High-Gain Disturbance Observer for Robust Trajectory Tracking of Quadrotors

This paper presents a simple method to boost the robustness of quadrotors in trajectory tracking. The presented method features a high-gain disturbance observer (HGDO) that provides disturbance estimates in real-time. The estimates are then used in a trajectory control law to compensate for disturbance effects. We present theoretical convergence results showing that the proposed HGDO can quickly converge to an adjustable neighborhood of actual disturbance values. We will then integrate the disturbance estimates with a typical robust trajectory controller, namely sliding mode control (SMC), and present Lyapunov stability analysis to establish the boundedness of trajectory tracking errors. However, our stability analysis can be easily extended to other Lyapunov-based controllers to develop different HGDO-based controllers with formal stability guarantees. We evaluate the proposed HGDO-based control method using both simulation and laboratory experiments in various scenarios and in the presence of external disturbances. Our results indicate that the addition of HGDO to a quadrotor trajectory controller can significantly improve the accuracy and precision of trajectory tracking in the presence of external disturbances

Virtual Reality Simulation of Glenoid Reaming Procedure

Glenoid reaming is a bone machining operation in Total Shoulder Arthroplasty (TSA) in which the glenoid bone is resurfaced to make intimate contact with implant undersurface. While this step is crucial for the longevity of TSA, many surgeons find it technically challenging. With the recent advances in Virtual Reality (VR) simulations, it has become possible to realistically replicate complicated operations without any need for patients or cadavers, and at the same time, provide quantitative feedback to improve surgeons\u27 psycho-motor skills. In light of these advantages, the current thesis intends to develop tools and methods required for construction of a VR simulator for glenoid reaming, in an attempt to construct a reliable tool for preoperative training and planning for surgeons involved with TSA. Towards the end, this thesis presents computational algorithms to appropriately represent surgery tool and bone in the VR environment, determine their intersection and compute realistic haptic feedback based on the intersections. The core of the computations is constituted by sampled geometrical representations of both objects. In particular, point cloud model of the tool and voxelized model of bone - that is derived from Computed Tomography (CT) images - are employed. The thesis shows how to efficiently construct these models and adequately represent them in memory. It also elucidates how to effectively use these models to rapidly determine tool-bone collisions and account for bone removal momentarily. Furthermore, the thesis applies cadaveric experimental data to study the mechanics of glenoid reaming and proposes a realistic model for haptic computations. The proposed model integrates well with the developed computational tools, enabling real-time haptic and graphic simulation of glenoid reaming. Throughout the thesis, a particular emphasis is placed upon computational efficiency, especially on the use of parallel computing using Graphics Processing Units (GPUs). Extensive implementation results are also presented to verify the effectiveness of the developments. Not only do the results of this thesis advance the knowledge in the simulation of glenoid reaming, but they also rigorously contribute to the broader area of surgery simulation, and can serve as a step forward to the wider implementation of VR technology in surgeon training programs

Fast and cross-vendor OpenCL-based implementation for voxelization of triangular mesh models

As the open standard for parallel programming of heterogeneous systems, OpenCL has been used in this study in the context of a particular and intensive computing task, namely the voxelization of tessellated objects. For this purpose, OpenCL platform has been utilized to develop a parallelized voxelization algorithm that relies on a fast and efficient triangular mesh facet/cube overlapping test. The extensive numerical tests conducted with heterogeneous hardware configurations on geometric objects of varying complexities, mesh/domain sizes, and voxel resolutions suggest that up to 99.6% or 260 times decrease in the computation time can be obtained when GPU- or CPU-based parallelized techniques are used instead of the conventional single-thread CPU approach. Future developments will attempt the integration of the current implementation into a virtual orthopaedic surgery platform

Sensor Fault Detection and Compensation with Performance Prescription for Robotic Manipulators

This paper focuses on sensor fault detection and compensation for robotic manipulators. The proposed method features a new adaptive observer and a new terminal sliding mode control law established on a second-order integral sliding surface. The method enables sensor fault detection without the need to impose known bounds on fault value and/or its derivative. It also enables fast and fixed-time fault-tolerant control whose performance can be prescribed beforehand by defining funnel bounds on the tracking error. The ultimate boundedness of the estimation errors for the proposed observer and the fixed-time stability of the control system are shown using Lyapunov stability analysis. The effectiveness of the proposed method is verified using numerical simulations on two different robotic manipulators, and the results are compared with existing methods. Our results demonstrate performance gains obtained by the proposed method compared to the existing results

Parallelized collision detection with applications in virtual bone machining

Background and objectives: Virtual reality surgery simulators have been proved effective for training in several surgical disciplines. Nevertheless, this technology is presently underutilized in orthopaedics, especially for bone machining procedures, due to the limited realism in haptic simulation of bone interactions. Collision detection is an integral part of surgery simulators and its accuracy and computational efficiency play a determinant role on the fidelity of simulations. To address this, the primary objective of this study was to develop a new algorithm that enables faster and more accurate collision detection within 1 ms (required for stable haptic rendering) in order to facilitate the improvement of the realism of virtual bone machining procedures. Methods: The core of the developed algorithm is constituted by voxmap point shell method according to which tool and osseous tissue geometries were sampled by points and voxels, respectively. The algorithm projects tool sampling points into the voxmap coordinates and compute an intersection condition for each point-voxel pair. This step is massively parallelized using Graphical Processing Units and it is further accelerated by an early culling of the unnecessary threads as instructed by the rapid estimation of the possible intersection volume. A contiguous array was used for implicit definition of voxmap in order to guarantee a fast access to voxels and thereby enable efficient material removal. A sparse representation of tool points was employed for efficient memory reductions. The effectiveness of the algorithm was evaluated at various bone sampling resolutions and was compared with prior relevant implementations. Results: The results obtained with an average hardware configuration have indicated that the developed algorithm is capable to reliably maintain \u3c 1 ms running time in severe tool-bone collisions, both sampled at 10243 resolutions. The results also showed the algorithm running time has a low sensitivity to bone sampling resolution. The comparisons performed suggested that the proposed approach is significantly faster than comparable methods while relying on lower or similar memory requirements. Conclusions: The algorithm proposed through this study enables a higher numerical efficiency and is capable to significantly enlarge the maximum resolution that can be used by high fidelity/high realism haptic simulators targeting surgical orthopaedic procedures

Parallel Haptic Rendering for Orthopedic Surgery Simulators

This study introduces a haptic rendering algorithm for simulating surgical bone machining operations. The proposed algorithm is a new variant of the voxmap point-shell method, where the bone and surgical tool geometries are represented by voxels and points, respectively. The algorithm encompasses computationally efficient methods in a data-parallel framework to rapidly query intersecting voxel-point pairs, remove intersected bone voxels to replicate bone removal and compute elemental cutting forces. A new force model is adopted from the composite machining literature to calculate the elemental forces with higher accuracy. The integration of the algorithm with graphic rendering for visuo-haptic simulations is also outlined. The algorithm is benchmarked against state-of-the-art methods and is validated against prior experimental data collected during bone drilling and glenoid reaming trials. The results indicate improvements in computational efficiency and the force/torque prediction accuracy compared to the existing methods, which can be ultimately translated into higher realism in simulating orthopedic procedures

Fast generation of cartesian meshes from micro-computed tomography data

© 2019 CAD Solutions, LLC. Micro-finite element models (μFEMs) are one of the critical components of the microscale analyses that are typically performed on trabecular bone. These models are often derived from on micro computed tomography (μCT) data and tend to encompass an extremely large number of elements that in turn require significant processing time and power. To address the increased computational demands, the main goal of the current study was to devise an algorithm capable to manage the large μCT data in order to construct Cartesian μFEMs. For this purpose, the developed technique relies on the projection of μCT voxels to a structured grid and were designed to involve fast integer operations and hashing techniques for fast mesh constructions. The numerical tests performed on common computer hardware revealed that only 55.16 seconds are required to discretize more than 36.2M voxels. Furthermore, the linear time complexity of the developed algorithm ensures that its efficiency will be preserved even in case of larger datasets that tend to be prevalent in micro-structural biomechanical analysis

Correction to: Material Mapping of QCT-Derived Scapular Models: A Comparison with Micro-CT Loaded Specimens Using Digital Volume Correlation (Annals of Biomedical Engineering, (2019), 47, 11, (2188-2198), 10.1007/s10439-019-02312-2)

© 2019, Biomedical Engineering Society. The article Material Mapping of QCT-Derived Scapular Models: A Comparison with Micro-CT Loaded Specimens Using Digital Volume Correlation, written by Knowles et al, was originally published electronically on the publisher’s internet portal (currently SpringerLink) on 11 July 2019 without open access. With the author(s)’ decision to opt for Open Choice the copyright of the article changed on [August 30] to © The Author(s) 2019 and the article is forthwith distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, duplication, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made

Development of a validated glenoid trabecular density-modulus relationship

© 2018 Elsevier Ltd Incorporating subject-specific mechanical properties derived from clinical-resolution computed tomography data increases the accuracy of finite element models. Site-specific relationships between density and modulus are required due to variations in trabecular architecture and tissue density by anatomic location. Equations have been developed for many anatomic locations and have been shown to have excellent statistical agreement with empirical results; however, a shoulder-specific density-modulus relationship does not currently exist. This study used micro-finite element cores of glenoid trabecular bone and co-registered quantitative computed tomography finite element models to develop a validated glenoid trabecular density-modulus relationship. Micro finite element model tissue density was considered as either homogeneous or heterogeneous, scaled by CT-intensity. When heterogeneous tissue density was considered, near absolute statistical agreement was predicted in the co-registered QCT-derived finite element models. The validated relationships have also been adapted for use in whole bone scapular models and have the potential to dramatically increase the accuracy of clinical-resolution CT-derived shoulder finite element studies