*5.1. Preliminaries*

During all the experiments, the robot's end effector must be able to achieve a given position and orientation inside the workspace thus ensuring a precise contact with the surface that allows us to complete a hypothetical surface treatment task (polishing, deburring etc.). The details of the two different robots are given next.


During the experiments, our proposed algorithm will be used to find a trajectory that is able to complete the required task while, at the same time, optimising the manipulability at each time step and avoiding collisions.

**Figure 1.** Workspaces for simulation experiments. Experiment I (**a**), Experiment II (**b**) and Experiment III (**c**). The manipulator fixed base is located at the (0, 0) coordinates. The dark grey sections define the obstacle walls, with its surface identifying the contact line to be tracked by the manipulator end effector.
