Dynamic modelling and PFL-based trajectory tracking control for underactuated cable-driven truss-like manipulator

基于部分反馈线性化方法的欠驱动绳索桁架式机械臂轨迹跟踪控制

In recent years,an innovative underactuated robot was developed,named as underactuated cable-driven trusslike manipulator(UCTM),to be suitable in aerospace applications.However,there has been strong consensus that the stabilization of planar underactuated manipulators without gravity is a great challenge since the system includes a second order nonholonomic constraint and most classical control methods are not suitable for this kind of system.Furthermore,the complexity of the truss-like structure results in tremendous difficulty of computational complicacy and high nonlinearity during dynamic modelling in addition to controller design.It is paramount to solve these difficulties for UCTM's future applications.To solve the above difficulties,this paper presents a dynamic modelling method for UCTM and a trajectory tracking control method based on partial feedback linearization(PFL)that fulfills the control goal of moving UCTM from its original position to a desired position by tracking a given trajectory of the joint angles.To achieve this,a model equivalent method is proposed to make UCTM equivalent with a three-link manipulator in the sense of dynamic behavior.Then the Lagrangian equation combined with complex vector method is proposed in the dynamic modelling process of UCTM,which simplifies the derivation procedure.Based on the established dynamic model,a coordinate transformation method is proposed to transform the control force matrix into the conventional form of an underactuated system,so that the control force can be separated from the unactuated term.The PFL method in combination with the LQR control method is then proposed to realize the targets that the joint angles can track given desired trajectory.Simulation experiments are conducted to verify the correctness and effectiveness of the proposed methods.

近年来,一种新型的欠驱动绳索桁架式机械臂(UCTM)因适用于航空航天应用而引发了关注。然而,无重力平面欠驱动机械臂的轨迹跟踪控制问题是一个很大的挑战,因为该系统包含二阶非完整约束,大多数经典控制方法不适用于此类系统。此外,类桁架结构的复杂性导致动力学建模和控制器设计过程中产生计算复杂性和高度非线性的巨大困难。因此,解决这些困难对于UCTM未来的应用至关重要。针对上述问题,本文提出了一种UCTM的动力学模型建立方法和基于部分反馈线性化(PFL)的轨迹跟踪控制方法,通过跟踪给定的关节角轨迹,实现UCTM从初始位置到期望位置的控制目标。动力学建模过程中提出了一种模型等效方法,使UCTM与三连杆机械手在动力学行为上等效。提出了拉格朗日方程与复向量法相结合的方法,简化了推导过程。依据已建立的动力学模型,提出一种坐标变换方法,将控制力矩阵转化为欠驱动系统的常规形式,从而将控制力从未驱动项中分离出来,使其适用于PFL方法。然后,将PFL方法与线性二次型调节(LQR)控制方法相结合设计轨迹跟踪控制器,实现关节角跟踪给定期望轨迹的目标。仿真实验验证了所提方法的正确性和有效性。