  The need to guarantee safety of collaborative robots limits their
performance, in particular, their speed and hence cycle time. The standard
ISO/TS 15066 defines the Power and Force Limiting operation mode and prescribes
force thresholds that a moving robot is allowed to exert on human body parts
during impact, along with a simple formula to obtain maximum allowed speed of
the robot in the whole workspace. In this work, we measure the forces exerted
by two collaborative manipulators (UR10e and KUKA LBR iiwa) moving downward
against an impact measuring device. First, we empirically show that the impact
forces can vary by more than 100 percent within the robot workspace. The forces
are negatively correlated with the distance from the robot base and the height
in the workspace. Second, we present a data-driven model, 3D
Collision-Force-Map, predicting impact forces from distance, height, and
velocity and demonstrate that it can be trained on a limited number of data
points. Third, we analyze the force evolution upon impact and find that
clamping never occurs for the UR10e. We show that formulas relating robot mass,
velocity, and impact forces from ISO/TS 15066 are insufficient -- leading both
to significant underestimation and overestimation and thus to unnecessarily
long cycle times or even dangerous applications. We propose an empirical method
that can be deployed to quickly determine the optimal speed and position where
a task can be safely performed with maximum efficiency.
