Cellular Decomposition for Nonrepetitive Coverage Task With Minimum Discontinuities

Abstract

A mechanism to derive non-repetitive coverage path solutions with a proven minimal number of discontinuities is proposed in this work, with the aim to avoid unnecessary, costly end effector lift-offs for manipulators. The problem is motivated by the automatic polishing of an object. Due to the non-bijective mapping between the workspace and the joint-space, a continuous coverage path in the workspace may easily be truncated in the joint-space, incuring undesirable end effector lift-offs. Inversely, there may be multiple configuration choices to cover the same point of a coverage path through the solution of the Inverse Kinematics. The solution departs from the conventional local optimisation of the coverage path shape in task space, or choosing appropiate but possibly disconnected configurations, to instead explicitly explore the least number of discontinuous motions through the analysis of the structure of valid configurations in joint-space. The two novel contributions of this paper include proof that the least number of path discontinuities is predicated on the surrounding environment, independent from the choice of the actual coverage path; thus has a minimum. And an efficient finite cellular decomposition method to optimally divide the workspace into the minimum number of cells, each traversable without discontinuities by any arbitrary coverage path within.Extensive simulation examples and real-world results on a 5 DoF manipulator are presented to prove the validity of the proposed strategy in realistic settings.

Coverage Path Planning for UAV Based on Improved Back-and-Forth Mode

“…The basic idea of the Cellular Decomposition (CD) algorithms is decomposing the free space into "simple" cells to achieve coverage [34]. Complete coverage can be achieved after the robot visits all cells in the decomposition.…”

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

“…In earlier work [20], the optimal NCPP problem with least discontinuities was also modelled as a topological cell graph, and the solution transformed into an optimal design strategy of a colour (configuration) scheme whereby the strategic placement of cutting paths would invariably lead to different colour vertices on both sides of a partition. An illustrative example is provided by Fig 1 . In proving the finiteness of simply-connected cells, the following claims were validated:…”

“…The kinematic relationship of a typical manipulator makes mapping between work-and joint-space non-bijective [11], which in effect drives coverage paths to be traditionally carried out in the former to ensure no revisiting of points in the surface [15]. However, in further pursuing motions where the manipulator may minimise the number of reconfigurations is obliged to undertake to follow a desirable continous endeffector (EE) path, a global optimal cellular decomposition problem in joint-space has been proposed to incur joint-space partitions with minimum sets [20]. This is illustrated in the example shown by Fig.…”

“…The addition of obstacles and the relative pose of robot and object further condition the final solution. For further details please refer to [20].…”

“…Section IV proves the necessary conditions to apply the proposed algorithm. Section V briefly restates the existing results in [20] to solve for simply-connected cells. Section VI goes into further details about the finiteness of solving elementary genus-one cells, whilst a multi-stage iterative strategy to solve for larger genusn cells is described in Section VII.…”