Estimating 3-D location parameters using dual number quaternions

This paper describes a new algorithm for estimating the position and orientation of objects. The problem is formulated as an optimization problem using dual number quaternions. The advantage of using this representation is that the method solves for the location estimate by minimizing a single cost function associated with the sum of the orientation and position errors and thus is expected to have a better performance on the estimation, both in accuracy and in speed. Several forms of sensory information can be used by the algorithm. That is, the measured data can be a combination of measured points on an object's surfaces and measured unit direction vectors located on the object. Simulations have been carried out on a Compaq 386/20 computer and the simulation results are analyzed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/29059/1/0000092.pd

Tele-autonomous control involving contacts: The applications of a high precision laser line range sensor

The object localization algorithm based on line-segment matching is presented. The method is very simple and computationally fast. In most cases, closed-form formulas are used to derive the solution. The method is also quite flexible, because only few surfaces (one or two) need to be accessed (sensed) to gather necessary range data. For example, if the line-segments are extracted from boundaries of a planar surface, only parameters of one surface and two of its boundaries need to be extracted, as compared with traditional point-surface matching or line-surface matching algorithms which need to access at least three surfaces in order to locate a planar object. Therefore, this method is especially suitable for applications when an object is surrounded by many other work pieces and most of the object is very difficult, is not impossible, to be measured; or when not all parts of the object can be reached. The theoretical ground on how to use line range sensor to located an object was laid. Much work has to be done in order to be really useful

Methods and strategies of object localization

An important property of an intelligent robot is to be able to determine the location of an object in 3-D space. A general object localization system structure is proposed, some important issues on localization discussed, and an overview given for current available object localization algorithms and systems. The algorithms reviewed are characterized by their feature extracting and matching strategies; the range finding methods; the types of locatable objects; and the mathematical formulating methods

Tele-Autonomous control involving contact

Object localization and its application in tele-autonomous systems are studied. Two object localization algorithms are presented together with the methods of extracting several important types of object features. The first algorithm is based on line-segment to line-segment matching. Line range sensors are used to extract line-segment features from an object. The extracted features are matched to corresponding model features to compute the location of the object. The inputs of the second algorithm are not limited only to the line features. Featured points (point to point matching) and featured unit direction vectors (vector to vector matching) can also be used as the inputs of the algorithm, and there is no upper limit on the number of the features inputed. The algorithm will allow the use of redundant features to find a better solution. The algorithm uses dual number quaternions to represent the position and orientation of an object and uses the least squares optimization method to find an optimal solution for the object's location. The advantage of using this representation is that the method solves for the location estimation by minimizing a single cost function associated with the sum of the orientation and position errors and thus has a better performance on the estimation, both in accuracy and speed, than that of other similar algorithms. The difficulties when the operator is controlling a remote robot to perform manipulation tasks are also discussed. The main problems facing the operator are time delays on the signal transmission and the uncertainties of the remote environment. How object localization techniques can be used together with other techniques such as predictor display and time desynchronization to help to overcome these difficulties are then discussed

A Solution for Multi-Alignment by Transformation Synchronisation

The alignment of a set of objects by means of transformations plays an important role in computer vision. Whilst the case for only two objects can be solved globally, when multiple objects are considered usually iterative methods are used. In practice the iterative methods perform well if the relative transformations between any pair of objects are free of noise. However, if only noisy relative transformations are available (e.g. due to missing data or wrong correspondences) the iterative methods may fail. Based on the observation that the underlying noise-free transformations can be retrieved from the null space of a matrix that can directly be obtained from pairwise alignments, this paper presents a novel method for the synchronisation of pairwise transformations such that they are transitively consistent. Simulations demonstrate that for noisy transformations, a large proportion of missing data and even for wrong correspondence assignments the method delivers encouraging results.Comment: Accepted for CVPR 2015 (please cite CVPR version

A Survey on Dual-Quaternions

Over the past few years, the applications of dual-quaternions have not only developed in many different directions but has also evolved in exciting ways in several areas. As dual-quaternions offer an efficient and compact symbolic form with unique mathematical properties. While dual-quaternions are now common place in many aspects of research and implementation, such as, robotics and engineering through to computer graphics and animation, there are still a large number of avenues for exploration with huge potential benefits. This article is the first to provide a comprehensive review of the dual-quaternion landscape. In this survey, we present a review of dual-quaternion techniques and applications developed over the years while providing insights into current and future directions. The article starts with the definition of dual-quaternions, their mathematical formulation, while explaining key aspects of importance (e.g., compression and ambiguities). The literature review in this article is divided into categories to help manage and visualize the application of dual-quaternions for solving specific problems. A timeline illustrating key methods is presented, explaining how dual-quaternion approaches have progressed over the years. The most popular dual-quaternion methods are discussed with regard to their impact in the literature, performance, computational cost and their real-world results (compared to associated models). Finally, we indicate the limitations of dual-quaternion methodologies and propose future research directions.Comment: arXiv admin note: text overlap with arXiv:2303.1339

A surgical system for automatic registration, stiffness mapping and dynamic image overlay

In this paper we develop a surgical system using the da Vinci research kit (dVRK) that is capable of autonomously searching for tumors and dynamically displaying the tumor location using augmented reality. Such a system has the potential to quickly reveal the location and shape of tumors and visually overlay that information to reduce the cognitive overload of the surgeon. We believe that our approach is one of the first to incorporate state-of-the-art methods in registration, force sensing and tumor localization into a unified surgical system. First, the preoperative model is registered to the intra-operative scene using a Bingham distribution-based filtering approach. An active level set estimation is then used to find the location and the shape of the tumors. We use a recently developed miniature force sensor to perform the palpation. The estimated stiffness map is then dynamically overlaid onto the registered preoperative model of the organ. We demonstrate the efficacy of our system by performing experiments on phantom prostate models with embedded stiff inclusions.Comment: International Symposium on Medical Robotics (ISMR 2018