The problem is best described with the image below. An robot (the diamond shape) is only allowed to move in a piecewise linear fashion, with each halt being a point of a curve (the red curve). The robot always attempts a linear motion toward the end (on the right), but the motion is not always possible (note the "X", indicating collision).
As you can see, even if the robot moves from position 0 to position 1, the linear motion to the end is still impossible. But the motion 0-1, followed by f-End is acceptable because there are no collisions.
The question is: do you know of any paper studying a similar problem? I am interested in a mathematically sound solution (possibly with certain bounds on, e.g., number of linear segments or an error measure). Another way to approach the problem is studying ways to piecewise linear approximation of an arbitrary curves; a suggestion on a related work is highly appreciated.
ps. A simple solution would be a recursive splitting the curve into two parts, an process which would eventually give one an acceptable sequence; however, bounds are hard to establish in this case.
