Download Algorithmic Foundations of Robotics VI by Bruce Randall Donald (auth.), Michael Erdmann, Mark PDF

By Bruce Randall Donald (auth.), Michael Erdmann, Mark Overmars, David Hsu, Frank van der Stappen (eds.)

Robot algorithms are abstractions of computational tactics that keep watch over or cause approximately movement and notion within the actual international. simply because activities within the actual international are topic to actual legislation and geometric constraints, the layout and research of robotic algorithms increases a special mixture of questions up to speed thought, computational and differential geometry, and laptop technology. Algorithms function a unifying topic within the multi-disciplinary box of robotics.

This quantity involves chosen contributions to the 6th Workshop at the Algorithmic Foundations of Robotics. it is a hugely aggressive assembly of specialists within the box of algorithmic matters concerning robotics and automation.

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To examine the effect of surface Gaussian curvature K on the geodesic curvature κg of the offset curves, we apply the Gauss-Bonnet theorem to the region B bounded between the start curve, Cst , and its offset curve, Cof , (see Fig. 3(a)) and arrive at    κg . (1) K+ κg = Cof B Cst Equation 1 tells us that the more the surface bounded between the offset curve and the geodesic start curve bends, the more the geodesic curvature of the offset curve increases. On a surface where the sign of the Gaussian curvature stays the same, the further away we place the offset curve from the start curve, the higher the geodesic curvature of the offset curve is.

We seek to make the optimization of coverage variables tractable by decomposing the coverage problem into three relatively independent subproblems: i) selection of a “seed” pass termed the start curve on the surface (see Fig. 1(c)), ii) selection of the speed profile along a given pass, and iii) selection of the optimum spacing between a given pass and its adjacent pass. Based on these three subproblems, we generate the coverage trajectory using the procedure described in Algorithm 1. Data : Target surface CAD model, parameters for deposition model Result : Spray gun trajectory Select a pass termed the start curve on the surface; Optimize end-effector speed along the start curve; repeat Offset the most recently generated pass within the surface to its “right” side to obtain a new offset pass; Optimize end-effector speed along the new offset pass; until Offset pass lies completely outside the surface; Designate the start curve as the most recently generated pass; repeat Offset the most recently generated pass within the surface to its “left” side to obtain a new offset pass; Optimize end-effector speed along the new offset pass; until Offset pass lies completely outside the surface; Algorithm 1: Path Planning algorithm The rationale behind decomposing the coverage problem into the three subproblems is that each subproblem can be solved in a reasonable amount of Uniform Coverage of Simple Surfaces 29 time independently from the others.

In this section, we present procedures for index Uniform Coverage of Simple Surfaces 35 width optimization on surfaces with increasing geometric complexity: planar surfaces, extruded surfaces, and surfaces with non-zero Gaussian curvature. 1 Determining Index Widths on Planar Surfaces On a planar surface, geodesics are simply straight lines. 3, will be a straight line. The offsets of the start curve are parallel straight lines and accordingly the resultant coverage path consists of a family of parallel lines.

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