Modeling of Continuum Manipulators Using Pythagorean Hodograph Curves

Research on continuum manipulators is increasingly developing in the context of bionic robotics because of their many advantages over conventional rigid manipulators. Due to their soft structure, they have inherent flexibility, which makes it a huge challenge to control them with high performances. Before elaborating a control strategy of such robots, it is essential to reconstruct first the behavior of the robot through development of an approximate behavioral model. This can be kinematic or dynamic depending on the conditions of operation of the robot itself. Kinematically, two types of modeling methods exist to describe the robot behavior; quantitative methods describe a model-based method, and qualitative methods describe a learning-based method. In kinematic modeling of continuum manipulator, the assumption of constant curvature is often considered to simplify the model formulation. In this work, a quantitative modeling method is proposed, based on the Pythagorean hodograph (PH) curves. The aim is to obtain a three-dimensional reconstruction of the shape of the continuum manipulator with variable curvature, allowing the calculation of its inverse kinematic model (IKM). It is noticed that the performances of the PH-based kinematic modeling of continuum manipulators are considerable regarding position accuracy, shape reconstruction, and time/cost of the model calculation, than other kinematic modeling methods, for two cases: free load manipulation and variable load manipulation. This modeling method is applied to the compact bionic handling assistant (CBHA) manipulator for validation. The results are compared with other IKMs developed in case of CBHA manipulator.