  Robotic assistance allows surgeons to perform dexterous and tremor-free
procedures, but robotic aid is still underrepresented in procedures with
constrained workspaces, such as deep brain neurosurgery and endonasal surgery.
In these procedures, surgeons have restricted vision to areas near the surgical
tooltips, which increases the risk of unexpected collisions between the shafts
of the instruments and their surroundings. In this work, our
vector-field-inequalities method is extended to provide dynamic
active-constraints to any number of robots and moving objects sharing the same
workspace. The method is evaluated with experiments and simulations in which
robot tools have to avoid collisions autonomously and in real-time, in a
constrained endonasal surgical environment. Simulations show that with our
method the combined trajectory error of two robotic systems is optimal.
Experiments using a real robotic system show that the method can autonomously
prevent collisions between the moving robots themselves and between the robots
and the environment. Moreover, the framework is also successfully verified
under teleoperation with tool-tissue interactions.
