A first extension of geometric control theory to underwater vehicles

This paper serves as a first study on the implementation of control strategies developed using a kinematic reduction onto test bed autonomous underwater vehicles (AUVs). The equations of motion are presented in the framework of differential geometry, including external dissipative forces, as a forced affine connection control system. We show that the hydrodynamic drag forces can be included in the affine connection, resulting in an affine connection control system. The definitions of kinematic reduction and decoupling vector field are thus extended from the ideal fluid scenario. Control strategies are computed using this new extension and are reformulated for implementation onto a test-bed AUV. We compare these geometrically computed controls to time and energy optimal controls for the same trajectory which are computed using a previously developed algorithm. Through this comparison we are able to validate our theoretical results based on the experiments conducted using the time and energy efficient strategies.

Decoupled trajectory planning for a submerged rigid body subject to dissipative and potential forces

This paper studies the practical but challenging problem of motion planning for a deeply submerged rigid body. Here, we formulate the dynamic equations of motion of a submerged rigid body under the architecture of differential geometric mechanics and include external dissipative and potential forces. The mechanical system is represented as a forced affine-connection control system on the configuration space SE(3). Solutions to the motion planning problem are computed by concatenating and reparameterizing the integral curves of decoupling vector fields. We provide an extension to this inverse kinematic method to compensate for external potential forces caused by buoyancy and gravity. We present a mission scenario and implement the theoretically computed control strategy onto a test-bed autonomous underwater vehicle. This scenario emphasizes the use of this motion planning technique in the under-actuated situation; the vehicle loses direct control on one or more degrees of freedom. We include experimental results to illustrate our technique and validate our method.

Geometric Control Theory and its Application to Underwater Vehicles

This dissertation is based on theoretical study and experiments which extend geometric control theory to practical applications within the field of ocean engineering. We present a method for path planning and control design for underwater vehicles by use of the architecture of differential geometry. In addition to the theoretical design of the trajectory and control strategy, we demonstrate the effectiveness of the method via the implementation onto a test-bed autonomous underwater vehicle. Bridging the gap between theory and application is the ultimate goal of control theory. Major developments have occurred recently in the field of geometric control which narrow this gap and which promote research linking theory and application. In particular, Riemannian and affine differential geometry have proven to be a very effective approach to the modeling of mechanical systems such as underwater vehicles. In this framework, the application of a kinematic reduction allows us to calculate control strategies for fully and under-actuated vehicles via kinematic decoupled motion planning. However, this method has not yet been extended to account for external forces such as dissipative viscous drag and buoyancy induced potentials acting on a submerged vehicle. To fully bridge the gap between theory and application, this dissertation addresses the extension of this geometric control design method to include such forces. We incorporate the hydrodynamic drag experienced by the vehicle by modifying the Levi-Civita affine connection and demonstrate a method for the compensation of potential forces experienced during a prescribed motion. We present the design method for multiple different missions and include experimental results which validate both the extension of the theory and the ability to implement control strategies designed through the use of geometric techniques. By use of the extension presented in this dissertation, the underwater vehicle application successfully demonstrates the applicability of geometric methods to design implementable motion planning solutions for complex mechanical systems having equal or fewer input forces than available degrees of freedom. Thus, we provide another tool with which to further increase the autonomy of underwater vehicles.

Controlling a submerged rigid body : a geometric analysis

In this paper we analyze the equations of motion of a submerged rigid body. Our motivation is based on recent developments done in trajectory design for this problem. Our goal is to relate some properties of singular extremals to the existence of decoupling vector fields. The ideas displayed in this paper can be viewed as a starting point to a geometric formulation of the trajectory design problem for mechanical systems with potential and external forces.

Multi-objective four-dimensional vehicle motion planning in large dynamic environments

This paper presents Multi-Step A* (MSA*), a search algorithm based on A* for multi-objective 4D vehicle motion planning (three spatial and one time dimension). The research is principally motivated by the need for offline and online motion planning for autonomous Unmanned Aerial Vehicles (UAVs). For UAVs operating in large, dynamic and uncertain 4D environments, the motion plan consists of a sequence of connected linear tracks (or trajectory segments). The track angle and velocity are important parameters that are often restricted by assumptions and grid geometry in conventional motion planners. Many existing planners also fail to incorporate multiple decision criteria and constraints such as wind, fuel, dynamic obstacles and the rules of the air. It is shown that MSA* finds a cost optimal solution using variable length, angle and velocity trajectory segments. These segments are approximated with a grid based cell sequence that provides an inherent tolerance to uncertainty. Computational efficiency is achieved by using variable successor operators to create a multi-resolution, memory efficient lattice sampling structure. Simulation studies on the UAV flight planning problem show that MSA* meets the time constraints of online replanning and finds paths of equivalent cost but in a quarter of the time (on average) of vector neighbourhood based A*.

Geometric and force relationships for the development of a scaled model hydraulic excavator

Hydraulic excavators in the mining industry are widely used owing to the large payload capabilities these machines can achieve. However, there are very few optimisation studies for producing efficient hydraulic excavator backets. An efficient bucket can avoid unnecessary weight; greatly influence the payload and optimise the efficiency of hydraulic mining excavators. This paper presents a framework for the development of a scaled hydraulic excavator by examining the geometry and force relationships. A small hydraulic excavator was purchased and fitted with a broom scaled to a factor. Geometric and force relationships of the model were derived to assist computer instrumentation to retrieve necessary variable input for bucket design.

A Modified inverse integer Cholesky decorrelation method and the performance on ambiguity resolution

One of the research focuses in the integer least squares problem is the decorrelation technique to reduce the number of integer parameter search candidates and improve the efficiency of the integer parameter search method. It remains as a challenging issue for determining carrier phase ambiguities and plays a critical role in the future of GNSS high precise positioning area. Currently, there are three main decorrelation techniques being employed: the integer Gaussian decorrelation, the Lenstra–Lenstra–Lovász (LLL) algorithm and the inverse integer Cholesky decorrelation (IICD) method. Although the performance of these three state-of-the-art methods have been proved and demonstrated, there is still a potential for further improvements. To measure the performance of decorrelation techniques, the condition number is usually used as the criterion. Additionally, the number of grid points in the search space can be directly utilized as a performance measure as it denotes the size of search space. However, a smaller initial volume of the search ellipsoid does not always represent a smaller number of candidates. This research has proposed a modified inverse integer Cholesky decorrelation (MIICD) method which improves the decorrelation performance over the other three techniques. The decorrelation performance of these methods was evaluated based on the condition number of the decorrelation matrix, the number of search candidates and the initial volume of search space. Additionally, the success rate of decorrelated ambiguities was calculated for all different methods to investigate the performance of ambiguity validation. The performance of different decorrelation methods was tested and compared using both simulation and real data. The simulation experiment scenarios employ the isotropic probabilistic model using a predetermined eigenvalue and without any geometry or weighting system constraints. MIICD method outperformed other three methods with conditioning improvements over LAMBDA method by 78.33% and 81.67% without and with eigenvalue constraint respectively. The real data experiment scenarios involve both the single constellation system case and dual constellations system case. Experimental results demonstrate that by comparing with LAMBDA, MIICD method can significantly improve the efficiency of reducing the condition number by 78.65% and 97.78% in the case of single constellation and dual constellations respectively. It also shows improvements in the number of search candidate points by 98.92% and 100% in single constellation case and dual constellations case.

Continuous appearance-based trajectory SLAM

This paper describes a novel probabilistic approach to incorporating odometric information into appearance-based SLAM systems, without performing metric map construction or calculating relative feature geometry. The proposed system, dubbed Continuous Appearance-based Trajectory SLAM (CAT-SLAM), represents location as a probability distribution along a trajectory, and represents appearance continuously over the trajectory rather than at discrete locations. The distribution is evaluated using a Rao-Blackwellised particle filter, which weights particles based on local appearance and odometric similarity and explicitly models both the likelihood of revisiting previous locations and visiting new locations. A modified resampling scheme counters particle deprivation and allows loop closure updates to be performed in constant time regardless of map size. We compare the performance of CAT-SLAM to FAB-MAP (an appearance-only SLAM algorithm) in an outdoor environment, demonstrating a threefold increase in the number of correct loop closures detected by CAT-SLAM.

Interfacial debonding behavior of composite beam/plates with PZT patch

This paper studies interfacial debonding behavior of composite beams which include piezoelectric materials, adhesive and host beam. The focus is put on crack initiation and growth of the piezoelectric adhesive interface. Closed-form solutions of interface stresses and energy release rates are obtained for adhesive layer in the piezoelectric composite beams. Finite element analyses have been carried out to study the initiation and growth of interfaces crack for piezoelectric beams with interface element by ANSYS, in which the interface element of FE model is based on the cohesive zone models to characterize the fracture behavior of the interfacial debonding. The results have been compared with analystical solution, and the influence of different geometry and material parameters on the interfacial behavior of piezoelectric composite beams have been discussed.

Patient-specific computational biomechanics for simulating adolescent scoliosis surgery : predicted vs clinical correction for a preliminary series of six patients

Scoliosis is a spinal deformity that requires surgical correction in progressive cases. In order to optimize surgical outcomes, patient-specific finite element models are being developed by our group. In this paper, a single rod anterior correction procedure is simulated for a group of six scoliosis patients. For each patient, personalised model geometry was derived from low-dose CT scans, and clinically measured intra-operative corrective forces were applied. However, tissue material properties were not patient-specific, being derived from existing literature. Clinically, the patient group had a mean initial Cobb angle of 47.3 degrees, which was corrected to 17.5 degrees after surgery. The mean simulated post-operative Cobb angle for the group was 18.1 degrees. Although this represents good agreement between clinical and simulated corrections, the discrepancy between clinical and simulated Cobb angle for individual patients varied between -10.3 and +8.6 degrees, with only three of the six patients matching the clinical result to within accepted Cobb measurement error of +-5 degrees. The results of this study suggest that spinal tissue material properties play an important role in governing the correction obtained during surgery, and that patient-specific modelling approaches must address the question of how to prescribe patient-specific soft tissue properties for spine surgery simulation.

Vibration characteristics of slender structures under human induced loads

This paper presents the outcome of investigations and studies of the vibratioon characteristics and response of low frequency structural systems for a composite concrete steel floor plate and a reverse profiled cable tensioned foot bridge. These highly dynamic and slender structure are the engineering response to planning, aesthetic and environmental influences, but are prone to excessive and complex vibration. A number of design codes and practice guides provided information to engineers for vibration mitigation However, they are limited to very simple load function applied to a few uncoupled translational modes of excitation. Motivated by the need to address the knowledge gaps in this area, the investigations described in this paper focused on synchronous multi-modal and coupled excitation of the floor plate and footbridge with considerations for torsinal effects. The results showed the potential for adverse dynamic response from multi-modal and coupled excitation influenced by patterned loading, structure geometry, stiffness distribution, directional effects, forcing functions based on activity frequency and duration of foot contact, and modal participation. It was also shown that higher harmonics of the load frequency can excite higher modes in the composite floor structure. Such responsive behaviour is prevalent mainly in slender and lightweight construction and not in stiffer and heavier structural systems. The analytical techniques and methods used in these investigations can supplement the current limited code and best practice provisions for mitigating the impact of human induced vibrations in slender structural systems.

Identifying relationship between skid resistance, road characteristics and crashes using probability-based risk approach

Road accidents are of great concerns for road and transport departments around world, which cause tremendous loss and dangers for public. Reducing accident rates and crash severity are imperative goals that governments, road and transport authorities, and researchers are aimed to achieve. In Australia, road crash trauma costs the nation A$ 15 billion annually. Five people are killed, and 550 are injured every day. Each fatality costs the taxpayer A$1.7 million. Serious injury cases can cost the taxpayer many times the cost of a fatality. Crashes are in general uncontrolled events and are dependent on a number of interrelated factors such as driver behaviour, traffic conditions, travel speed, road geometry and condition, and vehicle characteristics (e.g. tyre type pressure and condition, and suspension type and condition). Skid resistance is considered one of the most important surface characteristics as it has a direct impact on traffic safety. Attempts have been made worldwide to study the relationship between skid resistance and road crashes. Most of these studies used the statistical regression and correlation methods in analysing the relationships between skid resistance and road crashes. The outcomes from these studies provided mix results and not conclusive. The objective of this paper is to present a probability-based method of an ongoing study in identifying the relationship between skid resistance and road crashes. Historical skid resistance and crash data of a road network located in the tropical east coast of Queensland were analysed using the probability-based method. Analysis methodology and results of the relationships between skid resistance, road characteristics and crashes are presented.

The patella morphology in trochlear dysplasia : a comparative MRI study

BACKGROUND: Trochlear dysplasia is suspected to have a genetic basis and causes recurrent patellar instability due to insufficient anatomical geometry. Numerous studies about trochlear morphology and the optimal surgical treatment have been carried out, but no attention has been paid to the corresponding patellar morphology.----- ----- PURPOSE: The aim of this study was the evaluation of the patellar morphology in normal and trochlear dysplastic knees. ----- ----- STUDY DESIGN: Biometric analysis. ----- ----- METHODS: Twenty two patellae with underlying trochlear dysplasia (study group--SG) were compared with 22 matched knees with normal trochlear shape (control group--CG) on transverse and sagittal MRI slices. We compared transverse diameter, cartilaginous thickness, Wiberg-index and -angle, length and radius of lateral and medial facet, patellar shape and angle, retropatellar length, and type of trochlear dysplasia. For statistical analysis we used the Wilcoxon signed ranks test. ----- ----- RESULTS: The transverse and sagittal diameter, mean length of medial patellar facet, and mean cartilaginous and subchondral Wiberg-index showed statistical differences between the two groups. ----- ----- CONCLUSIONS: Although the insufficient trochlear depth and decreased lateral trochlear slope are responsible for patellofemoral instability, the patella shows morphological changes in trochlear dysplastic knees. Its overall size and the medial facet are smaller. Although the femoral sulcus angle is larger, the Wiberg-angle and -index are equal to the control group. This may indicate that the patellar morphology may not be a result of missing medial patellofemoral pressure in trochlear dysplastic knees, but a decreased medial patellofemoral traction. This seems to be caused by hypotrophic medial patellofemoral restraints in combination with an increased lateral patellar tilt, both resulting in a decreased tension onto the medial patella facet. Whether there is a genetic component to the patellar morphology remains open.

Impact of traffic oscillations on freeway crash occurrences

Traffic oscillations are typical features of congested traffic flow that are characterized by recurring decelerations followed by accelerations (stop-and-go driving). The negative environmental impacts of these oscillations are widely accepted, but their impact on traffic safety has been debated. This paper describes the impact of freeway traffic oscillations on traffic safety. This study employs a matched case-control design using high-resolution traffic and crash data from a freeway segment. Traffic conditions prior to each crash were taken as cases, while traffic conditions during the same periods on days without crashes were taken as controls. These were also matched by presence of congestion, geometry and weather. A total of 82 cases and about 80,000 candidate controls were extracted from more than three years of data from 2004 to 2007. Conditional logistic regression models were developed based on the case-control samples. To verify consistency in the results, 20 different sets of controls were randomly extracted from the candidate pool for varying control-case ratios. The results reveal that the standard deviation of speed (thus, oscillations) is a significant variable, with an average odds ratio of about 1.08. This implies that the likelihood of a (rear-end) crash increases by about 8% with an additional unit increase in the standard deviation of speed. The average traffic states prior to crashes were less significant than the speed variations in congestion.