  In this paper, a method to achieve smooth transitions between sequential
reachability tasks for a continuous time mobile robotic system is presented.
Control barrier functions provide formal guarantees of forward invariance of
safe sets and finite-time reachability and are able to enforce task execution.
Barrier functions used in quadratic programs result in implementation of
controllers with real-time performance guarantees. Existing approaches for
multi-objective task execution using control barrier functions leverage
discretely switched, sequential quadratic programs to achieve successive tasks.
However, discrete switching can lead to control input discontinuities which can
affect a robot's performance. Hence, we propose a method which ensures
continuous transitions between sequential quadratic programs. In particular, a
time varying component to the barrier function constraint is introduced which
allows for a smooth transition between objectives. Robotic implementation
results are also provided.
