Abstract:

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.

Key words: cloth grabbing manipulator, dynamic model, position tracking, immersion and invariance adaptive, backstepping method