  This paper solves the optimization problem for a simplified one-dimensional
worm model when the friction force depends on the direction of the motion. The
motion of the worm is controlled by the actuator force $f(t)$ which is assumed
to be piecewise continuous and always generates the same force in the opposite
directions. The paper derives the necessary condition for the force which
maximizes the average velocity or minimizes the power over a unit distance. The
maximum excursion of the worm body and the force are bounded. A simulation is
given at the end of the paper.
