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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We present a multi-contact walking pattern generator based on preview-control of the 3D acceleration of the center of mass (COM). A key point in the design of our algorithm is the calculation of contact-stability constraints. Thanks to a mathematical observation on the algebraic nature of the frictional wrench cone, we show that the 3D volume of feasible COM accelerations is always an upward-pointing cone. We reduce its computation to a convex hull of (dual) 2D points, for which optimal C(nlog n) algorithms are readily available. This reformulation brings a significant speedup compared to previous methods, which allows us to compute time-varying contact-stability criteria fast enough for the control loop. Next, we propose a conservative trajectory-wide contact-stability criterion, which can be derived from COM-acceleration volumes at marginal cost and directly applied in a model-predictive controller. We finally implement this pipeline and exemplify it with the HRP-4 humanoid model in multi-contact dynamically walking scenarios. Traditional motion planning approaches for multilegged locomotion divide the problem into several stages, such as contact search and trajectory generation. However, reasoning about contacts and motions simultaneously is crucial for the generation of complex whole-body behaviors. Currently, coupling theses problems has required either the assumption of a fixed gait sequence and flat terrain condition, or nonconvex optimization with intractable computation time. In this letter, we propose a mixed-integer convex formulation to plan simultaneously contact locations, gait transitions, and motion, in a computationally efficient fashion. In contrast to previous works, our approach is not limited to flat terrain nor to a prespecified gait sequence. Instead, we incorporate the friction cone stability margin, approximate the robot's torque limits, and plan the gait using mixed-integer convex constraints. We experimentally validated our approach on the HyQ robot by traversing different challenging terrains, where nonconvexity and flat terrain assumptions might lead to suboptimal or unstable plans. Our method increases the motion robustness while keeping a low computation time. In this letter, we propose a two-stage strategy for optimal control problems of robotic mechanical systems that proves to be more robust, and yet more efficient, than straightforward solution strategies. Specifically, we focus on a simplified humanoid model, represented as a two-dimensional articulated serial chain of rigid bodies, in the tasks of getting up (sitting down) from (to) the supine and prone postures. Interactions with the environment are integral parts of these motions, and a priori unscheduled contact sequences are discovered by the solver itself, opportunistically making or breaking contacts with the ground through feet, knees, hips, elbows, and hands. The present investigation analyzes the effects on the computational performance of: 1) the explicit introduction of contact forces among the optimization variables, 2) the substitution of undesired contact forces with geometric constraints that prevent interpenetrations, and 3) the splitting of the planning problem into two consecutive phases of increasing complexity. To the best of our knowledge, these tests represent the only quantitative analysis of the performances achievable with different solution strategies for optimization-based, whole-body dynamic motion planning in the presence of contacts. This paper formalizes qualitative test of 3D frictional form-closure grasps of n robotic fingers as a problem of linear programming (LP). It is well-known that a sufficient and necessary condition for form-closure grasps is that the origin of the wrench space lies inside the convex hull of primitive contact wrenches. We demonstrate that the problem of querying whether the origin lies inside the convex hull is equivalent to a ray-shooting problem, which is dual to a LP problem based on the duality between convex hulls and convex polytopes. Furthermore, this paper addresses a problem of minimizing the L sub 1 norm of the grasp forces balancing an external wrench, which can be also transformed to a ray-shooting problem. We have implemented the algorithms and confirmed their real-time efficiency for qualitative test and grasp force optimization.