We study the effect of point dependent (heteroscedastic) and identically distributed anisotropic fiducial localization noise on fiducial target registration error (TRE). We derive an analytic expression, based on the concept of mechanism spatial stiffness, for predicting TRE. The accuracy of the predicted TRE is compared to simulated values where the optimal registration transformation is computed using the heteroscedastic errors in variables algorithm. The predicted values are shown to be contained by the 95% confidence intervals of the root mean square TRE obtained from the simulations.

A method is presented to validate the segmentation of computed tomography (CT) image sequences, and improve the accuracy and efficiency of the subsequent registration of the three-dimensional surfaces that are reconstructed from the segmented slices. The method compares the shapes of contours extracted from neighborhoods of slices in CT stacks of tibias. The bone is first segmented by an automatic segmentation technique, and the bone contour for each slice is parameterized as a one-dimensional function of normalized arc length versus inscribed angle. These functions are represented as vectors within a K-dimensional space comprising the first K amplitude coefficients of their Fourier Descriptors. The similarity or coherency of neighboring contours is measured by comparing statistical properties of their vector representations within this space. Experimentation has demonstrated this technique to be very effective at identifying low-coherency segmentations. Compared with experienced human operators, in a set of 23 CT stacks (1,633 slices), the method correctly detected 87.5% and 80% of the low-coherency and 97.7% and 95.5% of the high coherency segmentations, respectively from two different automatic segmentation techniques. Removal of the automatically detected low-coherency segmentations also significantly improved the accuracy and time efficiency of the registration of 3-D bone surface models. The registration error was reduced by over 500% (i.e., a factor of 5) and 280%, and the computational performance was improved by 540% and 791% for the two respective segmentation methods.

We present empirical studies that consider the effects of stereopsis and simulated aerial perspective on depth perception in translucent volumes. We consider a purely absorptive lighting model, in which light is not scattered or reflected, but is simply absorbed as it passes through the volume. A purely absorptive lighting model is used, for example, when rendering digitally reconstructed radiographs (DRRs), which are synthetic X-ray images reconstructed from CT volumes. Surgeons make use of DRRs in planning and performing operations, so an improvement of depth perception in DRRs may help diagnosis and surgical planning.

The normal direction of the bone contour in computed tomography (CT) images provides important anatomical information and can guide segmentation algorithms. Since various bones in CT images have different sizes, and the intensity values of bone pixels are generally nonuniform and noisy, estimation of the normal direction using a single scale is not reliable. We propose a multiscale approach to estimate the normal direction of bone edges. The reliability of the estimation is calculated from the estimated results and, after re-scaling, the reliability is used to further correct the normal direction. The optimal scale at each point is obtained while estimating the normal direction; this scale is then used in a simple edge detector. Our experimental results have shown that use of this estimated/corrected normal direction improves the segmentation quality by decreasing the number of unexpected edges and discontinuities (gaps) of real contours. The corrected normal direction could also be used in postprocessing to delete false edges. Our segmentation algorithm is automatic, and its performance is evaluated on CT images of the human pelvis, leg, and wrist.

Determination of the magnitudes and directions of the constraints of a mechanical system can be achieved by finding the basis of the system's characteristics compliance matrix. When little is known about the geometry of the system, conventional methods cannot be used to calculate the system's compliance matrix. A new method has been developed that uses experimental data to calculate a passive system's compliance matrix,and an eigenvalue decomposition to extract the directions and magnitudes of the system constraints. The data were wrenches applied to the system and the mechanism's resulting displacement from equilibrium. Computer simulations suggest that the method reliably finds eigenscrew pitches, compliances and directions for well-conditioned matrices. Eigenscrew pitches and compliances can be found for ill-conditioned matrices. This analytical technique can be used to evaluate the static behaviour of a system. It may prove valuable as a design and analysis tool for biomechanics, robotics and automation.

Many manipulation tasks involve transition from unconstrained to constrained motion marked by the contact with a constrained surface. This phenomenon divides the task into more than one phase, each of which requires a different control strategy. Switching from one control strategy to another leads to control discontinuities. The paper seeks to design a controller that avoids such discontinuities. The principle is based on the analysis of impulsive constraints. It is argued that, in theory, such a discontinuity can be avoided by modeling the cause of the force discontinuity of the end-effector as the velocity discontinuity of the constraint surface as opposed to the discontinuity of the Lagrange multiplier. This velocity discontinuity can then be dealt with by a continuous control strategy. A controller is designed based on this principle. Input-output linearization is performed to linearize and decouple the system. Simulation and experimental results are presented to demonstrate the effectiveness of this new approach.

Detecting the surface shape or pressure distribution of a tactile sensor made of a homogeneous and elastic material, given internal stresses or strains, is an ill-posed problem. The difficulties are further compounded by introduction of inhomogeneities into the sensor material in order to perform the transduction, which significantly change the sensor's mechanical behaviour. In order to investigate the numerical stability of curvature detection, we discretized a linear elastic half-space. Using closed-form solutions of surface pressures for rigid indentors, a regularized solution can be formulated. From finite-element models of inhomogeneous 3D tactile sensors, subsurface strains can be estimated in a physically realistic fashion. Using these as input to the regularized solution, we have found that it is not possible to reliably deduce the difference between contacting the sensor's surface with various axisymmetric objects.>

The authors have developed a method for calculating stable grasps of an object by enclosing it with a robotic finger, accounting for the rigid-body dynamics of both the finger and the object. Beginning with a set of contact points and assuming a local Coulomb friction model, a penalty method finds a set of contact forces that produce a stable grasp. From the known relationship between the finger-joint forces and the forces exerted by the finger links, the additional grasping force can be found and added to the joint force that is required to hold the finger in the grasping configuration. The authors illustrate their algorithm by some examples to show how to grasp and move an object using the whole finger.>

A common approach to formulating the dynamics of closed-chain mechanisms requires finding the forces of constraint at the loop closures. However, there are indications that this approach leads both to ill conditioned systems that must be inverted and to numerically unstable differential equations of motion. We derive a sufficient condition for ill conditioning of augmented dynamical systems/spl minus/that the mechanism's trajectory passes through, or very near, a kinematic singularity. In singular regions the equations of motion are also numerically stiff, and they frequently require special numerical methods for computer solution. We propose a new method of calculating closed-chain dynamics, based on the systematic elimination of variables that are both redundant and that may adversely affect the computations. This approach produces numerically stable solutions of the differential equations of motion, and the equations are apparently much less stiff than the equations produced by the traditional force-closure approach.>

Many physical systems, particularly robotic linkages, can be modeled as mechanisms. In order to simulate the dynamical behavior of such systems as the number of links become large, the algorithms must produce efficient and stable computations. The mechanisms studied here include those which have tree-structured topologies, that is, a link may have more than one successor link but there are no loops in the linkage topology. The authors present a formulation of the dynamics based on representing Lagrangian mechanics with spatial, or screw, displacements. This shows that several existing algorithms are equivalent to recursive calculations on an inertial supermatrix, which is a matrix the elements of which are matrices. The result is numerically stable forward and inverse computations of the second-order terms that grow linearly with the number of links, and provides a new insight into the nature of the dynamics of mechanisms.>

A common approach to formulating the dynamics of closed-chain mechanisms requires finding the forces of constraint at the loop closures. However, there are indications that this approach leads to ill-conditioned systems that must be inverted and to numerically unstable differential equations of motion. The authors derive a sufficient condition for ill conditioning of augmented dynamical systems, namely, that the mechanism's trajectory passes through, or very near, a kinematic singularity. In singular regions the equations of motion are also numerically stiff, and frequently require special numerical methods for computer solution. The authors propose a novel method of calculating closed-chain dynamics, based on the systematic elimination of variables that are both redundant and that may adversely affect the computations. This approach produces numerically stable solutions of the differential equations of motion, and the equations are apparently much less stiff than the equations produced by the traditional force-closure approach.>

A method is described for modeling and controlling a 2-DOF master system of a bilateral force-reflecting teleoperational device. The primary method of control involves the open-loop inversion of the system dynamics. It differs from previous methods in that: (1) it uses an experimentally derived black box nonlinear model of the system; and (2) it does not assume an infinitely stiff actuator chain in the master system (i.e., it considers the nonlinear effects of the operator on the dynamics of the chain). Preliminary results are included.>

It is shown, by direct geometric construction, that previously published uncertainty bounds on the location of polygonal or polyhedral objects can be tightened considerably. The improvement of the bounds is a result of considering the cross-coupling between rotational and translation uncertainties in the interpretation of the sensor data. Both two-dimensional and three-dimensional uncertainty bounding are tested in simulation. The two-dimensional studies are implemented as part of a robotic system for tactile recognition. These implementations prove to be useful vehicles for exploring the computational issues involved in a detailed analysis of the geometric uncertainties present in model-based object recognition systems. Among other results it is found that rotational uncertainty is independent of the scale of the models, and translational uncertainty is highly dependent on the relative angles of the model components that are sensed.>

The author present a detailed analysis of uncertainty propagation in model-based object recognition, for both two-dimensional and three-dimensional objects that have linear boundaries. It is shown by direct geometric construction that previous uncertainty bounds on the location of polygonal or polyhedral objects can be tightened considerably. The improvement of the bounds is a result of considering the cross-coupling between rotational and translational uncertainties in the interpretation of the sensor data. The author states several general principles regarding geometric uncertainty in model-based recognition, readily deduced by examining the uncertainty equations presented: rotational uncertainty is independent of the scale of the models; translational uncertainty is highly dependent on the relative angles of the model components that are sensed; translational uncertainty is intimately related to rotational uncertainty, although the relationship is nontrivial; pose uncertainty varies roughly linearly with sensor error; and the poorer a valid match set is within the error bounds, the less uncertainty there is in deducting the pose parameters.>

Model-based recognition of objects by robot systems requires the acquisition of new data when the old data are insufficient in number or quality to uniquely identify the object(s) under investigation. In particular, the initial data set can often be interpreted in several, ambiguous ways. This paper proposes a framework for the acquisition of new data in the tactile domain, concentrating upon the case of two-dimensional objects that are modelled as polygons confined to a plane. A computationally feasible method is presented for finding linear paths for a tactile sensor so that effective data acquisition can occur. Also presented is a representation of the ambiguity present in the data, and how this ambiguity can be reduced and analysed.

A method is proposed for the extraction of features that are useful in the classification of tactile texture. It is shown that accumulation of simple statistics on step edges and local extrema, calculated at multiple scales of resolution, can provide linearly separable features. The scale can be varied continuously, thus facilitating adjustment of the scale parameters to optimise the effectiveness of the method for a given tactile array sensor.