Inverse Kinematics of Concentric Tube Steerable Needles
- Resource Type
- Conference
- Authors
- Sears, Patrick; Dupont, Pierre E.
- Source
- Proceedings 2007 IEEE International Conference on Robotics and Automation Robotics and Automation, 2007 IEEE International Conference on. :1887-1892 Apr, 2007
- Subject
- Robotics and Control Systems
Computing and Processing
Signal Processing and Analysis
Needles
Surgery
Shape
Equations
Aerospace engineering
Mechanical engineering
Jacobian matrices
Robot kinematics
Robotics and automation
Boundary value problems
- Language
- ISSN
- 1050-4729
Prior papers have introduced steerable needles composed of precurved concentric tubes. The curvature and extent of these needles can be controlled by the relative rotation and translation of the individual tubes. Under certain assumptions on the geometry and design of these needles, the forward kinematics problem can be solved in closed form by means of algebraic equations. The inverse kinematics problem, however, is not as straightforward owing to the nonlinear map between relative tube displacements and needle tip configuration as well as to the multiplicity of solutions as the number of tubes increases. This paper presents a general approach to solving the inverse kinematics problem using a pseudoinverse solution together with gradients of nullspace potential functions to enforce geometric and mechanical constraints.