Point to point time optimal handling of unmounted rigid objects and liquid-filled containers

Time optimal handling of parts loosely placed at the end-effector (EE) of a robot, known as waiter motion problem, has high practical relevance, which becomes more challenging if the object is a liquid-filled container. The waiter motion problem was often restricted to a time -optimal path following problem, which limits the flexibility and task efficiency. To overcome this restriction, in this paper, the general point to point (PtP) time-optimal motion planning problem is formulated and solved with a multiple shooting method. The formulation includes all relevant dynamic effects (joint friction, contact, motor limits, etc.) assuming rigid behavior of the robot as well as of the object placed at the EE. The trajectory is C2-continuous, avoiding bang-bang behavior of motor torques. The CasADi framework and the Ipopt solver are used for numerical computations. The reported experimental results confirm applicability of the trajectory to real robotic setup in case of rigid objects. Further, handling of containers filled with liquid is addressed. Experiments are compared with numerical results obtained with SPH particle simulation. Experiment and simulation indicate that sloshing effects must be taken into account in the control formulation.