  A flexible active safety motion (FASM) control approach is proposed for the
avoidance of dynamic obstacles and the reference tracking in robot
manipulators. The distinctive feature of the proposed method lies in its
utilization of control barrier functions (CBF) to design flexible CBF-guided
safety criteria (CBFSC) with dynamically optimized decay rates, thereby
offering flexibility and active safety for robot manipulators in dynamic
environments. First, discrete-time CBFs are employed to formulate the novel
flexible CBFSC with dynamic decay rates for robot manipulators. Following that,
the model predictive control (MPC) philosophy is applied, integrating flexible
CBFSC as safety constraints into the receding-horizon optimization problem.
Significantly, the decay rates of the designed CBFSC are incorporated as
decision variables in the optimization problem, facilitating the dynamic
enhancement of flexibility during the obstacle avoidance process. In
particular, a novel cost function that integrates a penalty term is designed to
dynamically adjust the safety margins of the CBFSC. Finally, experiments are
conducted in various scenarios using a Universal Robots 5 (UR5) manipulator to
validate the effectiveness of the proposed approach.
