Using Euler Curves to Model Continuum Robots

Abstract

Due to the continuous and flexible nature of con-tinuum robot backbones and the infinite number of parametersrequired to represent them in configuration space, modelingthem accurately and in real-time is challenging. While theconstant curvature assumption provides a simple alternative,it is limited in its capabilities as it cannot account for externaltip forces. In cases where the backbone deviates from theconstant curvature backbone, Euler curves are an interestingalternative for modeling continuum robots. In this paper, weshow that a linear approximation of the backbone curvatureis sufficiently accurate for estimating the shape of a robotsubject to external tip forces. Next, we propose a numericalstatic model for tendon-driven continuum robots experiencingin-plane external tip forces. In this model, we use Euler arcsplines to circumvent the limitations of standard numericalintegration schemes required to calculate these curves. Thesystem reduces to solving two nonlinear equations, allowingfast approximation of the backbone shape. The proposed modelis validated experimentally on a robot prototype. Average tiperror of 3.07% of the robot length is obtained for an averagecomputation time of 0.51 ms.

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