Robot Trajectory Optimization for Safe Transport of Deformable Packages

Efficient and safe transport of deformable packages using suction cups is crucial in warehouse automation. Unlike rigid packages, deformable packages exhibit complex oscillatory behaviors and can detach under aggressive motions. Traditional motion planners typically overlook these oscillations, often resulting in either unsafe trajectories or overly conservative, slow motions. This paper addresses that gap by formulating package oscillation dynamics as constraints and incorporating them into a Cartesian trajectory optimization framework. These constraints are formulated to be state-dependent - i.e., they adapt according to the instantaneous conditions along the planned trajectory (such as acceleration and gripper orientation) - to ensure that oscillations remain within safe limits. We derive a pendulum-like model to characterize package swing, enforcing constraints on peak oscillation angles. Our approach then optimizes end-effector trajectories under these state-dependent constraints, ensuring safe transport when the end-effector follows constant-acceleration profiles. Real-world experiments demonstrate that our optimized trajectories reduce transport time by up to 18% compared to baseline motions while strictly adhering to safety limits on package swing.