Time optimal paths and acceleration lines of robotic manipulators

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Abstract
The concept of acceleration lines and their correlation with time optimal paths of robotic manipulators is presented. The acceleration lines represent the directions of maximum tip acceleration from a point in the manipulator work-space, starting at a zero velocity. These lines can suggest the number and shapes of time optimal paths for a class of manipulators. It is shown that nonsingular time optimal paths are tangent to one of the acceleration lines near the end-points. A procedure for obtaining near-optimal paths, utilizing the acceleration lines, is developed. These paths are obtained by connecting the end points with B splines tangent to the acceleration lines. The near-minimum paths are shown to yield better traveling times than the straight line path between the same end points. The near-minimum paths can be used as initial conditions in existing optimization methods to speed-up convergence and computation time. Also, this method is potentially a powerful tool for on-line robot path planning, and for interactive designs of robotic-cell layouts. Examples of time optimal paths of a two link manipulator, obtained by other optimization procedures [1], and their acceleration lines, are shown.

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