  Differential drive robots that can be modeled as a kinematic unicycle are a
standard mobile base platform for many service and logistics robots. Safe and
smooth autonomous motion around obstacles is a crucial skill for unicycle
robots to perform diverse tasks in complex environments. A classical control
approach for unicycle control is feedback linearization using a headway point
at a fixed headway distance in front of the unicycle. The unicycle headway
control brings the headway point to a desired goal location by embedding a
linear headway reference dynamics, which often results in an undesired offset
for the actual unicycle position. In this paper, we introduce a new unicycle
headway control approach with an adaptive headway distance that overcomes this
limitation, i.e., when the headway point reaches the goal the unicycle position
is also at the goal. By systematically analyzing the closed-loop unicycle
motion under the adaptive headway controller, we design analytical feedback
motion prediction methods that bound the closed-loop unicycle position
trajectory and so can be effectively used for safety assessment and safe
unicycle motion design around obstacles. We present an application of adaptive
headway motion control and motion prediction for safe unicycle path following
around obstacles in numerical simulations.
