Fast robotic pick-and-place with suction cups is a crucial component in the current development of automation in logistics (factory lines, e-commerce, etc.) By "critically fast" we mean the fastest possible movements for transporting an object such that it does not slip or fall from the suction cup. The main difficulties are: (i) handling the contact between the suction cup and the object, which fundamentally involves kinodynamic constraints, and (ii) doing so at a low computational cost, typically a few hundreds of milliseconds. To address these difficulties, we propose (a) a model for suction cup contacts, (b) a procedure to identify the contact stability constraint based on that model, and (c) a procedure to parameterize, in a time-optimal manner, arbitrary geometric paths under the identified contact stability constraint. We experimentally validate the proposed pipeline on a physical robot system: the cycle time for a typical pick-and-place task was less than 5 seconds, planning and execution times included. The full pipeline is released as open-source for the robotics community.
In contrast, our proposed approach utilizes polyhedral computational theory @cite_0 to derive grasp stability conditions that can account for general contact configuration (suction cup) and at the same time, allow efficient computations. Our use of polyhedral computational theory is inspired by the development of the Gravito-Inertia Wrench Cone in humanoid locomotion @cite_12 .
@cite_0 @cite_12
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The double description method is a simple and useful algorithm for enumerating all extreme rays of a general polyhedral cone in ℝd, despite the fact that we can hardly state any interesting theorems on its time and space complexities. In this paper, we reinvestigate this method, introduce some new ideas for efficient implementations, and show some empirical results indicating its practicality in solving highly degenerate problems. We propose a method for checking and enforcing multicontact stability based on the zero-tilting moment point (ZMP). The key to our development is the generalization of ZMP support areas to take into account: 1) frictional constraints and 2) multiple noncoplanar contacts. We introduce and investigate two kinds of ZMP support areas. First, we characterize and provide a fast geometric construction for the support area generated by valid contact forces, with no other constraint on the robot motion. We call this set the full support area. Next, we consider the control of humanoid robots by using the linear pendulum mode (LPM). We observe that the constraints stemming from the LPM induce a shrinking of the support area, even for walking on horizontal floors. We propose an algorithm to compute the new area, which we call the pendular support area. We show that, in the LPM, having the ZMP in the pendular support area is a necessary and sufficient condition for contact stability. Based on these developments, we implement a whole-body controller and generate feasible multicontact motions where an HRP-4 humanoid locomotes in challenging multicontact scenarios.