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 the robotic literature, many researchers have investigated the waiter problem'': a manipulator, equipped with a flat plate, transports an object that is on the plate. This problem is closely related to the one considered in this paper. A popular approach to achieve grasp stability guarantee, proposed in @cite_20 @cite_1 @cite_13 , is to constrain the Zero-tilting Moment Point (ZMP) @cite_22 of the object to its support area on the flat plate. This clearly demonstrates the similarity between object transportation and humanoid locomotion. Similar to the classical ZMP concept for humanoid locomotion, this approach has two limitations: (i) it can only be applied if the object is on a flat surface and (ii) there is no guarantee that the object does not slip or twist @cite_10 . In a more recent work @cite_11 , Luo and Hauser proposed to consider the contact forces explicitly, eliminating the use of the ZMP and its limitations. However, their formulation resulted in a non-convex non-linear optimization problem that is computationally demanding, taking several seconds to terminate.
@cite_22 @cite_10 @cite_1 @cite_13 @cite_20 @cite_11
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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. This paper presents a direct solution approach for the so-called general waiter motion problem, which consists in moving a tablet as fast as possible from one pose to the other such that non of the objects resting on the tablet slides at any time. The question is akin to several industrial problems in which tangential forces are restricted due to functional reasons, such as suction grippers, motion of sensitive goods, etc. In contrast to existing approaches which parametrize the problem in configuration (joint) space, we decompose the overall task into two cascaded main components: shaping the optimal geometry of the spatial path, and finding the time optimal one-dimensional motion of the system along this path. The spatial path is parametrized using via poses in SE(3), making it possible to reduce the search space to significant physical subspaces, and to interact intuitively with the user. The overall optimization is subdivided into a series of subproblems with cost functions and search spaces of increasing fineness, such that each subproblem can be solved with the output of its predecessor. A solution of the waiter motion problem with four objects illustrates the applicability of the algorithm. In this paper, we present a convex optimization problem to generate Center of Mass (CoM) and momentum trajectories of a walking robot, such that the motion robustly satisfies the friction cone constraints on uneven terrain. We adopt the Contact Wrench Cone (CWC) criterion to measure a robot's dynamical stability, which generalizes the venerable Zero Moment Point (ZMP) criterion. Unlike the ZMP criterion, which is ideal for walking on flat ground with unbounded tangential friction forces, the CWC criterion incorporates non-coplanar contacts with friction cone constraints. We measure the robustness of the motion using the margin in the Contact Wrench Cone at each time instance, which quantifies the capability of the robot to instantaneously resist external force torque disturbance, without causing the foot to tip over or slide. For pre-specified footstep location and time, we formulate a convex optimization problem to search for robot linear and angular momenta that satisfy the CWC criterion. We aim to maximize the CWC margin to improve the robustness of the motion, and minimize the centroidal angular momentum (angular momentum about CoM) to make the motion natural. Instead of directly minimizing the non-convex centroidal angular momentum, we resort to minimizing a convex upper bound. We show that our CWC planner can generate motion similar to the result of the ZMP planner on flat ground with sufficient friction. Moreover, on an uneven terrain course with friction cone constraints, our CWC planner can still find feasible motion, while the outcome of the ZMP planner violates the friction limit. In this paper we consider the motion planning problem of humanoid with articulated-spine for object manipulation in double support phase. Complexity of motion planning increases due to higher degrees-of-freedom (DOF), redundancy arising due to articulated spine, inherent underactuation and stability constraint. Additionally, loop-closure constraints arise during double-support phase, and self-collision constraints exist independent of the task to be performed. These problems make motion planning of humanoids a challenging task. In this work, we address the above issues by proposing a sampling based approach for planning the motion of the humanoid. Our approach to the problem is based on RRT* which can generate asymptotically optimal paths. The proposed approach deals with the stability constraints by rejective sampling approach which divides random configurations generated into valid and invalid configurations. Additionally, the loop-closure constraints are tackled by separating the humanoid into two open-kinematic sub-chains, and then generating random configurations in one sub-chain whereas the remaining sub-chain uses inverse kinematics for closure. Efficacy of the proposed approach is demonstrated for whole-body motion planning of a 25-DOF humanoid in generating asymptotically optimal end-effector paths.