  Safe and smooth motion control is essential for mobile robots when performing
various automation tasks around obstacles, especially in the presence of people
and other mobile robots. The total turning and space used by a mobile robot
while moving towards a specified goal position play a crucial role in
determining the required control effort and complexity. In this paper, we
consider a standard unicycle control approach based on angular feedback
linearization and provide an explicit analytical measure for determining the
total turning effort during unicycle control in terms of unicycle state and
control gains. We show that undesired spiral oscillatory motion around the goal
position can be avoided by choosing a higher angular control gain compared to
the linear control gain. Accordingly, we establish an accurate, explicit
triangular motion range bound on the closed-loop unicycle trajectory using the
total turning effort. The improved accuracy in motion range prediction results
from a stronger dependency on the unicycle state and control parameters. To
compare alternative circular, conic, and triangular motion range prediction
approaches, we present an application of the proposed unicycle motion control
and motion prediction methods for safe unicycle path following around obstacles
in numerical simulations.
