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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This paper is devoted to the permanence of the concept of Zero-Moment Point, widelyknown by the acronym ZMP. Thirty-five years have elapsed since its implicit presentation (actually before being named ZMP) to the scientific community and thirty-three years since it was explicitly introduced and clearly elaborated, initially in the leading journals published in English. Its first practical demonstration took place in Japan in 1984, at Waseda University, Laboratory of Ichiro Kato, in the first dynamically balanced robot WL-10RD of the robotic family WABOT. The paper gives an in-depth discussion of source results concerning ZMP, paying particular attention to some delicate issues that may lead to confusion if this method is applied in a mechanistic manner onto irregular cases of artificial gait, i.e. in the case of loss of dynamic balance of a humanoid robot. After a short survey of the history of the origin of ZMP a very detailed elaboration of ZMP notion is given, with a special review concerning “boundary cases” when the ZMP is close to the edge of the support polygon and “fictious cases” when the ZMP should be outside the support polygon. In addition, the difference between ZMP and the center of pressure is pointed out. Finally, some unresolved or insufficiently treated phenomena that may yield a significant improvement in robot performance are considered. In the area of biped robot research, much progress has been made in the past few years. However, some difficulties remain to be dealt with, particularly about the implementation of fast and dynamic walking gaits, in other words anthropomorphic gaits, especially on uneven terrain. In this perspective, both concepts of center of pressure (CoP) and zero moment point (ZMP) are obviously useful. In this paper, the two concepts are strictly defined, the CoP with respect to ground-feet contact forces, the ZMP with respect to gravity plus inertia forces. Then, the coincidence of CoP and ZMP is proven, and related control aspects are examined. Finally, a virtual CoP-ZMP is defined, allowing us to extend the concept when walking on uneven terrain. This paper is a theoretical study. Experimental results are presented in a companion paper, analyzing the evolution of the ground contact forces obtained from a human walker wearing robot feet as shoes. 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. Abstract Time-optimal motion planning is one of the most essential problems in robotic theories. The presented direct transcription approach uses convex optimisation method to obtain a minimum-time control for robot manipulators. One subset of motion planning is the waiter motion problem that consists of moving a tablet from one place to another as fast as possible, avoiding the slip of the object that is placed upon it. In this paper the direct transcription method is presented in order to solve the waiter problem. This path tracking problem is also approximated by sequential two dimensional second-order cone programs (SOCP) using nonlinear change of variables. The computational benefit of the sequential method compared to the direct transcription approach is presented. The waiter motion problem is validated by real-life experimental results with a 6-DoF robotic arm. When possible, non-prehensile transportation (i.e. transporting objects without grasping them) can be faster and more efficient than prehensile transportation. However, the need to explicitly consider reaction and friction forces yields kino-dynamic constraints that are difficult to take into account by traditional planning algorithms. Based on the recently developed Admissible Velocity Propagation algorithm, we propose here a fast and general non-prehensile transportation scheme. Our contribution is twofold. First we show how to cast the dynamic balance constraints of a 3D object (e.g. a bottle) into a form compatible with the AVP algorithm. Second, we extend the AVP-RRT algorithm into a more efficient AVP-biRRT algorithm, which makes use of the idea of concurrently growing two trees, one rooted at the starting configuration and one rooted at the goal configuration. We also show both in simulations and on a real robot how our algorithm allows planning fast and dynamic trajectories for the non-prehensile transportation of a bottle. Optimization is often difficult to apply to robots due to the presence of errors in model parameters, which can cause constraints to be violated during execution on the robot. This paper presents a method to optimize trajectories with large modeling errors using a combination of robust optimization and parameter learning. In particular it considers the context of contact modeling, which is highly susceptible to errors due to uncertain friction estimates, contact point estimates, and sensitivity to noise in actuator effort. A robust time-scaling method is presented that computes a dynamically-feasible, minimum-cost trajectory along a fixed path under frictional contact. The robust optimization model accepts confidence intervals on uncertain parameters, and uses a convex parameterization that computes dynamically-feasible motions in seconds. Optimization is combined with an iterative learning method that uses feedback from execution to learn confidence bounds on modeling parameters. It is applicable to general problems with multiple uncertain parameters that satisfy a monotonicity condition that requires parameters to have conservative and optimistic settings. The method is applied to manipulator performing a “waiter” task, on which an object is moved on a carried tray as quickly as possible, and to a simulated humanoid locomotion task. Experiments demonstrate this method can compensate for large modeling errors within a handful of iterations.