Merging Variable Stiffness Fiber Patterns on Multi-Shape Robotic Sheets

Shape morphing can be achieved using thin, pla-nar sheets patterned with strain-limiting constraints to direct differential growth into desired shapes. Our previous work produced such shape-shifting sheets using an inflatable sheet with variable stiffness fibers placed in patterns optimized by a multi-objective evolutionary algorithm. With our pipeline, we generated two specialized fiber patterns
$\{P_{i},\ P_{j}\}$
to produce shapes
$\{S_{i},\ S_{j}\}$
, which we then layered onto the same sheet. However, this layering approach had translation inefficiencies in hardware, such as fiber redundancies. To reduce fiber crowding and increase shape fidelity, we propose that fibers identified as similar in both
$P_{i}$
and
$P_{j}$
can be implemented as a single fiber belonging to both patterns. Extending our previous work, herein we implement a post-optimization fiber merging protocol. Applying the protocol to sheets patterned with fibers targeting two shape-pairs, cylinder/sphere and simple saddle/monkey saddle, we demonstrate that fiber merging reduces the total number of fibers on each sheet, thus reducing sheet bulk and weight. We further measure the error between the target shapes and actual hardware shapes: For the cylinder/sphere shape-pair, the error increases with merging implemented when compared to the original, unmerged fiber patterns. For the monkey saddle/simple saddle shape-pair, the error decreases for one or both shapes for all fiber mergers implemented. The results indicate that fiber merging is increasingly useful with increasing fiber pattern complexity as measured by fiber count. Therefore, fiber merging is a potentially useful strategy to simplify the complexity of fiber designs required for shape-matching.