In everyday life, we often find that we can maintain an object's equilibrium on a tray by adjusting its orientation. Building upon this observation and extending the method we previously proposed to suppress sloshing in a moving vessel, this paper presents a feedforward control approach for transporting objects with a robot that are not firmly grasped but simply placed on a tray. The proposed approach combines smoothing actions and end-effector re-orientation to prevent object sliding. It can be integrated into existing robotic systems as a plug-in element between the reference trajectory generator and the robot control. To demonstrate the effectiveness of the proposed methods, particularly when dealing with unknown reference signals, we embed them in a direct teleoperation scheme. In this scheme, the user commands the robot carrying the tray by simply moving their hand in free space, with the hand's 3D position detected by a motion capture system. Furthermore, in the case of point-to-point motions, the same feedforward control, when fed with step inputs representing the desired goal position, dynamically generates the minimum-time reference trajectory that complies with velocity and acceleration constraints, thus avoiding sloshing and slipping. More information and accompanying videos can be found at https://sites.google.com/view/robotwaiter/
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