Motion planning for an actuated flexible polyhedron manifold

Stepping or crawling translation manoeuvres are computationally complicated when applied to hyper-redundant mechanisms. We introduce a motion planner for a novel polyhedron-shaped Actuated Flexible Manifold (AFM). The AFM is a two-dimensional closed or open surface embedded in ℝ³. The AFM can reshape itself up to a given radius of curvature at any given location on its surface. Motion can be made possible using a mesh of linear actuators. Our first goal was to calculate the forward and inverse kinematics in the configuration space for a discrete flat AFM. We demonstrate our solution on some actuated flexible grid-shaped manifolds using different actuation methods. We then simulate a translation of a hyper-redundant discrete, polyhedron-shaped AFMs. In addition, we show how the AFM can use its excessive degrees of freedom to avoid obstacles while moving. Our algorithm is applicable for a set of hyper-redundant mechanisms of various geometries.