On the Collision Free-Trajectories of a Multiple-needle Robot Based on the Fibonacci Sequence

Modeling of the Flexible Needle Insertion into the Human Liver

“…The trajectories are determined from the restrictions of avoiding the collisions with blood vessels, ribs and surrounding tissues, and also the interference of needles with each other. We consider that more needles are planned to be inserted into the liver [45].…”

“…The workspace boundary for the needle is a 1D curve in each xy-plane means the z h -plane for z ¼ h, h ∈ 0, h max ½ with a clinical value h ¼ 200 mm. The S is the plan of the needle insertion trajectory, θ k , φ k ðÞ are the rotation angles with respect to y and z axes θ min ≤ θ k ≤ θ max , ϕ min ≤ φ k ≤ φ max [45].…”

“…The possible collision point between the needle and the tissue is analyzed by an identifier to check the minimum distance between needle and the surrounding tissue [45]. The minimum distance is expressed as…”