Quaternion broad learning system: A novel multi-dimensional filter for estimation and elimination tremor in teleoperation

Abstract

In this paper, a novel quaternion broad learning system is proposed in this paper for tremor estimation and elimination in teleoperation. In the new proposed QBLS, the architecture can be divided into three layers, including quaternion feature layer, enhancement layer and the output layer. In quaternion feature layer, a quaternion-value auto-encoder (QAE) based on the quaternion algebra is proposed and employed to extract the unsupervised features in quaternion domain. Moreover, the enhancement nodes are mapped to improve the system’s regression ability in enhancement layer. In the output layer, the nodes of feature layer and enhancement layer are concatenated to map the output of QBLS. The weight parameters of output layer can be calculated by the minimum norm least squares solutions. In addition, the semi-physical simulation experiment is completed and the new proposed QBLS has been compared with some existing methods. Finally, the effectiveness and efficiency of QBLS are demonstrated by experimental results.

Introduction

Nowadays, the operator’s manipulation and sensing capabilities are extended to a remote location by the tele-robotics [1]. The master-slave robot system facilitates off-site robotic performance of a desired task and ensures cost-effectiveness, safety and accessibility. Hence, tele-robotics systems have been widespread used in the range of mining, space medicine [2], underwater exploration, robotics-assisted minimally invasive surgery [3], [4], [5], robotic surgical training [6], [7], rehabilitation assistant [8], [9] and so on. In [10], a tele-robotic system consists of the following parts:

• a manipulator arm;

• a master device;

• a communication channel.

As shown in Fig. 1, the overall scheme of a simplified Master–Slave(MS) teleoperation system. In the teleoperation system, the communication random delay problem of adaptive control is inevitable. To overcome this challenge, some related research has been carried out in [11], [12]. Moreover, the precision of the control signal is critical for the high precision operations of the teleoperation robot. However, the control signal of telerobotics system is disturbed by the physiological tremor of operator which is defined as a roughly, involuntary, sinusoidal component inherent in normal hand motion [13]. Therefore, physiological tremor canceling has become an urgent problem in many fields.

In the past decade, a large number of filter have been proposed to solve this problem. In adaptive filter technology, the bandlimited multiple Fourier linear combiner (BMFLC) and weighted Fourier linear combiner (WFLC) which are relied on truncated Fourier series [14], [15], [16], [17] have been popular to estimate the physiological tremulous motion without any phase delay. Further, BMFLC, least squares support vector machines (MWLS-SVM) [18] methods and autoregressive methods [19] are proposed to perform a multi-step prediction of the hand tremor to tackle the unknown and known phase delays. Moreover, adaptive fuzzy wavelet neural network filter (FWNNF) and the time-sequence-based fuzzy support vector machine (TS-FSVM) are proposed in [20], [21] to cancel the physiological tremor of a minimally invasive surgery (MIS). The methods mentioned above are one-dimensional methods which have defects for estimation the multidimensional data of the actual teleoperating system.

Recently, the study of multi-dimensional method has become the focus gradually. In [22], quaternion algebra is defined as a calculation tool for multidimensional data. In the quaternion domain, the multi-dimensional features can be extracted better rather than extracted independently for each dimension. Therefore, there are some classical algorithms are extended to the quaternion version, such as the quaternion least square method (QLSM) [23], [24] and the quaternion weighted fourier linear combiner (QWFLC) [17] and so on. The quaternion-value algorithms have been experimentally verified that they have better performance in multidimensional signal processing than the real-value methods. In [25], [26], [27], a efficient machine learning algorithm which is named broad learning system (BLS) is proposed. Therefore, this paper further develops a quaternion version of this efficient BLS.

This paper proposes a novel quaternion broad learning system (QBLS) for estimation and elimination the tremor. In this work, the proposed QBLS is an extension of broad learning system (BLS) [26]. The architecture of the new proposed QBLS include quaternion feature layer, enhancement layer and the output layer. Meanwhile, the quaternion auto-encoder is proposed to extract the multi-dimensional features in the quaternion layer. In enhancement layer, the enhancement nodes are mapped by feature nodes. Moreover, all the nodes are concatenated as a matrix to map the output of the new proposed QBLS. In addition, the semi-physical simulation experiment is completed and the new proposed QBLS has been compared with some representative methods. Finally, the effectiveness and efficiency of QBLS are demonstrated by experimental results.

The remainder of this paper is organized as follows. In Section 2, some preliminaries are provided. The overview of teleoperation system is descried in Section 3. In Section 4, the details of the new proposed QBLS is given. Finally, the semi-physical simulation experiment is completed in Section 5 and conclusion is drown in Section 6.