An algebraic method to check the singularity-free paths for parallel robots

Trajectory planning is a critical step while programming the parallel manipulators in a robotic cell. The main problem arises when there exists a singular configuration between the two poses of the end-effectors while discretizing the path with a classical approach. This paper presents an algebraic method to check the feasibility of any given trajectories in the workspace. The solutions of the polynomial equations associated with the tra-jectories are projected in the joint space using Gr{\"o}bner based elimination methods and the remaining equations are expressed in a parametric form where the articular variables are functions of time t unlike any numerical or discretization method. These formal computations allow to write the Jacobian of the manip-ulator as a function of time and to check if its determinant can vanish between two poses. Another benefit of this approach is to use a largest workspace with a more complex shape than a cube, cylinder or sphere. For the Orthoglide, a three degrees of freedom parallel robot, three different trajectories are used to illustrate this method.Comment: Appears in International Design Engineering Technical Conferences & Computers and Information in Engineering Conference , Aug 2015, Boston, United States. 201

SIM-DSP: A DSP-Enhanced CAD Platform for Signal Integrity Macromodeling and Simulation

Macromodeling-Simulation process for signal integrity verifications has become necessary for the high speed circuit system design. This paper aims to introduce a “VLSI Signal Integrity Macromodeling and Simulation via Digital Signal Processing Techniques” framework (known as SIM-DSP framework), which applies digital signal processing techniques to facilitate the SI verification process in the pre-layout design phase. Core identification modules and peripheral (pre-/post-)processing modules have been developed and assembled to form a verification flow. In particular, a single-step discrete cosine transform truncation (DCTT) module has been developed for modeling-simulation process. In DCTT, the response modeling problem is classified as a signal compression problem, wherein the system response can be represented by a truncated set of non-pole based DCT bases, and error can be analyzed through Parseval’s theorem. Practical examples are given to show the applicability of our proposed framework

Cusp Points in the Parameter Space of Degenerate 3-RPR Planar Parallel Manipulators

This paper investigates the conditions in the design parameter space for the existence and distribution of the cusp locus for planar parallel manipulators. Cusp points make possible non-singular assembly-mode changing motion, which increases the maximum singularity-free workspace. An accurate algorithm for the determination is proposed amending some imprecisions done by previous existing algorithms. This is combined with methods of Cylindric Algebraic Decomposition, Gr\"obner bases and Discriminant Varieties in order to partition the parameter space into cells with constant number of cusp points. These algorithms will allow us to classify a family of degenerate 3-RPR manipulators.Comment: ASME Journal of Mechanisms and Robotics (2012) 1-1

Detecting Similarity of Rational Plane Curves

A novel and deterministic algorithm is presented to detect whether two given rational plane curves are related by means of a similarity, which is a central question in Pattern Recognition. As a by-product it finds all such similarities, and the particular case of equal curves yields all symmetries. A complete theoretical description of the method is provided, and the method has been implemented and tested in the Sage system for curves of moderate degrees.Comment: 22 page

Planning Support Systems: Progress, Predictions, and Speculations on the Shape of Things to Come

In this paper, we review the brief history of planning support systems, sketching the way both the fields of planning and the software that supports and informs various planning tasks have fragmented and diversified. This is due to many forces which range from changing conceptions of what planning is for and who should be involved, to the rapid dissemination of computers and their software, set against the general quest to build ever more generalized software products applicable to as many activities as possible. We identify two main drivers – the move to visualization which dominates our very interaction with the computer and the move to disseminate and share software data and ideas across the web. We attempt a brief and somewhat unsatisfactory classification of tools for PSS in terms of the planning process and the software that has evolved, but this does serve to point up the state-ofthe- art and to focus our attention on the near and medium term future. We illustrate many of these issues with three exemplars: first a land usetransportation model (LUTM) as part of a concern for climate change, second a visualization of cities in their third dimension which is driving an interest in what places look like and in London, a concern for high buildings, and finally various web-based services we are developing to share spatial data which in turn suggests ways in which stakeholders can begin to define urban issues collaboratively. All these are elements in the larger scheme of things – in the development of online collaboratories for planning support. Our review far from comprehensive and our examples are simply indicative, not definitive. We conclude with some brief suggestions for the future