The practice of achieving engineering functionality through folding and fold-like operations — known as origami engineering — is receiving increased attention in the research community. Self-folding systems are of particular interest due to their potential to operate (semi-) autonomously in applications across a wide range of length scales. In recent work, we created a reconfigurable self-folding sheet using shape memory alloy (SMA) layers to achieve fold-like behavior. The prior work was devoted to modeling, simulation, and experimentation with the sheet. No attempt had been made to control the sheet. This paper extends our prior work to include feedback control of the self-folding sheet. In particular, the goal is to perform fold control — the use of feedback control to ensure the sheet achieves a desired folded configuration.

Control of SMA material is difficult due to its hysteretic nature. This application involves a laminate material with embedded SMA wires, which further complicates control due to the interaction of the wires with each layer of the sheet. We explore two feedback control methods, On/Off and PID, using a simulation framework for controller evaluation. In the interest of computational efficiency, we introduce a new model for sheet behavior based on classical laminate theory. This allows for a significant reduction in computational cost compared to the finite element models we used in prior work with only a modest tradeoff in terms of accuracy. Our results show that both control methods are capable of performing fold control, but that the On/Off controller is superior in terms of energy requirements.

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