无根欠驱动冗余机器人动力耦合特性研究

无根多刚体系统和欠驱动冗余机器人系统实质上都属二阶非完整动力系统,其位姿空间约束方程不能满足控制要求,一般基于动力学方程对系统进行控制,即通过关节间动力耦合作用约束被动关节运动,因此此类机器人可控性分析的重点在于系统耦合运动特性研究。基于动力学虚设机构法及非完整系统微分变分原理,建立了无根欠驱动冗余机器人的动力学模型;针对虚设关节、主、被动关节进行动力学模型解耦,推导出了系统的二阶非完整约束方程及被动关节的加速度表达式;在此基础上,通过定义表征被动关节耦合运动的性能指标,针对不同位置主动关节输入参数对被动关节可控性的影响进行了仿真分析,得到了提高无根欠驱动冗余机器人可控性的有益结论,为实际欠驱动冗余机器人输入控制提供了参考。

Research on Dynamic Coupling Characteristic of Rootless Underactuated Redundant Robots

The general characteristic of rootless multi-body system and underactuated redundant robots is essentially dynamic systems with second-order nonholonomic constraints. The configuration space constraints equations can not realize the control request, which is generally based on dynamic equation. The constraints of these systems are mainly on velocity and acceleration and in general not integral. Therefore, the research on the characteristic of coupling motion of this kind of robots system is the basis of the controllability analysis. Based on dynamic nominal mechanism method and the differential and variation theory of nonholonomic system, the dynamic model of rootless underactuated redundant system is built, from which the second-order nonholonomic constraint equations of the system and the acceleration expressions of passive joints are derived based on the decoupling of nominal mechanism, active and passive joints. According to the defined performance indices for describing the coupling motion of passive joint, the influence of the active joints’ position on controllability of the robot are simulated. The beneficial conclusion for controllability performance advance of rootless underactuted redundant robot are obtained, which provides reference for actual input control of robots.