Planning smooth orientation trajectories is a complex challenge in robotic spray painting, especially due to the need to ensure continuity in velocity and acceleration while avoiding singularities associated with Euler angles. This paper introduces a method for planning the orientation trajectories of spray-painting robots. The proposed approach leverages cubic B-splines with cumulative basis functions and unit quaternions to achieve a global interpolation of input orientations, guiding the robot tool along the required path. The approach is first compared with a standard strategy in which orientations are expressed as Euler angles, to demonstrate that the use of unit quaternions for orientation representation helps circumvent potential singularity issues associated with Euler angles. Then, the experimental validation on an industrial spray-painting robot with six degrees of freedom, following the trajectory needed to paint a three-dimensional model of a car bumper, illustrates the effectiveness of the proposed strategy in approximating input orientations. The approach also allows maintaining continuity in velocity and acceleration, crucial for successful industrial spray painting, while meeting joint velocities and accelerations limits. Furthermore, the maximum variation of the tangential velocity of the robot end-effector, relative to the imposed value, reaches 4% near the car bumper headlights, where the orientation changes rapidly.
