The power dissipation method and kinematic reducibility of multiple-model robotic systems

This paper develops a formal connection between the power dissipation method (PDM) and Lagrangian mechanics, with specific application to robotic systems. Such a connection is necessary for understanding how some of the successes in motion planning and stabilization for smooth kinematic robotic systems can be extended to systems with frictional interactions and overconstrained systems. We establish this connection using the idea of a multiple-model system, and then show that multiple-model systems arise naturally in a number of instances, including those arising in cases traditionally addressed using the PDM. We then give necessary and sufficient conditions for a dynamic multiple-model system to be reducible to a kinematic multiple-model system. We use this result to show that solutions to the PDM are actually kinematic reductions of solutions to the Euler-Lagrange equations. We are particularly motivated by mechanical systems undergoing multiple intermittent frictional contacts, such as distributed manipulators, overconstrained wheeled vehicles, and objects that are manipulated by grasping or pushing. Examples illustrate how these results can provide insight into the analysis and control of physical systems

Sublabel-Accurate Relaxation of Nonconvex Energies

We propose a novel spatially continuous framework for convex relaxations based on functional lifting. Our method can be interpreted as a sublabel-accurate solution to multilabel problems. We show that previously proposed functional lifting methods optimize an energy which is linear between two labels and hence require (often infinitely) many labels for a faithful approximation. In contrast, the proposed formulation is based on a piecewise convex approximation and therefore needs far fewer labels. In comparison to recent MRF-based approaches, our method is formulated in a spatially continuous setting and shows less grid bias. Moreover, in a local sense, our formulation is the tightest possible convex relaxation. It is easy to implement and allows an efficient primal-dual optimization on GPUs. We show the effectiveness of our approach on several computer vision problems

Implementation of MPEG-4s Subdivision Surfaces Tools

This work is about the implementation of a MPEG-4 decoder for subdivision surfaces, which are powerful 3D paradigms allowing to compactly represent piecewise smooth surfaces. This study will take place in the framework of MPEG-4 AFX, the extension of the MPEG-4 standard including the subdivision surfaces. This document will introduce, with some details, the theory of subdivision surfaces in the two forms present in MPEG-4: plain and detailed/ wavelet subdivision surfaces. It will particularly concentrate on wavelet subdivision surfaces, which permit progressive 3D mesh compression

SilNet : Single- and Multi-View Reconstruction by Learning from Silhouettes

The objective of this paper is 3D shape understanding from single and multiple images. To this end, we introduce a new deep-learning architecture and loss function, SilNet, that can handle multiple views in an order-agnostic manner. The architecture is fully convolutional, and for training we use a proxy task of silhouette prediction, rather than directly learning a mapping from 2D images to 3D shape as has been the target in most recent work. We demonstrate that with the SilNet architecture there is generalisation over the number of views -- for example, SilNet trained on 2 views can be used with 3 or 4 views at test-time; and performance improves with more views. We introduce two new synthetics datasets: a blobby object dataset useful for pre-training, and a challenging and realistic sculpture dataset; and demonstrate on these datasets that SilNet has indeed learnt 3D shape. Finally, we show that SilNet exceeds the state of the art on the ShapeNet benchmark dataset, and use SilNet to generate novel views of the sculpture dataset.Comment: BMVC 2017; Best Poste

A survey of partial differential equations in geometric design

YesComputer aided geometric design is an area where the improvement of surface generation techniques is an everlasting demand since faster and more accurate geometric models are required. Traditional methods for generating surfaces were initially mainly based upon interpolation algorithms. Recently, partial differential equations (PDE) were introduced as a valuable tool for geometric modelling since they offer a number of features from which these areas can benefit. This work summarises the uses given to PDE surfaces as a surface generation technique togethe

Accessibility for Line-Cutting in Freeform Surfaces

Manufacturing techniques such as hot-wire cutting, wire-EDM, wire-saw cutting, and flank CNC machining all belong to a class of processes called line-cutting where the cutting tool moves tangentially along the reference geometry. From a geometric point of view, line-cutting brings a unique set of challenges in guaranteeing that the process is collision-free. In this work, given a set of cut-paths on a freeform geometry as the input, we propose a conservative algorithm for finding collision-free tangential cutting directions. These directions, if they exist, are guaranteed to be globally accessible for fabricating the geometry by line-cutting. We then demonstrate how this information can be used to generate globally collision-free cut-paths. We apply our algorithm to freeform models of varying complexity.RYC-2017-2264