Computing Jacobians and compliance matrices for externally loaded continuum robots
Computing Jacobians and compliance matrices for externally loaded continuum robots
复制标题
计算外部加载连续体机器人的雅可比行列式和柔量矩阵
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
R. Webster
中科院分区：
文献类型：
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作者：
D. C. Rucker;R. Webster
考虑到由于施加载荷引起的变形的运动学模型最近被开发用于各种连续体机器人。在这种情况下，通常需要求解一组带有边界条件的非线性微分方程来获得机器人的形状。因此，高效地计算机械臂雅可比矩阵和柔度矩阵并不简单。本文提出了一种求弧长参数化雅可比矩阵和柔度矩阵的方法。我们的方法包括通过在模型方程中传播必要的偏导数来获得增广雅可比矩阵，从而得到一组新的微分方程。这些方程可以通过单个数值积分作为初值问题来求解。我们的方法一般适用于各种连续体机器人结构，而不考虑所使用的具体驱动系统。我们提供了一个具体的案例研究，使用这种方法来获得一个同心管机器人的雅可比矩阵。
Kinematic models that account for deformation due to applied loads have recently been developed for a variety of continuum robots. In these cases, a set of nonlinear differential equations with boundary conditions must often be solved to obtain the robot shape. Thus, computing manipulator Jacobians and compliance matrices efficiently is not straightforward. In this paper, we propose a method for obtaining an arc length parametrized Jacobian and compliance matrix. Our approach involves obtaining an augmented Jacobian by propagating the necessary partial derivatives through the model equations, resulting in a new set of differential equations. These equations can be solved as an initial value problem, via a single numerical integration. Our method can be generally applied to various continuum robot architectures, regardless of the specific actuation system used. We provide a specific case study using this method to obtain the Jacobian for a concentric-tube robot.