  Multi-suction-cup grippers are frequently employed to perform pick-and-place
robotic tasks, especially in industrial settings where grasping a wide range of
light to heavy objects in limited amounts of time is a common requirement.
However, most existing works focus on using one or two suction cups to grasp
only irregularly shaped but light objects. There is a lack of research on
robust manipulation of heavy objects using larger arrays of suction cups, which
introduces challenges in modeling and predicting grasp failure. This paper
presents a general approach to modeling grasp strength in multi-suction-cup
grippers, introducing new constraints usable for trajectory planning and
optimization to achieve fast and reliable pick-and-place maneuvers. The primary
modeling challenge is the accurate prediction of the distribution of loads at
each suction cup while grasping objects. To solve for this load distribution,
we find minimum spring potential energy configurations through a simple
quadratic program. This results in a computationally efficient analytical
solution that can be integrated to formulate grasp failure constraints in
time-optimal trajectory planning. Finally, we present experimental results to
validate the efficiency and accuracy of the proposed model.
