Non-revisiting Coverage Task with Minimal Discontinuities for Non-redundant Manipulators

A theoretically complete solution to the optimal Non-revisiting Coverage Path Planning (NCPP) problem of any arbitrarily-shaped object with a non-redundant manipulator is proposed in this work. Given topological graphs of surface cells corresponding to feasible and continuous manipulator configurations, the scheme is aimed at ensuring optimality with respect to the number of surface discontinuities, and extends the existing provable solution attained for simply-connected configuration cell topologies to any arbitrary shape. This is typically classified through their genus, or the number of "holes" which appear increasingly as configurations are further constrained with the introduction of additional metrics for the task at hand, e.g., manipulability thresholds, clearance from obstacles, end-effector orientations, tooling force/torque magnitudes, etc. The novel contribution of this paper is to show that no matter what the resulting topological shapes from such quality cell constraints may be, the graph is finitely solvable, and a multi-stage iterative solver is designed to find all such optimal solutions.