  Translationally diffusive behavior arising from the combination of
orientational diffusion and powered motion at microscopic scales is a known
phenomenon, but the peculiarities of the evolution of expected position
conditioned on initial position and orientation have been neglected. A theory
is given of the spiral motion of the mean trajectory depending upon propulsion
speed, angular velocity, orientational diffusion and rate of random chirality
reversal. We demonstrate the experimental accessibility of this effect using
both tadpole-like and Janus sphere dimer rotating motors. Sensitivity of the
mean trajectory to the kinematic parameters suggest that it may be a useful way
to determine those parameters.
