Abstract-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 the present formulation, the tissue is treated as isotropic and no obstacles are present. The bevel tip of the needle is treated as a nonholonomic constraint that can be viewed as a 3D extension of the standard kinematic cart or unicycle. A deterministic model is used as the starting point, and reachability criteria are established. A stochastic differential equation and its corresponding Fokker-Planck equation are derived. The Euler-Maruyama method is used to generate the ensemble of reachable states of the needle tip. Inverse kinematics methods developed previously for hyperredundant and binary manipulators that use this probability density information are applied to generate needle tip paths that reach the desired targets.
Park et al. REF treated the kinematics of the bevel-tip needle as the 3D extension of the standard unicycle model, and proposed a diffusion-based motion planning method to numerically compute a path in the obstacle-free stiff tissue.
Diffusion-Based Motion Planning for a Nonholonomic Flexible Needle Model
Proceedings of the 2005 IEEE International Conference on Robotics and Automation
Proceedings of the 2005 IEEE International Conference on Robotics and Automation
Mathematics Computer Science