Design an adaptive controller and a state observer based on neural network for the 4dof parallel robot

HANOI UNIVERSITY OF SCIENCE AND TECHNOLOGY MASTER THESIS Design an adaptive controller and a state observer based on neural network for the 4DOF parallel robot NGUYEN MANH CUONG Control Engineering and Automation Supervisor: School: Assoc Prof Nguyen Tung Lam School of Electrical and Electronic Engineering HA NOI, 2022 HANOI UNIVERSITY OF SCIENCE AND TECHNOLOGY MASTER THESIS Design an adaptive controller and a state observer based on neural network for the 4DOF parallel robot NGUYEN MANH CUONG Control Engineering and Automation Supervisor: Assoc Prof Nguyen Tung Lam Supervisor’s Signature School: School of Electrical and Electronic Engineering HA NOI, 2022 CỘNG HÒA XÃ HỘI CHỦ NGHĨA VIỆT NAM Độc lập – Tự – Hạnh phúc BẢN XÁC NHẬN CHỈNH SỬA LUẬN VĂN THẠC SĨ Họ tên tác giả luận văn : Nguyễn Mạnh Cường Đề tài luận văn: Thiết kế điều khiển thích nghi quan sát trạng thái dựa mạng nơ ron cho robot song song bốn bậc tự (Design an adaptive controller and a state observer based on neural network for the 4DOF parallel robot) Chuyên ngành: Kỹ thuật Điều khiển Tự động hóa Mã số SV: 20202916M Tác giả, Người hướng dẫn khoa học Hội đồng chấm luận văn xác nhận tác giả sửa chữa, bổ sung luận văn theo biên họp Hội đồng ngày 04/05/2022 với nội dung sau: - Chỉnh sửa lỗi tả đánh đề mục Chỉnh sửa ký hiệu bổ sung danh mục từ viết tắt Giáo viên hướng dẫn Ngày 07 tháng 05 năm 2022 Tác giả luận văn CHỦ TỊCH HỘI ĐỒNG TABLE OF CONTENT CHAPTER OVERVIEW 1.1 The four degrees of freedom parallel robot (4DOFPR) model 1.2 Trajectory tracking controllers and state observers 1.3 1.2.1 Trajectory tracking controllers 1.2.2 State Observers Conclusion CHAPTER DESIGN AN ADAPTIVE CONTROLLER AND A STATE OBSERVER FOR THE FOUR DEGREES OF FREEDOM PARALLEL ROBOT 2.1 2.2 2.3 Mathematical model of the 4DOFPR 2.1.1 Kinematic model 2.1.2 Dynamic model 10 Controller design for 4DOFPR 10 2.2.1 Backstepping aggregated with SMC (BASMC) 10 2.2.2 RBFNN-based (RBFNNB) adaptive controller 13 2.2.3 High-gain observer for the adaptive controller 17 Conclusion 20 CHAPTER SIMULATION RESULTS 22 3.1 Results of the RBFNN based adaptive controller (RBFNNB) 22 3.2 Simulation results of the adaptive controller using the high-gain state observer 27 3.3 Conclusion 35 CHAPTER CONCLUSION AND FUTURE WORK 36 4.1 Results of the thesis 36 4.2 Future work 37 REFERENCES 38 LIST OF TABLES Table 3.1 Reference trajectory parameters 22 Table 3.2 Control parameters 23 Table 3.3 Trajectory reference parameters 28 LIST OF FIGURES Figure 1.1 Parallel robot applied in the car motion simulator Figure 1.2 Parallel robot applied in rehabilitation system [4] Figure 2.1 (a) Robot coordinate; (b) Vector diagram of 4DOFP Figure 2.2 Structure of BASMC controller 12 Figure 2.3 RBFNN structure 14 Figure 2.4 Structure of the adaptive controller 15 Figure 3.1 External force 23 Figure 3.2 Motion trajectory of p 24 Figure 3.3 Tracking error of p 25 Figure 3.4 Approximated values 26 Figure 3.5 Motion trajectory of q 27 Figure 3.6 Tracking error of q 27 Figure 3.7 Uncertain parts in the robot model 29 Figure 3.8 Observed values of q 30 Figure 3.9 Observed values of q 30 Figure 3.10 Observational error of q 31 Figure 3.11 Estimated values from RBFNN 32 Figure 3.12 Robot’s trajectory 33 Figure 3.13 Tracking error 33 Figure 3.14 Observed position with different values of  ob 34 Figure 3.15 Observed velocity with different values of  ob 34 LIST OF ABBREVIATIONS Abbreviation Definition 4DOFPR Four Degrees of Freedom Parallel Robot DOF Degrees of Freedom SMC Sliding Mode Control DSC Dynamic Surface Control RBFNN Radius Basis Function Neural Network BASMC Backstepping aggregated with Sliding Mode Control RBFNNB Radius Basis Function Neural Networkbased DSCNN Dynamic Surface Control Neural Network CHAPTER OVERVIEW 1.1 The four degrees of freedom parallel robot (4DOFPR) model Nowadays, robotic systems are being increasingly rapidly developed and applied in several economic and social life fields because they are designed for particularly complex and dangerous tasks or repetitive jobs and require high accuracy Moreover, apart from being almost precise and consistent, with their flexible operating ability, robots are capable of working in hazardous environments In addition, the robot can perform tasks with heavy loads and toxic substances and can adapt to particular environmental conditions Thus, these advantages have significantly contributed to productivity and quality improvement, preventing accidents and saving labor costs In state-of-the-art technology, parallel robots are increasingly prevalent in the industry, military, medical, and entertainment Various numbers of parallel structures in [1], [2], [3], [4], and [5] have been taken into account, including the six degrees of freedoms (DOF) robot in [1], which is capable of applied in medical surgery, as well as rehabilitation in [4], and some other structures applied into flight and automobile simulation Most of these models have been implemented based on the advantages of parallel structure, namely low inertia moment, high load, and smooth transmission capacity [6] From reality-based car models, to assist trainees and drivers have an alternative approach to getting familiar with the automobile’s movements, it is necessary to construct a driving simulation model based on a class of parallel architectures and motion platforms developed recently [3] Moreover, car driving simulation models are also constructed with the purpose of mitigating unexpected forces impacting drivers in practical and virtual reality environments in relation to health care and rehabilitation [4], [5] In order to describe the movement of the robot system, the demand for robot modeling is imperative Several studies [6], [7] showed the geometrical analysis of a six DOF constrained parallel robot Regarding the construction of the mathematical model, a forward and inverse kinematics model of Quanser’s Hexapod robot has been illustrated in [8] In addition, the six DOF parallel robots have a positive advantage of high accuracy movements However, the complexity of six actuators’ interaction and coordination gives the rising complexity in designing trajectory tracking controllers of parallel robots, especially in the presence of massive uncertainties Therefore, the configuration with fewer joints and DOF is able to mitigate the inevitable hysteresis and redundancy of actuators shown in [9], [10], and [11]; thereby, it would be more convenient in particular practical applications and controller design considered uncertain elements In addition, in the attempt to reduce computation complexity and redundant constraints, the group of authors has constructed the four DOF platform, comprising the movements of rotating and translating along the vertical axis OZ, rotating about the OX and OY axis Figure 1.1 Parallel robot applied in the car motion simulator Figure 1.2 Parallel robot applied in rehabilitation system [4] From the reference and analysis of the above scientific works, moreover, intending to reduce the computational complexity and redundant constraints while still ensuring the necessary motion, the thesis puts focus on the four degrees of freedom parallel robot platform with the movements of rotational and translational movements along the OZ axis, rotation in the OX axis and the OY axis 1.2 Trajectory tracking controllers and state observers 1.2.1 Trajectory tracking controllers In robot control, especially in orbital tracking control problems, modern methods specially put focus on designing control algorithms capable of handling problems related to uncertainties, perturbations, and unknown structural components in the system model while still ensuring stability and tracking quality The 4DOFPR parallel robot model is considered to be a model being commonly affected by nonlinear uncertain elements in practical applications, especially external forces acting in different directions on the system The parallel structures are considered a nonlinear model in the control design field; therefore, a control issue has attracted significant attention in the scientific community One of these designed methodologies for nonlinear control systems that have been interested in is the Backstepping technique as in [12], [13], [14], [15], and [16] in order to ensure the quality of trajectory tracking control However, when uncertainties or unmodeled components exist in the system model, the “explosion of terms” phenomena adversely affects the control quality Another prominent control method is sliding mode control (SMC) which has been widely used because of its robust characteristic as in [17], [18], and [19] when considering the existence of unknown elements However, the chattering phenomenon generated by the SMC controller is likely to demolish the system [20], as well as the computational burden with the high order systems Combining the two aforementioned controllers is an approach to improving control performance because it takes advantage of them Then, the robustness characteristic is enhanced, and the computational cost is reduced as in [20], [21], [22], and [23] Nevertheless, the combined controller cannot cope with the chattering and “explosion of terms” phenomena On the other hand, by taking advantage of the multiple sliding surface controller and Backstepping technique, dynamic surface control (DSC) has been proposed to address the problem “explosion of terms” in [24] and [25] by using a low-pass filter for each computation step However, the errors of the low-pass filter in the DSC controller are a dilemma, majorly depending on a filter time constant and being proven by complex mathematical conditions in [24], which may correlate with the frequency of experimental devices Alternatively, a more efficient method in this paper handling mathematics difficulty is utilizing a neural network to approximate virtual signals and alleviate the chattering phenomena In control theory, noise components are commonly considered to be an inevitable part of the whole system, and analyzing noise is the key to finding a way that assists the 4DOFPR system to be more stable and accurate To be more specific, stochastic disturbances are problematic, impacting the 4DOFPR system In terms of non-Gaussian noises, the modified extended Masreliez–Martin filter constructed in [26] is an efficient approach to handle nonlinear systems when environmental disturbances influence the whole system Besides, stochastic parameters have been taken into consideration in [27] by estimating stochastic nonlinear systems By taking into cautious consideration published in [28] and [29], it is assumed that some stochastic disturbances as to an unknown varying force from the input system act on actuators of the 4DOFPR system along the vertical direction because of body weight and moment disturbance as well as unknown parts However, there have been several kinds of noises in external and internal stochastic disturbances because of all range elements [30], from frictions, vibrations, and changes of sudden forces to the shift in environmental conditions, which are considered uncertainties In this thesis, we assume that the 4DOFPR is the model prone to the impact of stochastic uncertainty elements As mentioned above, for many conventional nonlinear controllers such as SMC or Backstepping, there have been drawbacks in improving control performances when it is challenging to identify the accurate model because of the neural network demand the available values of the position and velocity of the system in order to calculate the control signal and appropriate estimated values to guarantee the system’s stability These values will be derived from the state observer, so the control performance majorly depends on the observer’s output quality Therefore, a simulation scenario is built to analyze and evaluate the observer quality and its influence on the control system, especially in the presence of uncertainties, model errors, and noises For this scenario, the reference trajectory’s parameters are given in Table 3.3 The initial position for 4DOFPR is reselected as l01 =0.55(m), l02 =0.45(m), l03 = 0.58(m), and  = 0(rad ) Table 3.3 Trajectory reference parameters Initial position End position  0.(m / s)  0(rad / s)  ; to = 0; v0 =  0(rad / s)     0(rad / s)   0.0(m / s)  0.0(rad / s)  ; t f = 5; vf =  0.0(rad / s)    0.0(rad / s)   0.55(m)   −   (rad )   12   p0 =  −  (rad )       (rad )   12  0.65(m)     (rad )  8   pf =    (rad )  9     (rad )  3  28 Figure 3.7 Uncertain parts in the robot model Besides, to verify the ability of insensitivity to model errors and uncertainties, assuming that the ideal model parameters mp =15(kg) ; m1 =0.5(kg) ; m2 =3(kg) ; mdc =3(kg) and those of nominal models are mp = 25(kg) ; m1 =1(kg) ; m2 =10(kg) ; mdc =2(kg) Furthermore, the system is assumed to be experienced uncertain parts, as in Figure 3.7 The uncertain elements, as well as the model variation, have adverse impacts on the quality of both controller and observer However, as above-mentioned in the previous section, the RBFNNB adaptive controller can estimate the appropriate values for the controller 29 Figure 3.8 Observed values of q Figure 3.9 Observed values of q 30 Figure 3.10 Observational error of q The control parameters are chosen in Table 3.2, and the observer parameters are selected ob = 0.01; ki1 = 1.0; ki = 2.0(i = 1,2,3,4) Because the objective is to estimate the robot’s velocity values and the robot position is still necessary for the observer, assuming that the initial position of the observer coincides with that of the robot The observer outputs are given in Figure 3.8 and Figure 3.9 In Figure 3.8, it can be seen that the observed position tracks the actual values with minimal errors (approximate 10-4 (m) with the robot’s legs and 10-4 (rad) of the angle  ) within the assumption that it is not different in the initial stage However, this quantity is possibly measured to be used to calculate the observer outputs Therefore, the comparison of position values is to demonstrate the high-gain performance In addition, the observed velocity values in Figure 3.9 show that the observer can track the actual velocity At the initial time, the velocities rapidly increase because the robot’s initial position is different from that of the desired trajectory Thus, the controller generates the appropriate value to quickly steer the system to the reference Moreover, it is evident that, although affected by the uncertain components and model variation, the velocity values of the robot legs and the angular velocity around OZ are still able to follow actual values with minor deviations within the acceptable range Specifically, the observed velocity value errors are shown in Figure 3.10 In the beginning, the required observer will need time to calculate the appropriate value, hence the internal oscillation as shown in 31 Figure 3.10 However, this time interval is also minimal (about 0.03s), and the convergence speed is fast, which is also one of the outstanding advantages of the high-gain observer At the steady-state, the maximum deviation of the legs’ rate is only approximately 6.10-3 (m/s), and that of the angular velocity is roughly 5.10-4 (rad/s) In addition, it can be seen that there is a steady error phenomenon in the deviation values of the velocity observed because, according to (2.46), with a sufficiently small value of  ob , the observer is able to minimize the adverse effect of the mathematical model error However, because of  ob , this characteristic cannot eliminate errors entirely, but the parameter of the observer will be selected so that the deviation is kept in an acceptable range From the afore analysis, it can be seen that the high-gain observer can ensure fast convergence speed and simultaneously minimize the impact of uncertainty components and model noise With the ability to approximate the wide ranges of uncertainties, combined with the high-gain outputs, RBFNN still ensures that it can generate suitable values tracking ideal values for unknown parts to guarantee the system stability, as in Figure 3.11 Therefore, the control quality, as well as tracking performance, are ensured in Figure 3.12 Thus, the robot states can track their references with minor tracking errors (about 1,2.10-3 (m)) in Figure 3.13 Besides, there is also a steady error phenomenon occurring in the observer as evaluations mentioned above However, with the 4DOFPR, the errors are acceptable Figure 3.11 Estimated values from RBFNN 32 Figure 3.12 Robot’s trajectory Figure 3.13 Tracking error To more extensively demonstrate the ability to alleviate the influence of model errors, different values of  ob are chosen It can be seen that the minor  ob is, the better performance the system can achieve However, if it is determined to be extremely small, peaking phenomena [44] will affect the system, leading to instability 33 Figure 3.14 Observed position with different values of  ob Figure 3.15 Observed velocity with different values of  ob In Figure 3.14 and Figure 3.15, with ob = 0.05 and  ob = 0.1 the observed quality is not as good as ob = 0.01 The value ob = 0.01 ensures superior quality in comparison to that of the others On the contrary, with  ob = 0.1 , the observed 34 error is the most significant deviation Specifically, the steady error exists in both position and velocity values Thus it can have a significant deteriorative impact on the system performance 3.3 Conclusion This chapter illustrated the simulation results of the proposed adaptive controller based on the RBF neural network compared to existing methods in the literature Moreover, the controller performance supported by the high-gain observer is also presented and analyzed In general, the proposed approach demonstrated superior performance to other methods because of the ability to cope with uncertain parts, external noises, and problems of conventional controllers In detail, the tracking errors of RBFNNB are significantly more minor than those of the others, even in the presence of the assumed external force and unknown model parameters for both simulation scenarios Moreover, a standard high-gain observer can ensure the acceptable quality of the observed states Therefore, with the input generated from the observer, the control performance is still guaranteed However, both controller and observer parameters have to be moderately chosen Thus an appropriate method to tune them can remarkably improve the system performance The future work section in the following chapter will discuss this problem 35 CHAPTER CONCLUSION AND FUTURE WORK Parallel robots are increasingly widespread in various fields, including those in industry or essential operations Therefore, problems of tracking control, dealing with uncertain components, model variation, or the impact of exogenous noise are the content of interest Moreover, the design of intelligent controllers based on neural networks to improve control quality has also been a potential research field for this robot model In addition, the combined use of the state observer provides the basis for reducing reliance on complex sensor systems and machining costs 4.1 Results of the thesis The thesis has achieved the objectives of researching and proposing a new adaptive control algorithm based on a radius basis function neural network for the trajectory tracking problem of a four-degrees of freedom parallel robot The model is considered to experience the uncertain elements and the effects of exogenous noise components as well as model variability The controller has the ability to ensure system stability simultaneously and minimize the adverse impact on the control quality of conventional nonlinear controllers, even when combined with a high-gain state observer The main contributions of the thesis: - The thesis focuses on the problem of controller design for the uncertain model of the 4DOFPR The approach based on RBFNN does not majorly depend on the mathematical characteristics of parallel robots Thus, the developed controller can cope with the larger range of uncertain elements and bounded disturbances because of its outstanding characteristic in approximating nonlinear parts and compensating for the external noises The neural network outputs are presented in comparison to nominal uncertain values in order to verify the efficiency of approximating uncertainties as well as the influence of the neural network on the system performance (Publication 1) - The proposed adaptive controller is designed based on the Backstepping technique aggregated with SMC Therefore, it takes advantage of these controllers in eliminating nonlinear parts, as well as enhancing the robustness of the system Moreover, the adverse impacts of the two controllers, including “explosion of terms” and chattering, are remarkably alleviated because the unknown elements, which are the main factors causing the phenomena, are approximated and compensated by the neural network Thus, the developed controller not only overcomes the disadvantage of the above-mentioned techniques but also increases the robustness and adaptive behavior of the overall system (Publication 1) - The adaptive controller is designed using a high-gain state observer to estimate robot states to reduce the complexity of using sensor systems The highgain observer ensured observation quality, and thus it can guarantee the control quality and system stability even under the influence of model errors The simulation results show the availability and correctness of the theoretical analysis and the efficiency of the proposed controller (Publication 16) 36 In addition, in the process of completing the thesis, research on control algorithms as well as adaptive control algorithms for nonlinear objects and parallel robots have also been published at scientific conferences and in prestigious national and international journals (Publications 1, 2, 3, 9, 12, 14, 15, and 16) 4.2 Future work Parallel robots are not only affected by uncertainties, model variations, and exogenous noises, but there are many constraints, both in terms of robot state and motion of actuator structures Therefore, considering and using these constraints for the control law calculation is necessary to improve the control quality and calculate the reasonable control signal for the system The high-gain state observer has an observation quality that is majorly dependent on the appropriate choice of the parameters, especially when a wide range of model errors exists For each stage in the operational process, observer parameters have different appropriate values, and thus parameter tuning can improve the system’s quality Fuzzy logic rules can be designed to provide suitable values for them based on knowledge about the system as well as the 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CHAPTER DESIGN AN ADAPTIVE CONTROLLER AND A STATE OBSERVER FOR THE FOUR DEGREES OF FREEDOM PARALLEL ROBOT This chapter presents the design of an adaptive controller and a state observer for a. ..HANOI UNIVERSITY OF SCIENCE AND TECHNOLOGY MASTER THESIS Design an adaptive controller and a state observer based on neural network for the 4DOF parallel robot NGUYEN MANH CUONG Control... The high-gain state observer is to generate the input state signal for the adaptive controller designed in the previous chapter Both the controller and the 27 neural network demand the available