Smoothing of Piecewise Linear Paths

The pointwise traversal of a given path is a popular task in the area of robotics, e.g. in mobile, industrial or surgical robotics. The easiest method to describe paths is by a sequence of linear segments, and for many tasks the precision of a path approximated by linear segments is sufficient. The movements to be accomplished by a mobile robot or the robot’s end-effector are described by a sequence of points in space, that have to be traversed by the robot. However, in practice, a pre-computed path unfortunately often consists of more path points than are necessary for sufficiently accurate execution. An excessive number of path points renders the movement jerky if the path points are dispersed around the optimal path, leading to unnecessary mechanical stress of both robot and tool. A second problem is that many path points lying close to one another can lead to high computational cost when traversing the path and can reduce traversal speed. Paths described by teach-in methods are one example where the path can consist of too many path points. In these methods, the desired movement is recorded while the operator moves the robot’s arm, either directly, through a master device or by giving instructions through a control panel. Because of the rather intuitive input of the human operator, the path suffers from deficiencies and frequent unnecessary changes of direction. The taught-in path can be traversed better after smoothing the path. Another example is voxel-based path planning. Here, only space points with discrete coordinates can be traversed, which may lead to a stair shaped approximation of diagonal paths. Just as with smoothed taught-in paths, smoothed voxel-based paths can be traversed more efficiently, because there are fewer changes of speed and direction, and the total path length is reduced. The remainder of the text first provides a problem description (Section 2), after which the state of the art is presented (Section 3). Then, the proposed procedure is described in detail (Section 4), and different specializations of the proposed method are shown for points with fixed orientation (Section 5) as well as with variable orientation (Section 6). Finally, experiments are described (Section 7), and open issues and further enhancements are discussed ( Section 8).