A positioning system can include a drive unit having an actuator element and a control system. The actuator element can include a piezoelectric material. The control system can be configured to select a path between a first position and a second position, identify at least one change of direction of the actuator element along the selected path, generate a hysteresis-compensated drive signal based at least in part on the change in direction, and apply the hysteresis-compensated drive signal to the actuator element to move an object along the path.