Time-Optimal Transport of Loosely Placed Liquid Filled Cups along Prescribed Paths
Klaus Zauner, Hubert Gattringer, Andreas Mueller
TL;DR
This work tackles the problem of time-optimal transport of a loosely placed liquid-filled cup on a tray attached to a robotic end-effector, with the goal of avoiding spillage. The authors integrate sloshing dynamics by modeling the liquid as a spherical pendulum and formulate a time-optimal path-following problem that couples rigid-body motion with the internal liquid dynamics, solved using direct multiple shooting in CasADi with $N=400$ shooting intervals. The approach enforces task constraints to prevent lifting, slipping, and tipping, and introduces liquid-induced restrictions through the pendulum model, demonstrating feasibility on a lemniscate end-effector path under prescribed parameters. This framework advances time-efficient, constraint-aware robotic manipulation of uncertain payloads and sets the stage for real-robot validation and further refinements to capture center-of-gravity shifts due to liquid movement.
Abstract
Handling loosely placed objects with robotic manipulators is a difficult task from the point of view of trajectory planning and control. This becomes even more challenging when the object to be handled is a container filled with liquid. This paper addresses the task of transporting a liquid-filled cup placed on a tray along a prescribed path in shortest time. The objective is to minimize swapping, thus avoiding spillage of the fluid. To this end, the sloshing dynamics is incorporated into the dynamic model used within the optimal control problem formulation. The optimization problem is solved using a direct multiple shooting approach.