A Lanczos Method for Approximating Composite Functions

We seek to approximate a composite function h(x) = g(f(x)) with a global polynomial. The standard approach chooses points x in the domain of f and computes h(x) at each point, which requires an evaluation of f and an evaluation of g. We present a Lanczos-based procedure that implicitly approximates g with a polynomial of f. By constructing a quadrature rule for the density function of f, we can approximate h(x) using many fewer evaluations of g. The savings is particularly dramatic when g is much more expensive than f or the dimension of x is large. We demonstrate this procedure with two numerical examples: (i) an exponential function composed with a rational function and (ii) a Navier-Stokes model of fluid flow with a scalar input parameter that depends on multiple physical quantities

Lightweight means of actuation for use in space-based robotics applications

In the field of robotics many researchers have devoted a large amount of time to pursuing means to reduce the weight of robotic systems. For space robotics, this becomes even more important due to launch cost being directly affected by weight. During review, potential progress involving weight reduction of actuators has been encountered, which it is necessary to investigate further in order to ascertain the potential advantages and disadvantages of such work. The contribution to be put forth here is a review of means by which reductions in weight can be achieved, with particular emphasis on space robotic actuation sub-systems. Ideas will be posited about the possible configurations which could be explored to reduce weight whilst attempting to maintain performance. It is expected that this contribution will provide evidence-based support for some future research directions, and will also help to stimulate discussion and further work on the subject of lightweight robotics and lightweight actuators. The next stages of this project aim to enhance some of the actuation ideas investigated so far, test these comparatively against one another, and critically review them alongside existing lightweight actuation methods. Following this, simulation of actuation concepts being applied to robotic applications will take place. This is in order to evaluate their performance in microgravity environments and to test their versatility. This process, as part of this project, will also be discussed in this pape

A novel haptic model and environment for maxillofacial surgical operation planning and manipulation

This paper presents a practical method and a new haptic model to support manipulations of bones and their segments during the planning of a surgical operation in a virtual environment using a haptic interface. To perform an effective dental surgery it is important to have all the operation related information of the patient available beforehand in order to plan the operation and avoid any complications. A haptic interface with a virtual and accurate patient model to support the planning of bone cuts is therefore critical, useful and necessary for the surgeons. The system proposed uses DICOM images taken from a digital tomography scanner and creates a mesh model of the filtered skull, from which the jaw bone can be isolated for further use. A novel solution for cutting the bones has been developed and it uses the haptic tool to determine and define the bone-cutting plane in the bone, and this new approach creates three new meshes of the original model. Using this approach the computational power is optimized and a real time feedback can be achieved during all bone manipulations. During the movement of the mesh cutting, a novel friction profile is predefined in the haptical system to simulate the force feedback feel of different densities in the bone

The design of a robotic arm link using functionally graded materials : a case study

The development and design of a functionally-graded material (FGM) robotic arm for supporting and manipulating a vision system is discussed in this paper. The aim is to understand if using FGMs effectively reduce mass compared to single material parts. The evolution of ideas using topological optimisation (TO) and FGMs towards the design are shown and reviewed. The final design uses TO, and as such needs to be manufactured using additive manufacture (AM). Constraints have been put in place to ensure physical manufacturability is possible. The final design reduces the mass compared to the original arm by 61.4%

A methodology for design of lightweight robotic arm links in harsh environments

A methodology for the creation of functionally graded material (FGM) parts in harsh environments has been developed. It uses a two-stage optimisation approach that focusses first on the task-dependent material choice and then on the topological optimisation (TO) of the part. Constraints are in place to ensure the part can be manufactured, including the extent/smoothness of material blending and the minimum feature size and layer thickness. Thought is also put into space-specific concerns, such as radiation and cyclic thermal heating. The methodology assumes an initial design solution has already been generated, and covers from the beginning of the CAD phase to the end of the computational testing phase. Design constraints are created with additive manufacture (AM) in mind, and suggestions are made for material mixing processes for FGM, material layout strategies and manufacturability, including scanning strategies and surface finish

Autonomous navigation with ROS for a mobile robot in agricultural fields

Autonomous monitoring of agricultural farms and fields has recently become feasible due to continuing advances in robotics technology, but many notable challenges remain. In this paper, we describe the state of ongoing work to create a fully autonomous ground rover platform for monitoring and intervention tasks on modern farms that is built using inexpensive and off the shelf hardware and Robot Operating System (ROS) software so as to be affordable to farmers. The hardware and software architectures used in this rover are described along with challenges and solutions in odometry and localization, object recognition and mapping, and path planning algorithms under the constraints of the current hardware. Results obtained from laboratory and field testing show both the key challenges to be overcome, and the current successes in applying a low-cost rover platform to the task of autonomously navigating the outdoor farming environment

Monoidal Hom-Hopf algebras

Hom-structures (Lie algebras, algebras, coalgebras, Hopf algebras) have been investigated in the literature recently. We study Hom-structures from the point of view of monoidal categories; in particular, we introduce a symmetric monoidal category such that Hom-algebras coincide with algebras in this monoidal category, and similar properties for coalgebras, Hopf algebras and Lie algebras.Comment: 25 pages; extended version: compared to the version that appeared in Comm. Algebra, the Section Preliminary Results and Remarks 5.1 and 6.1 have been adde

Visual pose estimation system for autonomous rendezvous of spacecraft

In this work, a tracker spacecraft equipped with a short-range vision system is tasked with visually identifying a target spacecraft and determining its relative angular velocity and relative linear velocity using only visual information from onboard cameras. Focusing on methods that are feasible for implementation on relatively simple spacecraft hardware, we locate and track objects in three-dimensional space using conventional high-resolution cameras, saving cost and power compared to laser or infrared ranging systems. Identification of the target is done by means of visual feature detection and tracking across rapid, successive frames, taking the perspective matrix of the camera system into account, and building feature maps in three dimensions over time. Features detected in two-dimensional images are matched and triangulated to provide three-dimensional feature maps using structure-from-motion techniques. This methodology allows one, two, or more cameras with known baselines to be used for triangulation, with more images resulting in higher accuracy. Triangulated points are organized by means of orientation histogram descriptors and used to identify and track parts of the target spacecraft over time. This allows some estimation of the target spacecraft's motion even if parts of the spacecraft are obscured or in shadow. The state variables with respect to the camera system are extracted as a relative rotation quaternion and relative translation vector for the target. Robust tracking of the state variables for the target spacecraft is accomplished by an embedded adaptive unscented Kalman filter. In addition to estimation of the target quaternion from visual Information, the adaptive filter can also identify when tracking errors have occurred by measurement of the residual. Significant variations in lighting can be tolerated as long as the movement of the satellite is consistent with the system model, and illumination changes slowly enough for state variables to be estimated periodically. Inertial measurements over short periods of time can then be used to determine the movement of both the tracker and target spacecraft. In addition, with a sufficient number of features tracked, the center of mass of the target can be located. This method is tested using laboratory images of spacecraft movement with a simulated spacecraft movement model. Varying conditions are applied to demonstrate the effectiveness and limitations of the system for online estimation of the movement of a target spacecraft at close range