Recurrent neural network with noise rejection for cyclic motion generation of robotic manipulators
Introduction
Neural networks, as a robust algorithm, have become a hot topic and have been widely applied to information processing (Huang, Zhang, Zhang, & Husssain, 2020), optimization problems (Qi, Wang et al., 2020, Qin et al., 2015), robotics (Qi, Li et al., 2020, Yang et al., 2018, Zhang et al., 2020a), and other aspects (Liu and Qin, 2019, Stanimirovic et al., 2015, Wei et al., 2019). They are broadly divided into two categories: forward neural networks and recurrent neural networks (RNNs). Among them, RNNs, characterizing outstanding computing and learning capacities, as well as hardware implementability, are generally described as ordinary differential equations (ODE) (Cheng, Liu, Yang, Huang, Hou, & Tan, 2018). Their solutions (or the equilibrium points of the ODE dynamical systems) converge to the theoretical value along a continuous path from the initial value (Xia et al., 2004, Xiao et al., 2019). Furthermore, RNNs can be improved with additional functions such as finite-time convergence (Jin et al., 2016, Li et al., 2018, Xiao, Liao et al., 2018), which provides feasibility for applying to robotics. Lots of research have been done to obtain the relevant real-time joint data (i.e., joint angle, joint velocity, and joint acceleration) using neural control laws (Jarzebowska, 2008, Jin et al., 2017, Wang et al., 2020, Zhang et al., 2020b). In detail, through a control scheme with an optimization index, RNN gets the joint data, and then drive the end-effector to efficiently move along the predetermined trajectory (Guo et al., 2020, Xia et al., 2005, Zang and Constantinides, 1992, Zhang et al., 2019, Zhang et al., 2008). For example, the Lagrange neural network investigated in Zang and Constantinides (1992) is used to address a convex optimization problem with an equation constraint, reconstructed from kinematic redundancy in robot motion control. In Zhang et al. (2008), the researched dual neural network can further handle the inequality constraint problem by solving it in dual space, which provides an approach to deal with joint constraints in manipulators controlling.
Note that the joint-angle drift is a significant problem during the cyclic motion generation of robotics manipulators, which indicates that initial joint angles deviate from the initial ones (Lu et al., 2019, Xie et al., 2021). In industrial manufacture, robotic manipulators are usually required to conduct repetitive tasks. Thus, designing an optimization scheme for manipulators’ cyclic motion generation (CMG) becomes a primary problem (Jin and Li, 2018, Luo et al., 2017, Xiao, Zhang et al., 2018). The redundancy resolution at the velocity level researched in Xie, Jin, Du, Xiao, and Li (2019) can handle this problem. But it does not take account of joint-acceleration limitations. Therefore, it sometimes could lead to a velocity-discontinuity phenomenon, while this phenomenon could not happen in reality. Nevertheless, acceleration-level schemes can remedy these weaknesses (Jin and Zhang, 2015, Zhang and Zhang, 2013a). Besides, an acceleration-level strategy is able to control a robot with acceleration command or velocity command only via integrations, which is more feasible than a velocity-level one (Guo and Zhang, 2014, Zhang et al., 2013).
It is worth mentioning that most of the existing neural networks cannot resist disturbance during the cyclic motion generation of robotic manipulators (Bian et al., 2018, Guo and Zhang, 2014, Jin, Yan et al., 2020, Zhang et al., 2013). Nevertheless, noises such as the rounding noise, random noise, and other additive noises are inevitable in practice. Among these noises, the time-varying noise has a significant impact on the system because it accumulates over time. Once the effect of noises exceeds the processing capacity, the results of the neural network model could be inaccurate. Therefore, with the consideration of the safety and reliability in practical applications, research on the cyclic motion generation of manipulators in noisy environments can be deemed as a fundamental requirement. To this end, an RNN with noise rejection, particularly for the time-varying polynomial noise, is proposed in this paper and applied to the cyclic motion generation of manipulators. The core of the proposed RNN is to add several dynamic variables in the hidden layer to correct the errors caused by noises. Facilitated by these dynamic variables, the proposed RNN can effectively study the features of time-varying polynomial noises and eliminate them.
The rest of the paper is divided into the following sections. Basic kinematic equations of robots are shown in Section 2. In Section 3, a CMG scheme at the acceleration level is studied to eliminate the joint-angle drift. Then, an RNN for solving the CMG scheme is proposed, with its convergence proved. Section 4 presents an RNN with noise rejection and proves that the proposed RNN is convergent. To further illustrate the reliability of the proposed method, simulations and experiments are carried out, and related results are presented in Section 5. The last section concludes the paper. At the end of the introduction part, the contributions of this paper are summarized below.
- (1)
For the first time, this paper designs such an RNN-based model that can not only drive the manipulator to avoid joint drift during the cyclic motion generation but also efficiently eliminate the disturbance of time-varying polynomial noises.
- (2)
The proposed RNN model achieves the purpose of suppressing noises by designing dynamical variables to learn the dynamic characteristics of the polynomial time-varying noise. Its convergence in the absence and presence of noises is theoretically proved.
- (3)
Comparative simulations in the presence of various kinds of noises validate the feasibility and robustness of the proposed RNN. Besides, physical experiments are performed to show the realizability.
Section snippets
Preparatory work
In this section, the essential kinematic models of manipulators are discussed at the joint-acceleration level. For a degree-of-freedom manipulator, the relationship between the joint angle and the end-effector position in the workspace can be written as , with denoting the nonlinear mapping. Furthermore, the derivative concerning time is expressed as where is the Jacobian matrix of ;
CMG scheme and RNN construction
Based on the kinematic model (4) in Section 2, the CMG scheme for the cyclic motion generation of manipulators at the acceleration level is formulated. Subsequently, an RNN for solving the CMG scheme and the theorem on its convergence are presented.
RNN with noise rejection and theoretical analysis
Generally, noises such as time-varying noises have a significant influence on systems in the actual application. Thus, an RNN with noise rejection is proposed to deal with the time-varying polynomial noise, and its convergence is elucidated as well.
Simulation and experiment
In this section, simulations and experiments are conducted to illustrate that CMG scheme (10) aided with the proposed RNN shows a satisfactory performance on remedying joint-angle drift and eliminating noise interference.
Conclusions
In this paper, a CMG scheme to avoid the joint-angle drift that occasionally appears during the cyclic motion control for robotic manipulator has been studied. Accordingly, an RNN has been proposed to solve the CMG scheme under the zero-noise condition with its convergence proved. Then, considering the characteristic of time-varying noises, the RNN with noise rejection has been developed and proved to be exponential convergent. The simulation results on PUMA 560 and UR5 manipulators synthesized
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This work is supported by the National Natural Science Foundation of China under Grant 61703189, by the National Key Research and Development Program of China under Grant 2017YFE0118900, by the Team Project of Natural Science Foundation of Qinghai Province, China, China, under Grant 2020-ZJ-903, by the Key Laboratory of IoT of Qinghai, China under Grant 2020-ZJ-Y16, by the Fundamental Research Funds for the Central Universities, China under Grant lzujbky-2019-89, and also by the CAAI-Huawei
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