Origami crawlers: exploring a single origami vertex for complex path navigation

Abstract

The ancient art of origami, traditionally used to transform simple sheets into intricate objects, also holds potential for diverse engineering applications, such as shape morphing and robotics. In this study, we demonstrate that one of the most basic origami structures (i.e., a rigid, foldable degree-four vertex) can be engineered to create a crawler capable of navigating complex paths using only a single input. Through a combination of experimental studies and modeling, we show that modifying the geometry of a degree four vertex enables sheets to move either in a straight line or turn. Furthermore, we illustrate how leveraging the nonlinearities in folding allows the design of crawlers that can switch between moving straight and turning. Remarkably, these crawling modes can be controlled by adjusting the range of the actuation folding angle. Our study opens avenues for simple machines that can follow intricate trajectories with minimal actuation.

Figures (6)

• Figure 1: Multimodal crawling locomotion of a degree-four origami vertex. (A) Schematic of a degree-four origami vertex with mountain folds (blue lines), and a valley fold (red line). (B) Physical prototype actuated by pressurizing an inflatable pouch attached to the valley fold. The pressure profile used for actuation is shown on the right, together with the corresponding evolution of the folding angle $\beta$. (C)-(E) Experimental results for (C) Design I, (D) Design II, and (E) Design III. Snapshots of origami sheets at different times during loading cycles and frames from videos recorded during tests in which the samples were subjected to multiple inflation/deflation cycles.
• Figure 2: Comparison of experimental and numerical results for Design III. (A) Numerically predicted location of contacts (highlighted in red) for $\beta=157^\circ$ and $130^\circ$. (B) Numerically predicted evolution of the static friction forces at the contact nodes as a function of folding angle $\beta$. The ranges of $\beta$ used in the tests shown in Fig. \ref{['figure_1']}E to move straight and turn are indicated by the green and blue shaded areas, respectively. (C)-(D) Numerically predicted displacement of the center of mass of the sheet for a complete actuation cycle with (C) $157^\circ\leq\beta\leq 163^\circ$ and (D) and $130^\circ\leq\beta\leq 135^\circ$. (E) Comparison of the numerically predicted (dashed line) and experimentally observed (continuous line) trajectory traced by Design III when subjected to 14 loading cycles with $157^\circ\leq\beta\leq 163^\circ$ followed by 55 loading cycles with $130^\circ\leq\beta\leq 135^\circ$.
• Figure 3: Parametric study. (A) Schematic of a typical trajectory for the center of mass of an origami sheet upon a loading cycle. (B) Classification of the considered 229,073 designs based on their supported crawling modes. Bar colors indicate the number of contact changes, $N_\text{change}$.
• Figure 4: Designs supporting a single mode of crawling. (A) Normalized net step size, $L/b$, versus total curvature $\kappa_T$ (rad) for all designs supporting a single mode of crawling. Marker colors indicate the number of contact changes through a loading cycle, $N_\text{change}$ (B) Numerically predicted evolution of the position of the contact point during (i) inflation and (ii) deflation for Design IV. (C) Snapshots of Design IV at different times during a loading cycle and frames from videos recorded during tests in which the sample is subjected to multiple inflation/deflation cycles. The magenta dashed line indicates the numerically predicted trajectory.
• Figure 5: Designs capable of moving straight in two different directions. (A) Angle between the two supported directions ($\alpha$) versus normalized minimum step size ($L_{min}/b$) for all designs capable of moving straight in two different directions. (B)-(C) Snapshots of (B) Design V and (C) Design VI at different times during a loading cycle, with frames from videos recorded during tests in which the samples are subjected to multiple inflation/deflation cycles. Magenta dashed lines indicate the numerically predicted trajectory.