Abstract

The methods most commonly used to synthesize the Inverse Kinematic Model (IKM) of open-chain robotic systems strongly depend on the robot’s geometry, which make them difficult to systematize. In a previous work we presented a systematic procedure that relies on Groebner Bases to synthesize the IKM of non-redundant open-chain robots. This study expands the developed procedure with a methodology for the automatic selection of the basis’ monomial order. The procedure’s inputs are the robot’s Denavit-Hartenberg parameters and the movement range of its actuators, while the output is the synthesized IKM, ready to be used in the robot’s control system or in a simulation of its behavior. This procedure can synthesize the IKM of a wide range of open-chain robotic systems, such as Cartesian robots, SCARA, non-redundant multi-legged robots, and all non-redundant manipulators that satisfy the in-line wrist condition. The procedure’s performance is assessed through two study cases of open-chain robots: a walking hexapod and a PUMA manipulator. The optimal monomial order is successfully identified for all cases. Also the output errors of the synthesized IKMs are negligible when evaluated in their corresponding workspaces, while their computation times are comparable to those required by the kinematic models calculated by traditional methods.

摘要

最常用于合成开链机器人系统的逆运动学模型 (IKM) 的方法在很大程度上取决于机器人的几何形状，这使得它们难以系统化。在之前的工作中，我们提出了一个系统的程序，该程序依赖于 Groebner Bases 来合成非冗余开链机器人的 IKM。本研究使用自动选择基础的单项式顺序的方法扩展了开发的程序。该程序的输入是机器人的 Denavit-Hartenberg 参数及其执行器的运动范围，而输出是合成的 IKM，可用于机器人的控制系统或模拟其行为。此程序可以综合各种开链机器人系统的 IKM，例如笛卡尔机器人、SCARA、非冗余多足机器人、以及所有满足在线手腕条件的非冗余机械手。该程序的性能通过开链机器人的两个研究案例进行评估：步行六足机器人和 PUMA 机械手。已成功识别所有情况的最佳单项式顺序。此外，当在相应的工作空间中评估时，合成 IKM 的输出误差可以忽略不计，而它们的计算时间与传统方法计算的运动学模型所需的时间相当。