Controlling the fold: proprioceptive feedback in a soft origami robot.

We demonstrate proprioceptive feedback control of a one degree of freedom soft, pneumatically actuated origami robot and an assembly of two robots into a two degree of freedom system. The base unit of the robot is a 41 mm long, 3-D printed Kresling-inspired structure with six sets of sidewall folds and one degree of freedom. Pneumatic actuation, provided by negative fluidic pressure, causes the robot to contract. Capacitive sensors patterned onto the robot provide position estimation and serve as input to a feedback controller. Using a finite element approach, the electrode shapes are optimized for sensitivity at larger (more obtuse) fold angles to improve control across the actuation range. We demonstrate stable position control through discrete-time proportional-integral-derivative (PID) control on a single unit Kresling robot via a series of static set points to 17 mm, dynamic set point stepping, and sinusoidal signal following, with error under 3 mm up to 10 mm contraction. We also demonstrate a two-unit Kresling robot with two degree of freedom extension and rotation control, which has error of 1.7 mm and 6.1°. This work contributes optimized capacitive electrode design and the demonstration of closed-loop feedback position control without visual tracking as an input. This approach to capacitance sensing and modeling constitutes a major step towards proprioceptive state estimation and feedback control in soft origami robotics.