基于动力学模型的面料抓取机械臂轨迹跟踪控制方法

Trajectory tracking control method of cloth grabbing manipulator based on dynamic modeling

为提高纺织服装行业中面料抓取机械臂的轨迹跟踪精度,建立考虑参数不确定性的动力学模型,采用反步法在浸入与不变(immersion and invariance,I&I)自适应理论框架下设计了一种轨迹跟踪控制方法。首先,建立含未知参数的柔性关节机械臂动力学模型;其次,采用I&I自适应控制方法设计了关节转动惯量的自适应律,并通过构造光滑函数实现参数估计误差流形的不变性和吸引性,保证参数估计误差收敛到0;最后,将所设计的自适应律引入反步法设计控制律的递推过程中,使所设计的控制律对不确定参数具有自适应特性。仿真结果表明,与传统反步法相比,所设计的I&I自适应反步法能更快速、更稳定地达到对期望轨迹的跟踪效果,该算法对期望轨迹的跟踪误差可保持在±0.002 rad之内。

Objective With the development and popularization of advanced manufacturing technology,the fabric grabbing and transferring work in the textile and garment industry has been preliminarily realized by the use of manipulator.However,in practical applications,the parameters of the manipulator model cannot be accurately measured,and the tracking accuracy would decrease when using the traditional control method.Therefore,it is of great significance to study the trajectory tracking control problem of manipulator with consideration of the uncertain model parameter.Method Aiming at the dynamic model of the manipulator with parameter uncertainty,a trajectory tracking control method was designed by using backstepping method under the framework of I&I adaptive theory.The dynamic model of flexible joint manipulator with unknown parameters was established before,the adaptive joint moment of inertia was designed using Immersion and Invariance(I&I)adaptive control method,and the invariance and attraction characteristics of error manifold were facilitated through designing a smooth function to ensure that the parameter estimation error converge to zero.Finally,the designed adaptive law is introduced into the recursive process of control law designing to make it adaptive to the uncertain parameter.Results The adaptive law designed by the I&I adaptive control method has adaptiveness for the uncertain parameter,and the parameter estimation error response curve quickly converges to 0 after a short running time(Fig.9).Compared with the FPBC(fixed parameter model based backstepping control method),the proposed IABC(I&I adaptive based backstepping control method)was found not only to achieve the desired trajectory tracking effect faster and more stably,but also to stabilize the input torque of the motor faster.The manipulator using FPBC did not track the expected trajectory and has periodic tracking errors(Fig.5),and the manipulator using proposed IABC tracked the desired trajectory for the first time after about 0.12 s of joint position,and demonstrated good tracking performance,with the tracking error of desired trajectory within±0.002 rad.The motor input torque under FPBC entered a stable state around 0.14 s,while under the IABC proposed in this paper,the motor input torque tended to stabilize around 0.07 s(Fig.6 and Fig.7).It is obvious that the FPBC made the motor input torque enter a stable state at about 0.14 s,while the IABC proposed in this research made the motor input torque enter a stable state at about 0.07 seconds(Fig.6 and Fig.7).In order to verify the trajectory tracking of manipulator end in cloth grabbing and placing,the desired trajectory tracking experiment of manipulator end was simulated using MatLab.The proposed IABC was shown to be effective in achieving accurate trajectory tracking control of the cloth grabbing manipulator(Fig.10).Conclusion The proposed IABC can effectively improve the tracking performance of the manipulator joint position and improve the tracking accuracy of the cloth grabbing manipulator.This method takes into account the uncertainty of the moment of inertia of the manipulator dynamic model.I&I adaptive control method is used to design the parameter adaptive law to avoid the over-parameterization problem of the adaptive method based on the Certainty Equivalence principle,while retaining the nonlinear characteristics of the system.