An Improved Maximal Continuity Graph Solver for Non-Redundant Manipulator Non-Revisiting Coverage

This paper proposes an improved solver for the maximal continuity graph painting problem. The problem is motivated by the real-world surface non-revisiting coverage path planning (NCPP) task carried out by manipulators, where the physical meaning of maximising the colouring continuity in the graph translates to minimising the number of undesirable transitions between end-effector force/torque control discontinuities. Early works have formulated the graph-based representation of the task and finitely solved the graph. However, the exponential growth of its algorithmic complexity makes the problem intractable for even relatively simple graphs. The improved solver proposed in this paper demonstrates exponential improvement compared to the state-of-the-art algorithm, setting guaranteed bounds on performance, whereby the algorithmic complexity is proven reduced by a factor of $2^{N}$ , N being the number of internal edges in the graph. Challenging simulated experiments are presented to validate the computational advantage, and an open source implementation is also provided for the benefit of the community. Note to Practitioners—To solve a non-redundant manipulator NCPP task, the first step is collecting all valid inverse kinematics configurations that lead to coverage on the surface. Continuous configurations can then be grouped and assigned the same colour. This process creates a spatial distribution of colours on the target surface, forming a topological graph as detailed in this paper. Using the proposed algorithm, each coverable point on the surface is assigned a colour, which specifies the unique inverse kinematic configuration that the manipulator should adopt to cover such a point. A suitable geometric coverage planner can then be employed to generate the path that a manipulator end-effector must follow on the surface that is guaranteed to have the minimum number of end-effector discontinuities. In this paper, an (open-sourced) solver is proposed to solve the graph optimally from a computational point of view, most notably increasing productivity from a manufacturing/automated perspective.