An approach for smooth trajectory planning of high-speed pick-and-place parallel robots using quintic B-splines

This paper presents a new, highly effective approach for optimal smooth trajectory planning of high-speed pick-and-place parallel robots. The pick-and-place path is decomposed into two orthogonal coordinate axes in the Cartesian space and quintic B-spline curves are used to generate the motion profile along each axis for achieving C4-continuity. By using symmetrical properties of the geometric path defined, the proposed motion profile becomes essentially dominated by two key factors, representing the ratios of the time intervals for the end-effector to move from the initial point to the adjacent virtual and/or the via-points on the path. These two factors can then be determined by maximizing a weighted sum of two normalized single-objective functions and expressed by curve fitting as functions of the width/height ratio of the pick-and-place path, so allowing them to be stored in a look-up table to enable real-time implementation. Experimental results on a 4-DOF SCARA type parallel robot show that the residual vibration of the end-effector can be substantially reduced thanks to the very continuous and smooth joint torques obtained

Quality and productivity driven trajectory optimisation for robotic handling of compliant sheet metal parts in multi-press stamping lines

This paper investigates trajectory generation for multi-robot systems that handle compliant parts in order to minimise deformations during handling, which is important to reduce the risk of affecting the part’s dimensional quality. An optimisation methodology is proposed to generate deformation-minimal multi-robot coordinated trajectories for predefined robot paths and cycle-time. The novelty of the proposed optimisation methodology is that it efficiently estimates part deformations using a precomputed Response Surface Model (RSM), which is based on data samples generated by Finite Element Analysis (FEA) of the handled part and end-effector. The end-effector holding forces, plastic part deformations, collision-avoidance and multi-robot coordination are also considered as constraints in the optimisation model. The optimised trajectories are experimentally validated and the results show that the proposed optimisation methodology is able to significantly reduce the deformations of the part during handling, i.e. up to 12% with the same cycle-time in the case study that involves handling compliant sheet metal parts. This investigation provides insights into generating specialised trajectories for material handling of compliant parts that can systematically minimise part deformations to ensure final dimensional quality

Molecular motors: design, mechanism and control

Biological functions in each animal cell depend on coordinated operations of a wide variety of molecular motors. Some of the these motors transport cargo to their respective destinations whereas some others are mobile workshops which synthesize macromolecules while moving on their tracks. Some other motors are designed to function as packers and movers. All these motors require input energy for performing their mechanical works and operate under conditions far from thermodynamic equilibrium. The typical size of these motors and the forces they generate are of the order of nano-meters and pico-Newtons, respectively. They are subjected to random bombardments by the molecules of the surrounding aqueous medium and, therefore, follow noisy trajectories. Because of their small inertia, their movements in the viscous intracellular space exhibits features that are characteristics of hydrodynamics at low Reynold's number. In this article we discuss how theoretical modeling and computer simulations of these machines by physicists are providing insight into their mechanisms which engineers can exploit to design and control artificial nano-motors.Comment: 11 pages, including 8 embedded EPS figures; Invited article, accepted for Publication in "Computing in Science and Engineering" (AIP & IEEE

Spatial Aggregation: Theory and Applications

Visual thinking plays an important role in scientific reasoning. Based on the research in automating diverse reasoning tasks about dynamical systems, nonlinear controllers, kinematic mechanisms, and fluid motion, we have identified a style of visual thinking, imagistic reasoning. Imagistic reasoning organizes computations around image-like, analogue representations so that perceptual and symbolic operations can be brought to bear to infer structure and behavior. Programs incorporating imagistic reasoning have been shown to perform at an expert level in domains that defy current analytic or numerical methods. We have developed a computational paradigm, spatial aggregation, to unify the description of a class of imagistic problem solvers. A program written in this paradigm has the following properties. It takes a continuous field and optional objective functions as input, and produces high-level descriptions of structure, behavior, or control actions. It computes a multi-layer of intermediate representations, called spatial aggregates, by forming equivalence classes and adjacency relations. It employs a small set of generic operators such as aggregation, classification, and localization to perform bidirectional mapping between the information-rich field and successively more abstract spatial aggregates. It uses a data structure, the neighborhood graph, as a common interface to modularize computations. To illustrate our theory, we describe the computational structure of three implemented problem solvers -- KAM, MAPS, and HIPAIR --- in terms of the spatial aggregation generic operators by mixing and matching a library of commonly used routines.Comment: See http://www.jair.org/ for any accompanying file

SE(3)-DiffusionFields: Learning smooth cost functions for joint grasp and motion optimization through diffusion

Multi-objective optimization problems are ubiquitous in robotics, e.g., the optimization of a robot manipulation task requires a joint consideration of grasp pose configurations, collisions and joint limits. While some demands can be easily hand-designed, e.g., the smoothness of a trajectory, several task-specific objectives need to be learned from data. This work introduces a method for learning data-driven SE(3) cost functions as diffusion models. Diffusion models can represent highly-expressive multimodal distributions and exhibit proper gradients over the entire space due to their score-matching training objective. Learning costs as diffusion models allows their seamless integration with other costs into a single differentiable objective function, enabling joint gradient-based motion optimization. In this work, we focus on learning SE(3) diffusion models for 6DoF grasping, giving rise to a novel framework for joint grasp and motion optimization without needing to decouple grasp selection from trajectory generation. We evaluate the representation power of our SE(3) diffusion models w.r.t. classical generative models, and we showcase the superior performance of our proposed optimization framework in a series of simulated and real-world robotic manipulation tasks against representative baselines.Comment: diffusion models, SE(3), grasping