Inverse Kinematics of Concentric Tube Robots in the Presence of Environmental Constraints

Table 1

The list of the nomenclatures used in this paper.

Symbol	Definition
	The radius of curvature in the primary backbone is defined in the bending plate (the plate of )
	The bending angle in the primary backbone is defined in the bending plate ( plate) at the point .
	The orientation angle of the robot which can rotate in the plate
	Rotation and bending angles of the first part of the catheter
	Rotation and bending angles of the second part of the catheter
	Rotation and bending angles of the third part of the catheter
	The primary length of the primary backbone
	The position of the secondary backbone fixed in the lower platform
	The position of the secondary backbone fixed in the upper platform
	The center of the equilateral triangle made by the points in the platform of
	The center of the equilateral triangle made by the points in the platform of
	The position vector stating the center coordinate of the upper platform of each segment according to the lower platform
	Curvature
	The configuration space vector
	The number of robot segments
	The rotation matrix from the end disk coordinate system to the base coordinate system