Inverse Kinematics with a Geometrical Approximation for Multi-Segment Flexible Curvilinear Robots

Despite research related to flexible or continuum curvilinear robots, there lacks a common simulation tool for continuum robots, which are unlike rigid robots. Thus, in this paper, a robotics toolbox is utilized to model a wire-driven flexible manipulator as one of the continuum robots. Constant curvature property can enable the robotics toolbox to represent the flexible manipulator and validate its kinematics. Moreover, because the closed-form inverse kinematics methods developed previously for real-time control conceded limitations in modeling some continuum robots, we hereby develop an inverse kinematics method for the wire-driven flexible manipulator which can provide fast and reliable inverse results. Experimental results showed that geometrical information offered a stable starting point for the proposed inverse kinematics algorithm. Moreover, the first and second derivatives of a fitness function further contributed to a fast-converging solution within a few microseconds. Lastly, for the potential feasibility of an active compliance controller without physical force/torque sensors, a reaction torque observer was investigated for a flexible manipulator with direct drive mechanisms.