Compact modeling of spatial continuum robotic arms towards real-time control

Abstract

This paper presents a compact modeling approach of continuum robotic arms, with limited computations for faster numerical calculations in real-time implementations. It is assumed that the arm includes a backbone made of elastic rods, and the Cosserat rod theory is simplified for numerically faster modeling. The time-taking boundary-value problem (BVP) is detailed, and some numerical methods are introduced to solve the developed equations of modeling. Next, based on physical intuition, a fast and stable method is proposed to solve the BVP, as a moment-based approach. Also, a method to cancel some numerical integration errors with the least required computations and numerical efforts is presented. Next, a Jacobian-based control of multi-segment continuum robotic arms is developed. Finally, this procedure is experimentally verified to show the precision of proposed modeling approach and also to reveal the importance of faster solutions for real-time control.