Closed-Form Tilting Compensation for Slosh-Free Robotic Trajectories with Prescribed Yaw

The manipulation of liquid-filled containers in industrial robotics is inherently limited by sloshing phenomena, which may cause spillage, product loss, or reduced motion efficiency. While numerous slosh-suppression strategies have been proposed, most feedforward approaches assume that only the translational trajectory is prescribed. In practical pick-and-place tasks, however, the yaw orientation about the vertical axis is often constrained by process requirements, leading to so-called SCARA-like motions. This paper presents an analytical sloshing compensation method based on container tilting for robotic motions including a prescribed yaw profile. The liquid dynamics are modeled through a spherical pendulum approximation of the dominant sloshing mode, subject to three-dimensional translations and imposed rotations about the vertical axis. Closed-form expressions for the compensatory container orientation are derived from steady-state alignment conditions, enabling real-time implementation without numerical optimization. The proposed approach is experimentally validated on an industrial manipulator executing linear, planar, and spatial trajectories with simultaneous yaw rotations. Vision-based sloshing height reconstruction and force measurements confirm a significant reduction of peak sloshing during motion.