  We examine the problem of target tracking whilst simultaneously preserving
the target's privacy as epitomized by the robotic panda tracking scenario,
which O'Kane introduced at the 2008 Workshop on the Algorithmic Foundations of
Robotics in order to elegantly illustrate the utility of ignorance. The present
paper reconsiders his formulation and the tracking strategy he proposed, along
with its completeness. We explore how the capabilities of the robot and panda
affect the feasibility of tracking with a privacy stipulation, uncovering
intrinsic limits, no matter the strategy employed. This paper begins with a
one-dimensional setting and, putting the trivially infeasible problems aside,
analyzes the strategy space as a function of problem parameters. We show that
it is not possible to actively track the target as well as protect its privacy
for every nontrivial pair of tracking and privacy stipulations. Secondly,
feasibility can be sensitive, in several cases, to the information available to
the robot initially. Quite naturally in the one-dimensional model, one may
quantify sensing power by the number of perceptual (or output) classes
available to the robot. The robot's power to achieve privacy-preserving
tracking is bounded, converging asymptotically with increasing sensing power.
We analyze the entire space of possible tracking problems, characterizing every
instance as either achievable, constructively by giving a policy where one
exists (some of which depend on the initial information), or proving the
instance impossible. Finally, to relate some of the impossibility results in
one dimension to their higher-dimensional counterparts, including the planar
panda tracking problem studied by O'Kane, we establish a connection between
tracking dimensionality and the sensing power of a one-dimensional robot.
