Abstract:  In order to solve the difficulties of virtual fixture construction and adaptive adjustment according to the operators intention in robot programming by demonstration for complex surface machining,a Programming by Demonstration (PbD) strategy for virtual fixture generation and iterative updating was proposed. A prior virtual fixture was constructed offline by demonstrating surface manifold. If the prior virtual fixture matched the surfaces to be machined, the spring-damping system was used to online compensate the path deviations of demonstration. Otherwise, the iterative correction was realized by adaptive adjustment of virtual fixture stiffness and flexibility. The results show that the construction of virtual fixture based on surface manifold is simple and has generalization characteristics, which improves the construction efficiency of complex surface virtual fixtures; in the auxiliary demonstrating processes of the virtual fixtures by using the sinusoidal and fan track , the position and orientation errors of auxiliary demonstrated path may be decreased at least by 84% and 81% respectively, and the virtual fixture may be adjusted adaptively according to the operators intention to better match the target surfaces.

Key words:  robot programming by demonstration； complex surface； virtual fixture ； surface manifold, operators intention

摘要： 为解决面向复杂曲面加工的机器人示教编程中虚拟夹具构造困难、难以依据操作者意图自适应调整等问题,提出一种虚拟夹具离线构造和在线迭代更新的辅助机器人示教编程策略。采用示教曲面流形离线构造先验虚拟夹具，若先验虚拟夹具吻合待加工曲面，则利用弹簧阻尼系统对示教路径偏差进行在线补偿，否则通过虚拟夹具刚柔性自适应调整实现迭代修正。研究结果表明，由曲面流形构造虚拟夹具简单且具有泛化特性，提高了复杂曲面虚拟夹具构造效率；以正弦/风扇轨迹作为虚拟夹具辅助示教，能使辅助示教路径位置误差、姿态误差分别降低至少84%、81%，并能根据操作者意图自适应调整虚拟夹具以更加吻合目标曲面。

关键词: 机器人示教编程, 复杂曲面, 虚拟夹具, 曲面流形, 操作者意图