Joint-space tracking of workspace trajectories in continuous time

We present a controller for a class of robotics manipulators which provides exponential convergence to a desired end-effector trajectory using gains specified in joint-space. This is accomplished without appeal to the use of discrete inverse-kinematics algorithms, allowing the controller to be posed entirely in continuous time

Dynamic inversion and polar decomposition of matrices

Using the recently introduced concept of a "dynamic inverse" of a map, along with its associated analog computational paradigm. we construct continuous-time nonlinear dynamical systems which produce both regular and generalized inverses of time-varying and fixed matrices, as well as polar decompositions

Control for an Autonomous Bicycle

The control of nonholonomic and underactuated systems with symmetry is illustrated by the problem of controlling a bicycle. We derive a controller which, using steering and rear-wheel torque, causes a model of a riderless bicycle to recover its balance from a near fall as well as converge to a time parameterized path in the ground plane. Our construction utilizes new results for both the derivation of equations of motion for nonholonomic systems with symmetry, as well as the control of underactuated robotic systems

Tracking implicit trajectories

Output tracking of implcitly defined reference trajectories is examined. A continuous-time nonlinear dynamical system is constructed that produces explicit estimates of time-varying implicit trajectories. We prove that incorporation of this "dynamic inverter" into a tracking controller provides exponential output tracking of the implicitly defined trajectory for nonlinear control systems having vector relative degree and well-behaved internal dynanmics

A dynamic inverse for nonlinear maps

We consider the problem of estimating the time-varying root of a time-dependent nonlinear map. We introduce a "dynamic inverse" of a map, another generally time-dependent map which one composes with the original map to form a nonlinear vector-field. The flow of this vector field decays exponentially to the root. We then show how a dynamic inverse may be determined dynamically while being used simultaneously to find a root. We construct a continuous-time analog computational paradigm around the dynamic inverse

Cranial sutures work collectively to distribute strain throughout the reptile skull

The skull is composed of many bones that come together at sutures. These sutures are important sites of growth, and as growth ceases some become fused while others remain patent. Their mechanical behaviour and how they interact with changing form and loadings to ensure balanced craniofacial development is still poorly understood. Early suture fusion often leads to disfiguring syndromes, thus is it imperative that we understand the function of sutures more clearly. By applying advanced engineering modelling techniques, we reveal for the first time that patent sutures generate a more widely distributed, high level of strain throughout the reptile skull. Without patent sutures, large regions of the skull are only subjected to infrequent low-level strains that could weaken the bone and result in abnormal development. Sutures are therefore not only sites of bone growth, but could also be essential for the modulation of strains necessary for normal growth and development in reptiles

Characterizing the Galactic Gravitational Wave Background with LISA

We present a Monte Carlo simulation for the response of the Laser Interferometer Space Antenna (LISA) to the galactic gravitational wave background. The simulated data streams are used to estimate the number and type of binary systems that will be individually resolved in a 1-year power spectrum. We find that the background is highly non-Gaussian due to the presence of individual bright sources, but once these sources are identified and removed, the remaining signal is Gaussian. We also present a new estimate of the confusion noise caused by unresolved sources that improves on earlier estimates.Comment: 32 pages, 14 figures. Version to appear in PR

Dynamical methods for polar decomposition and inversion of matrices

AbstractWe show how to obtain polar decomposition as well as inversion of fixed and time-varying matrices using a class of nonlinear continuous-time dynamical systems. First we construct a dynamical system that causes an initial approximation of the inverse of a time-varying matrix to flow exponentially toward the true time-varying inverse. Using a time-parametrized homotopy from the identity matrix to a fixed matrix with unknown inverse, and applying our result on the inversion of time-varying matrices, we show how any positive definite fixed matrix may be dynamically inverted by a prescribed time without an initial guess at the inverse. We then construct a dynamical system that solves for the polar decomposition factors of a time-varying matrix given an initial approximation for the inverse of the positive definite symmetric part of the polar decomposition. As a by-product, this method gives another method of inverting time-varying matrices. Finally, using homotopy again, we show how dynamic polar decomposition may be applied to fixed matrices with the added benefit that this allows us to dynamically invert any fixed matrix by a prescribed time

How important is groundwater availability and stream perenniality to riparian and floodplain tree growth?

Riparian vegetation is important for stream functioning and as a major landscape feature. For many riparian plants, shallow groundwater is an important source of water, particularly in areas where rainfall is low, either annually or seasonally, and when extended dry conditions prevail for all or part of the year. The nature of tree water relationships is highly complex. Therefore, we used multiple lines of evidence to determine the water sources used by the dominant tree species Eucalyptus camaldulensis (river red gum), growing in riparian and floodplain areas with varying depth to groundwater and stream perenniality. Dendrometer bands were used to measure diel, seasonal, and annual patterns of tree water use and growth. Water stable isotopes (δ2H and δ18O) in plant xylem, soil water, and groundwater were measured to determine spatial and temporal patterns in plant water source use. Our results indicated riparian trees located on relatively shallow groundwater had greater growth rates, larger diel responses in stem diameter, and were less reactive to extended dry periods, than trees in areas of deep groundwater. These results were supported by isotope analysis that suggested all trees used groundwater when soil water stores were depleted at the end of the dry season, and this was most pronounced for trees with shallow groundwater. Trees may experience more frequent periods of water deficit stress and undergo reduced productivity in scenarios where water table accessibility is reduced, such as drawdown from groundwater pumping activities or periods of reduced rainfall recharge. The ability of trees to adapt to changing groundwater conditions may depend on the speed of change, the local hydrologic and soil conditions as well as the species involved. Our results suggest that E. camaldulesis growing at our study site is capable of utilizing groundwater even to depths \u3e10 m, and stream perenniality is likely to be a useful indicator of riparian tree use of groundwater

Identifying person re-occurrences for personal photo management applications

Automatic identification of "who" is present in individual digital images within a photo management system using only content-based analysis is an extremely difficult problem. The authors present a system which enables identification of person reoccurrences within a personal photo management application by combining image content-based analysis tools with context data from image capture. This combined system employs automatic face detection and body-patch matching techniques, which collectively facilitate identifying person re-occurrences within images grouped into events based on context data. The authors introduce a face detection approach combining a histogram-based skin detection model and a modified BDF face detection method to detect multiple frontal faces in colour images. Corresponding body patches are then automatically segmented relative to the size, location and orientation of the detected faces in the image. The authors investigate the suitability of using different colour descriptors, including MPEG-7 colour descriptors, color coherent vectors (CCV) and color correlograms for effective body-patch matching. The system has been successfully integrated into the MediAssist platform, a prototype Web-based system for personal photo management, and runs on over 13000 personal photos