一种丝驱连续体手术机械臂的设计及其运动学分析

Design and kinematics analysis of a tendon-driven surgical continuum arm

针对现有的连续体机械臂及其运动学模型无法得到运动学解析解的问题,设计了一种具有两个弯曲自由度的丝驱动连续体机械臂原型,并对其正逆运动问题进行了研究。基于分段常曲率假设,结合D-H法建立了连续体机械臂的正运动学模型,推导出了驱动丝长度到机械臂末端位置的映射关系,得到了正运动学解析解;通过提取机械臂骨干曲线,利用几何分析法建立了连续体机械臂逆运动学模型,推导出了机械臂末端位置到驱动丝长度的映射关系,并得到了部分逆运动学解析解;最后,通过实验对所提出运动学模型的有效性进行了验证。研究结果表明:所提出运动学模型的平均位置误差不超过2.56 mm,约占机械臂总长度的2.57%,能够很好地用于连续体机械臂末端位置控制。

Aiming at the problem that the kinematic analytical solution cannot be obtained in the existing continuum robotic arm and its kinematic model,a tendon-driven continuum arm was presented with two bending degrees of freedom(DOFs),and its forward kinematics and inverse kinematics were studied.Based on the constant curvature hypothesis and combined with the modified Denavit-Hartenberg(D-H)method,the mapping from the tendons lengths to the arm end position was derived and the forward kinematic analytical solution was obtained.By extracting the arm backbone curve,the inverse kinematics was established using the geometric analysis method and the mapping from the arm end position to the tendons lengths was derived.What s more,the partial inverse kinematics closed-form solution was obtained.Finally,the proposed model was validated by an experiment.The results indicate that the average position error of the proposed kinematics model is no more than 2.56 mm,which accounts for less than 2.57%of the total arm length,and therefore the model can be well used for the end position control of continuum arm.