of the haptic control methods are evaluated, hardware and software limitations are outlined and possible future improvements are suggested.