Models of continuum robots often trade off accuracy and speed. The constant curvature assumption model can perform fast calculations but with poor accuracy. Static models can obtain good calculation accuracy but with slower computation speed. In this paper, a precise and efficient method for establishing a non-constant curvature kinematic model for composite continuum robots is proposed. First, an algorithm based on the Beam Constraint Model is proposed to establish the static model of the continuum robot. The situation in which friction changes gradually in continuum robots is considered in the static model. Then, the Kepler elliptic curve is used to simplify the static model to build a non-constant curvature kinematic model of the continuum robot. Then, complex inverse kinematics solutions are transformed into explicit sets of equations by mathematical transformation. Finally, simulations and experiments are designed to demonstrate the algorithm proposed in this paper. The simulation results show that the proposed algorithm is 1572 times faster than the Levenberg–Marquardt algorithm. The experimental results show that the average error of the static model is 0.065 mm, accounting for 0.13% of its length. The maximum error is 0.309 mm, accounting for 0.618% of its length. The positioning accuracy of the non-constant curvature model proposed in this paper is 2.02 times that of the constant curvature model. The results show that the simplified kinematic model algorithm based on the static model has high accuracy and computational efficiency. This research is crucial for the practical application of continuum robots in engineering.

中文翻译：

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复合连续体机器人：精确建模和模型简化

连续机器人模型通常会在精度和速度之间进行权衡。常曲率假设模型计算速度快，但精度较差。静态模型可以获得较好的计算精度，但计算速度较慢。本文提出了一种精确有效的建立复合材料连续体机器人非等曲率运动学模型的方法。首先，提出了一种基于梁约束模型的算法来建立连续体机器人的静态模型。静态模型考虑了连续体机器人中摩擦力逐渐变化的情况。然后，利用开普勒椭圆曲线对静态模型进行简化，建立连续体机器人的非等曲率运动学模型。然后，通过数学变换将复杂的逆运动学解转化为显式方程组。最后，设计了仿真和实验来验证本文提出的算法。仿真结果表明，该算法比Levenberg-Marquardt算法快1572倍。实验结果表明，静态模型的平均误差为0.065 mm，占其长度的0.13%。最大误差为0.309mm，占其长度的0.618%。本文提出的非等曲率模型的定位精度是等曲率模型的2.02倍。结果表明，基于静态模型的简化运动模型算法具有较高的精度和计算效率。这项研究对于连续体机器人在工程中的实际应用至关重要。