Robotic Folding of Sheets with a Mechanics-based Approach

We report a mechanics-based approach for automatic folding of elastic sheets, e.g., rectangular towel. When manipulating deformable objects, robots must account for the deformation, which is often large and geometrically nonlinear. Challenges arise because the manipulation scheme should depend on the intrinsic properties (e.g., material and geometry) of the manipulated objects and environmental parameters (e.g., friction). We demonstrate that incorporating the mechanics of materials can improve the performance of robotic manipulation. A seemingly simple problem of folding a flexible sheet (e.g., a rectangular towel) into multiple layers is studied. A numerical simulation tool based on discrete differential geometry is used to model the folding process. We analyze the folding process with the numerical tool to compute the optimal trajectory of the robotic manipulator that is robust against friction of the surface and jittering of the manipulator. Simple energy scaling shows that a single parameter - the gravito-bending length – governs the folding process. The trajectories are implemented on a collaborative robot. Our experiments show that, even without any feedback control, the robot can fold sheets made of different materials into multiple layers. Compared with a mechanics-agnostic approach, the improvement in performance is demonstrated.