Modeling of Continuum Manipulators Using Pythagorean Hodograph Curves

Abstract

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.

PH Model-Based Shape Reconstruction of Heterogeneous Continuum Closed Loop Kinematic Chain: An Application to Skipping Rope

“…Continuum manipulators are continuously curving manipulators to produce a flexible motion. Pythagorean Hodograph curves are used in the context of continuum manipulators to reconstruct their optimal posture [18]. Let us consider two spatial poses P s and P f on the continuum manipulator as:…”

“…They can be computed using orientations (α s , β s , γ s ) and (α f , β f , γ f ). Using four conditions P s , d s , P f and d f , polynomials u(h), v(h), p(h) and q(h) are calculated which leads to the calculation of the control points as in [18]. Due to the presence of two free control points, there are infinite solutions in case of quintic PH curves.…”

“…1. Basic schematic of PH curve minimum potential energy as discussed in [18] to reconstruct the shape of the continuum manipulator. Because a physical system always tries to move from one point to the other point with minimum potential energy (combination of bending and twisting energy).…”

“…Therefore, solving eq. (14) in the matrix form, the length of the backbone of the continuum manipulator can be computed [18].…”

“…PH curves have been used in 3D path planning of three unmanned aerial vehicles (UAVs), as well as to avoid obstacles in their path [11]. In [18], PH curves are utilized to model spatial continuum manipulators for the first time, which is being extended in this paper. In this paper, work is focused on the concatenation of more than one PH curves to model more complex shapes of continuum manipulator or to model continuum closed loop kinematic chains.…”