Forward and inverse solution of a 9-DOF hybrid robot for minimally invasive surgery
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摘要: 针对北京航空航天大学机器人研究所最新开发的用于胸腹部冷冻穿刺手术的9自由度"5R+4T"混联机器人,基于指数积公式,利用反变换法和逆矩阵的特性,提出了一种在单约束条件下,得到该机器人解析形式正反解的新算法.通过数值算例验证了正反解的互推性,即算法的有效性,并经过对算例的分析给出了修正方案,扩大了算法的适用范围.该方法克服了因为混联机器人自由度多、结构复杂而带来的难以完成正反解计算的困难,为多自由度混联机器人的运动学求解提供了一种新的思路.Abstract: Focusing on the recently developed "5R+4T" 9-DOF(degree-of-freedom) hybrid robot for thoracoabdominal percutaneous cryosurgery by the robotics institute of Beijing University of Aeronautics and Astronautics, an original single-constraint-condition algorithm was put forward to obtain analytic solutions to the forward and inverse kinematics of the robot, based on the product of exponentials (POE) formula using inverse transformation method and characteristics of inverse matrix. The mutual derivation between the forward and the inverse solution, namely, the effectiveness of the algorithm, was demonstrated by several sets of numeric data. A modification for the algorithm was also advanced by discussing the demonstration results, so as to expand the range of its applicability. This algorithm overcomes the difficulties in performing the forward and inverse kinematic calculations which result from the DOF redundancy and the structure complexity of the hybrid robot, bringing a new idea about solving kinematic problems of multi-DOF hybrid robots.
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