  Accurately following a geometric desired path in a two-dimensional space is a
fundamental task for many engineering systems, in particular mobile robots.
When the desired path is occluded by obstacles, it is necessary and crucial to
temporarily deviate from the path for obstacle/collision avoidance. In this
paper, we develop a composite guiding vector field via the use of smooth bump
functions, and provide theoretical guarantees that the integral curves of the
vector field can follow an arbitrary sufficiently smooth desired path and avoid
collision with obstacles of arbitrary shapes. These two behaviors are reactive
since path (re)-planning and global map construction are not involved. To deal
with the common deadlock problem, we introduce a switching vector field, and
the Zeno behavior is excluded. Simulations are conducted to support the
theoretical results.
