  Executing multiple tasks concurrently is important in many robotic
applications. Moreover, the prioritization of tasks is essential in
applications where safety-critical tasks need to precede application-related
objectives, in order to protect both the robot from its surroundings and vice
versa. Furthermore, the possibility of switching the priority of tasks during
their execution gives the robotic system the flexibility of changing its
objectives over time. In this paper, we present an optimization-based task
execution and prioritization framework that lends itself to the case of
time-varying priorities as well as variable number of tasks. We introduce the
concept of extended set-based tasks, encode them using control barrier
functions, and execute them by means of a constrained-optimization problem,
which can be efficiently solved in an online fashion. Finally, we show the
application of the proposed approach to the case of a redundant robotic
manipulator.
