Time optimal paths and acceleration lines of robotic manipulators

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.