Exact cellular decompositions represent a robot's free space by dividing it into regions with simple structure such that the sum of the regions fills the free space. These decompositions have been widely used for path planning between two points, but can be used for mapping and coverage of free spaces. In this paper, we define exact cellular decompositions where critical points of Morse functions indicate the location of cell boundaries. Morse functions are those whose critical points are non-degenerate. Between critical points, the structure of a space is effectively the same, so simple control strategies to achieve tasks, such as coverage, are feasible within each cell. This allows us to introduce a general framework for coverage tasks because varying the Morse function has the effect of changing the pattern by which a robot covers its free space. In this paper, we give examples of different Morse functions and comment on their corresponding tasks. In a companion paper, we describe the sensor-based algorithm that constructs the decomposition.
This research is focused on developing trajectory planning tools for the automotive painting industry. The geometric complexity of automotive surfaces and the complexity of the spray patterns produced by modern paint atomizers combine to make this a challenging and interesting problem. This paper documents our efforts to develop computationally tractable analytic deposition models for electrostatic rotating bell (ESRB) atomizers, which have recently become widely used in the automotive painting industry. The models presented in this paper account for both the effects of surface curvature as well as the deposition pattern of ESRB atomizers in a computationally tractable form, enabling the development of automated trajectory generation tools. We present experimental results used to develop and validate the models, and verify the interaction between the deposition pattern, the atomizer trajectory, and the surface curvature. Limitations of the deposition model with respect to predictions of paint deposition on highly curved surfaces are discussed.Note to Practitioners-The empirical paint deposition models developed herein, which are fit to experimental data, offer a significant improvement over models that are typically used in industrial robot simulations. The improved simulation results come without the computational cost and complexity of finite element methods. The models could be incorporated, as is, into existing industrial simulation tools, provided the users are cognizant of the model limitations with respect to highly curved surfaces. Although the models are based on readily available information, incorporating the models into existing robot simulation software would likely require support from the software vendor.
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