Set Of Relative Motions Research Articles

Simultaneous Merging Multiple Grid Maps Using the Robust Motion Averaging

Mapping in the GPS-denied environment is an important and challenging task in the field of robotics. In the large environment, mapping can be significantly accelerated by multiple robots exploring different parts of the environment. Accordingly, a key problem is how to integrate these local maps built by different robots into a single global map. In this paper, we propose an approach for simultaneous merging of multiple grid maps by the robust motion averaging. The main idea of this approach is to recover all global motions for map merging from a set of relative motions. Therefore, it firstly adopts the pair-wise map merging method to estimate relative motions for grid map pairs. To obtain as many reliable relative motions as possible, a graph-based sampling scheme is utilized to efficiently remove unreliable relative motions obtained from the pair-wise map merging. Subsequently, the accurate global motions can be recovered from the set of reliable relative motions by the motion averaging. Experimental results carried on real robot data sets demonstrate that proposed approach can achieve simultaneous merging of multiple grid maps with good performances.

Robust algorithm for multiview registration

Multiview registration is an important stage in three‐dimensional modelling pipeline. Motion averaging is an efficient approach for multiview registration which utilises the redundancy in overlap among the scans. The averaging of the underlying relative motions is performed in the corresponding Lie‐algebra elements of the SE(3) transformation matrices. However, this method is non‐robust and affected by the presence of outliers in the set of relative motions. The authors present a graph‐based approach to filter out the outliers before performing averaging of motions. The relative motions are assigned weights based on their agreement with global motions and other relative motions. The results indicate that the authors’ approach can efficiently filter out the outliers and can thus introduce robustness to multiview registration using motion averaging.

Analysis of Constraint Configurations in Mechanical Assembly via Screw Theory

The essential function of a mechanical assembly is the removal of degrees of freedom (DOF) to enable the transfer of load between two bodies. Assembly constraint features serve to provide this DOF removal, so their locations and orientations greatly affect the quality of an assembly as measured by its ability to resist relative motion between the parts. This paper addresses attachment-level design in which design decisions are made to establish the types, locations, and orientations of assembly features. The analysis methodology in this paper models assembly features such as point, pin, line, and plane constraints with equivalent first, second, and third order wrench systems. The set of relative motions to be evaluated is generated by composing from among these constraints a five-system pivot wrench combination to which a freedom screw motion is reciprocal. The effectiveness of each constraint to resist these motions is calculated as the ratio of the reaction forces at each resisting constraint to the input wrench magnitude. Based on these resistance values, multiple rating metrics are calculated to rate the overall assembly’s performance in resisting the motion. This work represents the first tool available to analyze a constraint configuration’s effectiveness to resist motion with a quantitative metric. Case studies are presented to demonstrate the utility of the analysis tool.

Discontinuously Movable Seven-Link Mechanisms Via Group-Algebraic Approach

Combining planar and spherical 4R chains generates three kinds of new discontinuously movable (DM) seven-link mechanisms. The mobility analysis is based on algebraic concepts of set theory. These mechanisms are called hybrid planar-spherical 7R, hybrid spherical-spherical 7R, and hybrid planar-planar 6RIP DM mechanisms. Their discontinuous mobility is explained employing the Lie group algebraic properties of the displacement set. Moreover, the same given spatial arrangement of joints can be linked in two ways constituting two distinct chains, which have a quite different mobility. One chain has two global degrees of freedom (d.o.f.), which disobey the general Grubler-Kutzbach mobility criterion. The other chain exhibits a singular pose, which is a bifurcation towards two distinct working modes of mobility with one d.o.f. Then the set of relative motions between any two specific links is not manifold but consists of the union of displacement one-dimensional manifolds. In general, when two or more subgroups are involved in a closed-loop chain, the discontinuous mobility can happen by changing the order of the kinematic pair linking.

Newton's Bucket Experiment

IN THIS PAPER I WILt ARGUE that Newton did not intend his bucket experiment to be interpreted as showing either that absolute space exists or that a relativistic mechanics is not possible. The intended function of the bucket experiment is more modest. It is to be used, as Newton clearly states, as an illustration of a case where absolute rotations can be distinguished from relative motions, given Newton's dynamical theory. It can also be used, again as Newton noted (although this time not so clearly), to refute Descartes's system of dynamics. It is not to be used to show, for example, that no set of relative motions (such as, with respect to the stars) could be used as a suitable reference frame for this particular case. A suitable reference frame is one that would provide a set of motions and water surface behavior that are coherent with the then accepted causal notions. I will also challenge the usual analysis of the log ic of the bucket experiment, which is that Newton showed experimentally that the curvature of the water surface is independent of the relative motion of the water with respect to the sides of the bucket. I will show that Newton's argument is that the experiment demonstrates that the degree of surface curvature is inversely related to this relative motion. Therefore, relative motion with respect to the bucket sides cannot be true motion since true motion even for Descartes is directly proportional to its effects. This clarification of the logic of the bucket experiment (as a refuter) will allow for a more adequate appreciation of the parallels between Newton 's early work in dynamics and his Principia. After I develop and substantiate these claims I will briefly consider Mach's criticisms given my reading of the bucket experiment. Finally, I will consider some of Newton's direct arguments for the existence of absolute space. The only purpose of this latter examination will be to contrast these direct arguments with the indirect support that the bucket experiment gives to the existence of absolute space. The thesis, contrary to mine, that Newton held that the bucket experiment does show the existence of absolute space and the untenability of a relativistic mechanics is one of the standard items in the repertoires of many historians and philosophers of science. In close association with this interpretation of Newton is the claim that the bucket experiment is unsuccessful with respect to its purported purpose, that Mach showed why, and that therefore Newton was in error. In a recent paper, for example, Ian Hacking gives this version of Newton 's error.