Robotic spray painting of car bodies motivates our work in constrained controlled coverage. This task has three parts: complete coverage, uniform coverage and control, i.e. it is a hybrid motion planning control problem. Complete coverage means visiting every point of the given environment at least once. We have developed complete coverage strategies for the planar environments. However, the automobile body surfaces are embedded in three dimensions, so we have to lift the coverage strategies to three dimensions. The car body surface is painted by tracing a sequence of points which are a fixed distance away from the car surface. These points lie on the surface termed offset surface every point of which is a fixed distance away from the car surface. To ensure complete coverage of the car surface, it is necessary to completely cover the offset surface. Based on the complete coverage strategies for planar environments, we use critical points on offset surface to ensure complete coverage of the offset surface. However, the nature of the offset surface is not known a priori, and hence it becomes challenging to determine all its critical points. We use critical points on the car surface to determine critical points on the offset surface, but unfortunately there are critical points on offset surface that do not have any corresponding critical points on the target surface. We identify these cases, that is, how to detect them. Thus, we have developed algorithms which completely cover the offset surface for polyhedral environments.
Not only covering the desired target surface completely is necessary, but it is also important that every point on the target surface receives the same amount of paint. Uniform coverage, thus necessarily requires uniform paint deposition in addition to the complete coverage. Uniform coverage is difficult to achieve even for a planar environment and a deposition model as simple as a circle. Curvature and tangent discontinuities on the target surface make the problem very challenging. When the spray gun is negotiating a tangent discontinuity or a portion of the car surface with high curvature, it should suddenly jump to a very high (infinite) speed, and jump back to the normal speed as soon as the corner is negotiated. However, this is practically impossible as real world robotic manipulators have bounds on the velocity as well as on the acceleration. Thus, we have to adopt some different strategy to paint areas on a target surface with high curvature.
Different deposition models make uniform coverage even more challenging. The paint comes out of the spray gun in the form of a cone-like structure. When the spray gun traces a curve on the offset surface, a strip is painted on the target surface. Usually in order to achieve good deposition of paint, these strips are made to overlap each other. There exist different models for the paint distribution coming out of the spray gun, and each model has a different optimum overlap ratio which yields uniform coverage. We are developing methods to determine these optimum ratios. When the spray has to start painting a new strip, either it has to overspray which results in waste of paint, or it has to negotiate the boundary of the car surface, which again causes more paint to deposit near the boundaries. We are developing strategies which will yield uniform coverage.
We will also look into the control side of the coverage .
|The Robotics Institute is part of the School of Computer Science, Carnegie Mellon University.|
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