In some robotic manufacturing processes, a displacement between the nominal tool trajectory and the actual can be tolerated, provided that the displacement occurs along a specific direction/rotation axis. For instance, in wire sawing, a translation along the wire axis is permitted. Such an admissible displacement can be thought of as an additional degree of freedom that could be exploited for accomplishing further tasks, e.g., collision avoidance. In the case of offline programming, the operator can manually adapt the trajectory in order to exploit such additional degree of freedom. However, when the tool trajectory is automatically generated, as in modern flexible automation systems, an automatic way to adjust the displacement is needed. We propose an approach that, based on virtual redundancy (introduced originally for singularity avoidance purposes) and barrier functions, can automatically exploit the additional degree of freedom while satisfying the constraints on the admissible displacement.
