Kinematic instability in concentric-tube robots: Modeling and analysis

In this paper the issue of kinematic instability for concentric tube robots is studied when the following two conditions are considered: (a) the robot consists of more than two concentric tubes, and (b) the tubes consist of straight sections followed by curved sections. In this paper, we use the term “kinematic instability” when the tip position of robot in the Cartesian domain jumps from one equilibrium point to another while having a constant joint space configuration. This implies that in unstable configurations, the “forward kinematics” of the robot will have multiple solutions for one set of joint space variables. In this paper a novel framework is proposed that can calculate the stability condition for the robots consisting of multiple tubes with straight sections without solving the nonlinear ordinary differential equations. The resulting conditions restrict the pre-curvatures and length of the tubes, as a design factor, to guarantee kinematic stability within the whole workspace of the robot.