Wooram Park

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— Fine needles facilitate diagnosis and therapy because they enable minimally invasive surgical interventions. This paper formulates the problem of steering a very flexible needle through firm tissue as a nonholonomic kinematics problem, and demonstrates how planning can be accomplished using diffusion-based motion planning on the Euclidean group, SE(3). In(More)
This chapter describes how advances in needle design, modeling, planning , and image guidance make it possible to steer flexible needles from outside the body to reach specified anatomical targets not accessible using traditional needle insertion methods. Steering can be achieved using a variety of mechanisms, including tip-based steering, lateral(More)
A nonholonomic system subjected to external noise from the environment, or internal noise in its own actuators, will evolve in a stochastic manner described by an ensemble of trajectories. This ensemble of trajectories is equivalent to the solution of a Fokker-Planck equation that typically evolves on a Lie group. If the most likely state of such a system(More)
In this paper we develop a new framework for path planning of flexible needles with bevel tips. Based on a stochastic model of needle steering, the probability density function for the needle tip pose is approximated as a Gaussian. The means and covariances are estimated using an error propagation algorithm which has second order accuracy. Then we adapt the(More)
Flexible needles with bevel tips are being developed as useful tools for minimally invasive surgery and percutaneous therapy. When such a needle is inserted into soft tissue, it bends due to the asymmetric geometry of the bevel tip. This insertion with bending is not completely repeatable. We characterize the deviations in needle tip pose (position and(More)
– The ability of natural organisms to self-assemble, self-repair and reproduce in an environment with sufficient nutrients is one of the defining features of life. In this paper, we build on both our own previous work and that of others to demonstrate the feasibility of robotic systems that can assemble functional copies of themselves from either basic sets(More)
In this paper, we propose an approach for the accurate rotation of a digital image using Hermite expansions. This exploits the fact that if a 2-D continuous bandlimited Hermite expansion is rotated, the resulting function can be expressed as a Hermite expansion with the same bandlimit. Furthermore, the Hermite coefficients of the initial 2-D expansion and(More)
In this paper, we propose an algorithm for lossless conversion of data between Cartesian and polar coordinates, when the data is sampled from a 2-D real-valued function (a mapping: R2 --> R) expressed as a particular kind of truncated expansion. We use Laguerre functions and the Fourier basis for the polar coordinate expression. Hermite functions are used(More)
In this paper we propose a computationally efficient method for the steering of flexible needles with a bevel tip in the presence of uncertainties for the case when there are no obstacles in the environment. Based on the stochastic model for the needles, we develop a new framework for path planning of a flexible needle with a bevel tip. This consists of(More)
We present algorithms for fast and stable approximation of the Hermite transform of a compactly supported function on the real line, attainable via an application of a fast algebraic algorithm for computing sums associated with a three-term relation. Trade-offs between approximation in bandlimit (in the Hermite sense) and size of the support region are(More)