  This work proposes a novel singularity avoidance approach for real-time
trajectory optimization based on known singular configurations. The focus of
this work lies on analyzing kinematically singular configurations for three
robots with different kinematic structures, i.e., the Comau Racer 7-1.4, the
KUKA LBR iiwa R820, and the Franka Emika Panda, and exploiting these
configurations in form of tailored potential functions for singularity
avoidance. Monte Carlo simulations of the proposed method and the commonly used
manipulability maximization approach are performed for comparison. The
numerical results show that the average computing time can be reduced and
shorter trajectories in both time and path length are obtained with the
proposed approach
