As an exercise, they ask the following interesting question.
Suppose that the interpolation algorithm is constrained so as to produce paths that are not physically possible. For instance, for the situation where a ball is thrown into the air from the ground and then returns to the ground ten seconds later, suppose that the derivatives at the endpoints are constrained so that the ball begins by moving upward, but also is moving upward at the ending time.
Then, they ask, what will the above search method produce, as a progressive sequence of paths, and what will the associated sequence of action-estimates converge to?
They suggest actually programming it, and say that it is an instructive exercise to perform.