Important diagnostic criteria for glaucoma are changes in the 3D structure of the optic disc due to optic nerve damage. We propose an automatic approach for detecting these changes in 3D models reconstructed from fundus images of the same patient taken at different times. For each time session, only two uncalibated fundus images are required. The approach applies a 6-point algorithm to estimate relative camera pose assuming a constant camera focal length. To deal with the instability of 3D reconstruction associated with fundus images, our approach keeps multiple candidate reconstruction solutions for each image pair. The best 3D reconstruction is found by optimizing the 3D registration of all images after an iterative bundle adjustment that tolerates possible structure changes. The 3D structure changes are detected by evaluating the reprojection errors of feature points in image space. We validate the approach by comparing the diagnosis results with manual grading by human experts on a fundus image dataset.

We address the problem of developing feedback controllers for a group of robots with second-order dynamics in an obstacle-filled, D-dimensional environment. Our control algorithm takes into account communication constraints, obstacle avoidance, and inter-robot collision avoidance, by synthesizing a piecewise smooth vector field for safe navigation. First, the feasible free joint configuration space is tessellated into polytopes that account for the desired constraints. We search the graph of these polytopes to find a discrete path to the goal polytope. We then use a novel navigation function-based feedback controller that drives the system from one polytope to the next and eventually to the goal. The controller exploits the fact that two adjoining polytopes in the planned discrete path together form a star-shaped object that is obstacle free; this enables the design of navigation function-based controller for kinematic and dynamic fully actuated robots without spurious minima. We sequentially compose these controllers to drive the state to the goal. For a polygonal space, the algorithm we propose is complete. We present successful simulation results of the algorithm on a group of ground vehicles and quadrotors performing a cooperative navigation task in constrained environments.

In this study, we consider the problem of safely steering a planar nonholonomic cart around obstacles to reach a goal state. We achieve this by the decomposition of the free workspace into triangular tori and generation of local smooth feedback laws that drive the robot from one cell to an adjoining cell. These control laws exploit the fact that for nonholonomic systems, one can generate smooth controllers to reach a particular subset in the configuration space, even though smooth feedback laws cannot be obtained to reach a particular state. These local controllers are then sequenced using discrete motion planning algorithms like A* or incremental D* to reach the goal. We demonstrate the practical efficacy of this methodology by applying it to two experimental platforms: (1) a differential drive robot in which inertial effects are negligible and (2) a hexapedal robot in which inertial effects are significant but difficult to model. In both cases, we use the abstraction of a planar kinematic cart with process noise to develop feedback controllers. We present successful implementation of the controllers to navigate the hexapedal robot in both static and dynamic environments with obstacles.

Image guidance promises to improve targeting accuracy and broaden the scope of medical procedures performed with needles. This paper takes a step toward automating the guidance of a flexible tip-steerable needle as it is inserted into human tissue. We build upon a previously proposed nonholonomic model of needles that derive steering from asymmetric bevel forces at the tip. The bevel-tip needle is inserted and rotated at its base in order to steer it in six degrees of freedom. As a first step for control, we show that the needle tip can be automatically guided to a planar slice of tissue as it is inserted. Our approach keeps the physician in the loop to control insertion speed. The distance of the needle tip position from the plane of interest is used to drive an observer-based feedback controller which we prove is locally asymptotically stable. Numerical simulations demonstrate a large domain of attraction and robustness of the controller in the face of parametric uncertainty and measurement noise. Physical experiments with tip-steerable Nitinol needles inserted into a transparent plastisol tissue phantom under stereo image guidance validate the effectiveness of our approach.

Given point correspondences in multiple perspective views of a scene containing multiple rigid-body motions, we present an algorithm for segmenting the correspondences according to the multiple motions. We exploit the fact that when the depths of the points are known, the point trajectories associated with a single motion live in a subspace of dimension at most four. Thus motion segmentation with known depths can be achieved by methods of subspace separation, such as GPCA or LSA. When the depths are unknown, we proceed iteratively. Given the segmentation, we compute the depths using standard techniques. Given the depths, we use GPCA or LSA to segment the scene into multiple motions. Experiments on the Hopkins 155 motion segmentation database show that our method compares favorably against existing affine motion segmentation methods in terms of segmentation error and execution time.

Physicians perform percutaneous therapies in many diagnostic and therapeutic procedures. Image guidance promises to improve targeting accuracy and broaden the scope of needle interventions. In this paper, we consider the possibility of automating the guidance of a flexible bevel-tip needle as it is inserted into human tissue. We build upon a previously proposed nonholonomic kinematic model to develop a nonlinear observer-based controller. As a first step for control, we show that flexible needles can be automatically controlled to remain within a planar slice of tissue as they are inserted by a physician; our approach keeps the physician in the loop to control insertion speed. In the proposed controller, the distance of the needle tip position from the plane of interest is used as a feedback signal. Numerical simulations demonstrate the stability and robustness of the controller in the face of parametric uncertainty. We also present results from pilot physical experiments with phantom tissue under stereo image guidance.

Lie group symmetry in a mechanical system can lead to a dimensional reduction in its dynamical equations. Typically, the symmetries that one exploits are intrinsic to the mechanical system at hand, e.g. invariance of the system's Lagrangian to some group of motions. In the present work we consider symmetries that arise from an extrinsic control task, rather than the intrinsic structure of configuration space, constraints, or system dynamics. We illustrate this technique with several examples. In the examples, the reduction enables us to design essentially global feedback controllers on the reduced systems.We apply task-induced symmetry and reduction to a recently developed 6 DOF kinematic model of steerable bevel-tip needles. The resulting controllers cause the needle tip to track a subspace of its configuration space. We envision that the methodology presented in this paper will form the basis for a new planning and control framework for needle steering.

Traditionally, visual servoing is separated into tracking and control subsystems. This separation, though convenient, is not necessarily well justified. When tracking and control strategies are designed independently, it is not clear how to optimize them to achieve a certain task. In this work, we propose a framework in which spatial sampling kernels - borrowed from the tracking and registration literature - are used to design feedback controllers for visual servoing. The use of spatial sampling kernels provides natural hooks for Lyapunov theory, thus unifying tracking and control and providing a framework for optimizing a particular servoing task. As a first step, we develop kernel-based visual servos for a subset of relative motions between camera and target scene. The subset of motions we consider are 2D translation, scale, and roll of the target relative to the camera. Our approach provides formal guarantees on the convergence/stability of visual servoing algorithms under putatively generic conditions.

In order to engage in useful activities, upright legged creatures must be able to maintain balance. Despite recent advances, the understanding, prediction and control of biped balance in realistic dynamical situations remain an unsolved problem and the subject of much research in robotics and biomechanics. Here we study the fundamental mechanics of the rotational stability of multi-body systems with the goal of identifying a general stability criterion. Our research focuses on H/sub G/, the rate of change of centroidal angular momentum of a robot, as the physical quantity containing its stability information. We propose three control strategies using H/sub G/ that can be used for stability recapture of biped robots. For free walk on horizontal ground, a derived criterion refers to a point on the foot/ground surface of a robot where the total ground reaction force would have to act such that H/sub G/=0. This new criterion generalizes earlier concepts such as GCoM, CoP, ZMP, and FRI point, and extends their applicability.