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FUZZY INFORMATION AND ENGINEERING 2020, VOL. 12, NO. 4, 435–451 https://doi.org/10.1080/16168658.2021.1921378 Imperialist Competitive Algorithm Optimised Adaptive Neuro Fuzzy Controller for Hybrid Force Position Control of an Industrial Robot Manipulator: A Comparative Study a b c d Himanshu Chaudhary , Vikas Panwar , N. Sukavanam and Bhawna Chahar Department of Electronics and Communication Engineering, Manipal University Jaipur, Jaipur, India; b c School of Vocational Studies & Applied Sciences, GBU, Greater Noida, India; Department of Mathematics, IITR, Roorkee, India; Department of Business Administration, Manipal University Jaipur, Jaipur, India ABSTRACT ARTICLE HISTORY Received 3 April 2016 Due to the nonlinear nature of the dynamics of a robot manipu- Revised 24 March 2021 lator, controlling the robot meticulously is a challenging issue for Accepted 15 April 2021 control engineers. The key purpose of this paper is to provide an accurate intelligent method for refining the functionality of ortho- KEYWORDS dox PID controller in the problem of force/position control of a robot Adaptive neuro fuzzy control; manipulator with unspecified robot dynamics during external distur- evolutionary computation; bances. A grouping of imperialist competitive algorithm (ICA) and force control; imperialist competitive algorithm (ICA); adaptive neuro fuzzy logic is applied for the tuning of PID param- position control; PUMA robot eters. This, therefore, forms an intelligent structure, adaptive neuro manipulator fuzzy inference system with proportional derivative plus integral (ANFISPD + I) controller, which is more precise in definite and indef- inite circumstances. To show the efficiency of the proposed method, this algorithm is applied to solve constrained dynamic force/position control problem of PUMA robot manipulator. The simulated results are compared to those achieved from other evolutionary techniques such as Genetic Algorithm (GA) and Particle Swarm Optimisation (PSO). The simulation results exhibit that ICA-based ANFISPD + I out- performs the other evolutionary techniques. Highlights • An ICA-ANFISPD + I-based hybrid force/position controller has been proposed. • Easy to implement. • Works well in the case of disturbances. • Actuator Dynamics has been considered. • External disturbances have been considered. • Robot dynamics are unknown. 1. Introduction Various researchers have contributed to implementations of the modified conservative PD control scheme which only requires the joint position measurement as input. Two types CONTACT Vikas Panwar vikasdma@gmail.com © 2021 The Author(s). Published by Taylor & Francis Group on behalf of the Fuzzy Information and Engineering Branch of the Operations Research Society of China & Operations Research Society of Guangdong Province. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 436 H. CHAUDHARY ET AL. of observers may be used in the above instance: the observers developed a recognised model and the observers developed an unidentified model. In the primary cases one has the information regarding the dynamics of a robot manipulator to a little scope. It was pre- sumed that dynamics of robot manipulator was obtainable, if the adaptive observer [1]lacks knowledge of the parameters. The observer is based on an unknown model means that no accurate learning of the robot is essential. Broadly acknowledged observers based on unknown models were pre- sented in [2], which could approximate the velocity component from the actual output. To achieve the global asymptotic stability by integrating integral actions or computed feed forward, a PD control was proposed in [3]. A hybrid observer RBF neural network-based controller was offered in [4] which can not only approximate the joint velocities but also compensate the gravity and friction. In many industrial applications, it is desired for the robot manipulator to exert a pre- scribed force normal to a given surface, while following a prescribed motion trajectory tangential to the surface. A Modified Hybrid Control scheme was presented in [5]which accomplished an accurate position and force control for a robot manipulator in joint space by specifying the desired compliance in Cartesian space. A neural network-based adaptive control scheme for hybrid force/position control for rigid robot manipulators is presented in [6]. Based on the decomposed robot dynamics into force, position and redundant joint subspaces, a neural network-based controller is proposed to learn the parametric uncer- tainties, existing in the dynamical model of the robot manipulator. A novel neuro-adaptive force/position tracking controller for a robotic manipulator, in compliant contact with a surface under non-parametric uncertainties, is proposed in [7] which assumes structural uncertainties to characterise the compliance and surface friction models, as well as the robot dynamic model. The problem of the configuration-dependent dynamics of the manipulator in con- strained motion was dealt in [8] with the implementation of a hybrid force/velocity control for contour tracking tasks of unknown objects performed by industrial robot manipula- tors. An augmented hybrid impedance force/position control scheme is developed and presented in [9] for a redundant robot manipulator. The outer loop controller improves transient performance, while the inner loop controller consists of a Cartesian-level poten- tial difference controller, a redundancy resolution scheme at the acceleration level and a joint-space inverse dynamic controller. A hybrid adaptive fuzzy control approach-based position/force control of robot manipulators is proposed in [10] to solve the overwhelming complexity of the deburring process and imprecise knowledge about robot manipulators. A fuzzy neural network-based position/force control, which enables the controller to deal efficiently with force sensor signals, was presented in [11], which includes noise and/or unknown vibrations caused by the working tool, to search the direction of the constraint surface of an unknown object. There are many theoretical and practical hurdles, which are still unachievable, because of unspecified robot manipulator dynamics and environmental complexities. Standard approaches are appropriate when one has the precise mathematical modelling of all the fundamental and vital parameters that are available. On the other hand, most of the time one has to work in real environment where the dynamic model and external environmental variables are unidentified [12]. Conventional controllers, such as PD and PI alone, do not per- form well in the case of removing steady state error and enhancing the transient response. FUZZY INFORMATION AND ENGINEERING 437 Recently, for achieving high robustness opposed to noise and to unravel the nonlin- ear control snag, some of the hybrid intelligent type fuzzy proportional integral deriva- tive (FPID) controller techniques have been combined with conventional techniques and presented in [13–18], which illustrates the improved steady state and transient response. Optimisation provides the possibility to easily handle redundant mechanisms, to assign the degrees of freedom of the robot to multiple and possibly concurrent tasks, to enforce hard constraints corresponding to physical limitations, etc., to name just a few. Optimisa- tion is used in numerous schemes for generalised inverse kinematics, linear and non-linear control, direct and inverse optimal control, trajectory optimisation, planning, etc., with already impressive achievements. There are many optimisation algorithms and numerous ways to formulate a robotic problem. In the present paper, an ICA-based optimised hybrid force/position control approach is proposed for trajectory control of robot manipulator, which works well in the absence of anonymous dynamics of a robot manipulator in a constraint environment. The constraint has been taken in joint space by restricting the manipulator to move in the Z direction. The proposed ICA-ANFISPD + I force/position controller follows the trajectory exceptionally smoothly with bare minimum error. Section 2 establishes the actuator dynamic model for the n degrees of freedom (DOF) robot manipulator. The force/position control followed by ICA optimisation technique has been discussed in Section 3. Section 4 presents controller performance criteria used to sta- tistically demonstrate the validity of ANFISPD + I controller with discussed optimisation techniques. Simulation outcomes to reveal the efficiency of the controller with various optimisation techniques are discussed in Section 5, followed by conclusions in Section 6. 2. Dynamics of Robot Manipulator First, the traditional dynamic model of an n DOF robot manipulator is presumed to be in the subsequent form [19] M(q)q ¨ + V (q, q ˙ )q ˙ + G(q) + F(q ˙ ) = τ (1) nxn nxn whereM(q) ∈ R represents the inertia matrix, V (q, q ˙ ) ∈ R represents the centripetal- n n Coriolis matrix, G(q) ∈ R represents the gravity effects, F(q ˙ ) ∈ R denotes the friction n n effects, τ(t) ∈ R signifies the torque input control vector and q(t), q ˙ (t), q ¨ (t) ∈ R signify link position, velocity and acceleration, respectively. The actuator dynamics for a robot manipulator may be written as [19] M (q)q ¨ + V (q, q ˙ )q ˙ + G (q) + F (q ˙ ) = K v (2) where 2 2 M (q) = (J + R M); V (q, q ˙ ) = (B + R V ); M m M m 2 2 G (q) = R G; F (q ˙ ) = (RF + R F); ⎡ ⎤ Mi r 0 ⎢ ⎥ ai K = ; R = ; M ⎣ ⎦ Mi 0 r ai 438 H. CHAUDHARY ET AL. K K bi Mi B + 0 Mi ⎢ ⎥ ai B = ; ⎣ ⎦ K K bi Mi 0 B + Mi ai J 0 Mi K = RK ; J =;(3) M M 0 J Mi n n where v ∈ R is the control input motor voltage, q = vec{q }∈ R with q is the ith rotor M Mi Mi angle, J is the motor inertia,B is the rotor damping constant, F is the actuator friction, M M M R is the armature resistance, K is a torque constant,K is a back emf constant and J is ai Mi bi Mi the motor inertia of the ith motor. r is the gear ratio of the coupling. or q = r q ; q = Rq (4) i i M M where r is a constant less then1 if q is revolute, else unit of m/rad if q is prismatic. i i i After including nonlinear unmodelled disturbances, Equation (2) can be rewritten as M (q)q ¨ + V (q, q ˙ ) + G (q) + F (q ˙ ) + τ = K v (5) M (q)q ¨ + N (q, q ˙ ) + τ = K v = τ (6) 3. Intelligent ANFISPD+ I Force/Position Controller Design An optimised hybrid ANFISPD + I force/position controller, applied to six DOF PUMA robot arm, has been shown in Figure 1. The controller applied has two inputs and a single output (TISO) structure. The inputs used are position error (e) and velocity error (e ˙). The integral error (e ) has been used simply to perform orthodox integral action. 3.1. Force/Position Control The dynamic model of an n DOF robot manipulator with environmental contact on a prescribed surface is presumed to be in the subsequent form [19] M (q)q ¨ + V (q, q ˙ )q ˙ + G (q) + F (q ˙ ) + τ = τ + J (q)λ (7) where q(t) ∈ R , J(q) is a Jacobian matrix associated with the contact surface geometry, and λ is a vector of contact forces exerted normal to the surface described to the surface. The constraint surface for robot manipulator is considered in the Z direction in joint space. The Jacobian matrix is ∂Z J(q) = (8) ∂q The constraint equation reduces the number of degree of freedom to n ≡ n − m (9) To find the constraint motion along the Z direction, the reduced order dynamics for robot manipulator is M (q )L(q )q ¨ + V (q , q ˙ )q ˙ + F (q ˙ ) + G (q ) + τ = τ + J (q )λ (10) 1 1 1 1 1 1 1 1 1 m d FUZZY INFORMATION AND ENGINEERING 439 Figure 1. Complete block diagram for intelligent ANFISPD + I hybrid force/position controller. where q (t) ∈ R ,L(q ) is an extended Jacobian matrix given by 1 1 ⎡ ⎤ ⎣ ⎦ (11) L(q ) ≡ 1 ∂Z ∂q The reduced order dynamics describing the motion in the plane of constraint surface is ¯ ¯ ¯ ¯ Mq ¨ + V q ˙ + F + G +¯ τ =¯ τ (12) 1 1 1 d where T T T ¯ ¯ ˙ M = L M (q )L; V = V (q , q ˙ ); L = L (V L + M (q )L); 1 1 1 1 1 m 1 T T T T ¯ ¯ F = L F ; G = L G ; τ¯ = L τ ; τ¯ = L τ d d As J(q )L(q ) = 0 (13) 1 1 The suppositions and the necessary properties of the model given in Equation (6) utilised in the proposed controller development are given as Property 1: The inertia matrix M(q ) is positive definite symmetric and bounded above and below. ¯ ¯ Property 2: The matrix (M(q ) − 2V (q , q ˙ )) is skew symmetric. 1 1 1 1 Property 3: F(q ˙ ) = a + b q ˙ for some unknown positive constants a, b. 1 1 Property 4: ¯ τ ≤ c for some unknown positive constants c. d 440 H. CHAUDHARY ET AL. The joint space constraint by restricting the manipulator to move in the Z direction is given. Z = 0 =−d c + a s + a s (14) 4 23 3 23 2 2 2 2 2 θ = a tan 2(± a + b − c , c) − a tan 2(b, a) (15) a = a s − d c 3 3 4 3 b = a + a c + d s (16) 2 3 3 4 3 c = Z = 0 2 2 2 θ = a tan 2(± (a s − d c ) + (a + a c + d s ) − (0) ,0) 2 3 3 4 3 2 3 3 4 3 (17) - a tan 2((a + a c + d s ), (a s − d c )) 2 3 3 4 3 3 3 4 3 The Jacobian is ∂Z J(q) = = 0 (d s + a c + a c )(d s + a c ) 000 (18) 4 23 3 23 2 2 4 23 3 23 ∂q 3.2. ANFISPD+ I Force/Position Controller It combines the learning capabilities of neural networks with the processing power of fuzzy logic. Jang [20] proposed and explained the use of ANFIS for solving a fuzzy inference sys- tem under consideration having two inputs (x and y) and one output z, which contains the rule base of two fuzzy if–then rules as Rule 1: If x is A and y is B , then f = p x + q y + r 1 1 1 1 1 1 Rule 2: If x is A and y is B , then f = p x + q y + r 2 2 2 2 2 2 During the training of the network, the input is propagated layer by layer in forward direction, while the error is propagated in backward direction. In layer 1, the membership function is applied on premise parameters. To show the firing strength, layer 2 multiplies the incoming signals. Layer 3 calculates the firing strength of the signals received and for- wards it to layer 4, which calculates an adaptive output for giving them as input to the layer 5, which computes the overall output. The procedural equations used at different layers are given in the flowchart, as shown in Figure 2. Then the output of the hybrid ANFISPD + I force/position controller is, therefore, u(t) = [L + K e (t)dt] ∗ K (19) i i m u Here L is the output ANFISPD controller. τ¯ = u(t) − J (q)[λ + K λ] (20) d f 3.3. Objective Function The scalar valued L norm, for an entire error curve, is used as a performance index to match the performance of all controllers. The root mean square (RMS) average of the trajectory FUZZY INFORMATION AND ENGINEERING 441 Figure 2. Flow chart for using ANFISPD procedure. errors, measured by the L norm measures, is given by [21]as 2 2 L (e) = ||e(t)|| dt (21) t − t f 0 where t , t ∈ R represents the first and last values of times, respectively. The RMS error value are 0.0125, 0.0159 and 0.0255 in the case of ICA-ANFISPD + I, PSO-ANFISPD +Iand GA-ANFISPD + I controllers, respectively. A lesser L (e) value shows that, the controller is 442 H. CHAUDHARY ET AL. performing better because of the lesser tracking error, which is for the ICA-ANFISPD +Iin this case. A brief overview of ICA is discussed in the next section. 3.4. Imperialist Competitive Algorithm (ICA) Imperialist competitive algorithm (ICA), a new population-based stochastic search algorithm inspired by imperialistic competition, was originally proposed by Atashpai Gar- gari and Lucas [22,23]. In ICA, the countries can be viewed as population individuals and divided into two groups based on their power, i.e. colonies and imperialists. Also, one empire is formed by one imperialist with its colonies. Furthermore, two operators called assimilation and revolution and one strategy called imperialistic competition are the main building blocks that are employed in ICA. The main framework of ICA consists of eight steps: generating the initial empire, assim- ilation, revolution, exchanging positions of the imperialist and a colony, total power of an empire, imperialistic competition, eliminating the powerless empires and convergence. We describe the steps in detail in the following subsections. Imperialism is the standpoint of developing power and control by a government to fur- ther increase its own territory. A country may rule others out by either direct control or less obvious means such as a control of markets for goods or raw materials which is the so-called neocolonialism [24]. Imperialist Competitive Algorithm (ICA) is a new global heuristic and initiative search that utilises imperialism and imperialistic contest process as an origin of inspiration. The hierarchical steps of ICA are as follows: (1) Select some random points on the function and initialise the empires. To begin the ICA, initial population is randomly created and then objective func- tion for all solutions is computed. The most powerful countries (Nimp) are selected as imperialists and the remaining Ncol of the population are colonies that should be assigned to the imperialist. The colonies distribute among the imperialists with respect to their power. (2) Move the colonies towards their relevant imperialist. After all colonies among imperialists are distributed and the initial empires are created, the assimilation policy should be executed. According to this policy, all the colonies move and get closer to their relevant imperialist based on various socio-political axes (e.g. the culture, language and economic policy). (3) If there is a colony in an empire which is dominating its relevant imperialist, exchange the positions of that colony and the imperialist. Revolution is a powerful strategy that increases the power exploration of the algorithm and helps in escaping from local minimums. This strategy is similar to the mutation process in GA to create diversification in solutions. The probability of revolu- tion in ICA illustrates the percentage of colonies that randomly change their position. After applying revolution, numbers of colonies may reach to a better position (i.e. lower cost) in comparison with their imperialist. In such cases, the colony in each empire moves to the position of that imperialist. This process avoids the optimisation process getting stuck at locally optimal values. FUZZY INFORMATION AND ENGINEERING 443 Figure 3. Flowchart of the ICA. (4) Compute the total cost of all empires (related to the power of both imperialist and its colonies). The total power of an empire is defined as summation of imperialist power and a percentage of the mean power of its colonies. (5) Pick the weakest colony from the weakest empire and give it to the stronger empire. Imperialistic competition is a key process in ICA framework in which all empires attempt to take over the possession of colonies from other empires and also con- trol them. This event causes to reduce the power of weaker empires, while powerful empires tend to increase their powers. This strategy is formulated by choosing the poorest colony of the poorest empire and making a competition among all empires to possess these colonies. (6) Eliminate the powerless empires. When powerless empires lose all their colonies, they will collapse in the imperial- istic competition and their colonies are consequently divided among other empires. (7) If there is more than one empire, go to 2, if not stopped. The ICA is stopped when there is just one empire and all colonies are under the control of that empire. The implementation procedure is shown in Figure 3. In this paper, the applied methodology chooses the best values for these deterministic coefficients by utilising the Imperialist Competitive Algorithm (ICA). This algorithm opti- mises the 18 (K K K ) PID parameters in order to determine the appropriate P(6X1), D(6X1), I(6X1) values for them. In the ICA algorithm, the root mean square error is used to calculate the minimum cost function for each decade. The ICA is initialised by 50 initial countries, and 8 initial imperialist countries, 100 iterations and the revolution rate is equal to 0.3. The effectiveness of the proposed controller ANFISPD + I force position controller is evaluated using performance criteria discussed in the next session (Table 1). 444 H. CHAUDHARY ET AL. Table 1. Performance metrics and their formulas. Metrics Formulas NMSE = (q − q ) 2 di pi δ n i=1 NMSE 1 2 δ = (q − q ) di d n−1 i=1 |q −q |/q di pi di i=1 MAPE MAPE = X100% q and q are the desired and predicted joint di pi angle values. Table 2. PID gain parameters. ICA-ANFISPD + I PSO-ANFISPD + I GA-ANFISPD + I Sr. No. K K K K K K K K K P D I P D I P D I 1. 2.04 0.78 0.10 7.16 4.46 0.76 9.44 30.00 1.82 2. 0.98 2.78 0.10 2.62 13.26 0.29 30.00 30.00 2.81 3. 4.57 1.77 0.10 6.44 1.93 0.68 6.68 30.00 0.80 4. 4.81 0.26 0.10 8.83 3.31 1.28 9.84 30.00 2.64 5. 7.31 0.77 1.59 12.22 4.98 1.75 30.00 30.00 2.35 6. 5.59 0.93 0.92 8.47 3.55 1.82 29.91 30.00 7.82 4. Controller Performance Criteria The performance of discussed hybrid force/position controller has been evaluated statically using (1) Normalised Mean Square Error (NMSE) (2) Mean Absolute Percentage Error (MAPE) Table 2 shows these performance indices and their expressions to measure the deviation between the actual and predicted values. The smaller the values of NMSE and MAPE, the closer are the predicted values to the actual values. 5. Simulations and Results For showing the efficiency of the suggested ICA-ANFISPD + I controller over PSO- ANFISFPD + I, and GA-ANFISPD + I controller, the simulation has been performed for a six DOF PUMA robot manipulator using MATLAB 2012b by considering the PUMA-560 robot manipulator dynamics from [24]. The friction term and the gravity term and external disturbances taken are as follows: ⎡ ⎤ ⎢ ⎥ 2 2 3 2 −37.196 cos(t ) − 8.445 sin(t + t ) + 1.023 sin(t ) ⎢ ⎥ ⎢ ⎥ ⎢ 2 3 4 5 2 3 ⎥ 0.248 cos(t + t ) cos(t ) sin(t ) + sin(t + t ) ⎢ ⎥ G = ⎢ ⎥ 2 3 4 5 ⎢ ⎥ 0.028 sin(t − t ) sin(t ) sin(t ) ⎢ ⎥ ⎢ ⎥ 2 3 5 2 3 4 5 ⎣ 0.028[cos(t − t ) sin(t )] + [sin(t − t ) cos(t − t )] ⎦ 0 FUZZY INFORMATION AND ENGINEERING 445 2 2 3 3 τ = q sin(3t) + q ˙ 0.5q sin(2qt ) + 1.2qt 1.2q sin(t ) + 0.8qt 000 dc 2 3 τ = 0.2q ˙ sin(t) 0.1q ˙ sin(t ) 0.1q ˙ sin(t ) 000 dd F = 1052000 ⎡ ⎤ 2 ∗ Random Waveform Generated of (pi ∗ t) Sample Size ⎢ ⎥ 2 ∗ Random Waveform Generated of (pi ∗ t) Sample Size ⎢ ⎥ ⎢ ⎥ 2 ∗ Random Waveform Generated of (pi ∗ t) Sample Size ⎢ ⎥ F = ⎢ ⎥ ⎢ 2 ∗ Random Waveform Generated of (pi ∗ t) Sample Size ⎥ ⎢ ⎥ ⎣ ⎦ 2 ∗ Random Waveform Generated of (pi ∗ t) Sample Size 2 ∗ Random Waveform Generated of (pi ∗ t) Sample Size where τ = τ + τ ; F = F + F . d dc dd d The actuator parameters are K = K = [0.189 0.219 0.202 0.075 0.066 0.066] Mi bi −1 L = 1000; R = [2.1 2.1 2.1 6.7 6.7 6.7] a ai Gear Ratio = [62.61 107.36 53.69 76.01 71.91 76.73] The PID gain parameters, calculated with the help of various optimisation techniques, are given in Table 2. The desired force is λ = 20 nt. Table 3 shows the parameters used in the tuning of ICA, PSO as well as GA-based ANFISPD + I controller during the simulation process. The lower bound and upper bound values are 0.1 and 30, respectively, for the optimisa- tion process in all cases. To test the feasibility of the proposed controller tuned with ICA, PSO as well as GA opti- misation techniques, the following four cases have been considered to study the simulation results: 1. C (Complete Dynamics): In this, we developed all the controllers based on Equation (12), which represents the complete dynamical system including actuator dynamics. 2. WF (Dynamics without friction): In this, we developed all the controllers based on Equation (12), which represents the complete dynamical system including actuator dynamics. The only difference with the first case is that friction term is absent. 3. WG (Dynamics without gravity): In this, we have designed the controllers based on a modified version of Equation (12), which lacks gravity term in it only. 4. WTAU (Dynamics without external disturbances): In this case, controllers are devel- oped on a modified dynamic model based on Equation (12). The only difference from the first case is the absence of external disturbances. The simulation experiments were conducted for 5s, 10s and 15s to study the per- formance of the proposed ICA-ANFISPD + I controller with PSO-ANFISPD +IandGA- ANFISPD + I controllers. The two desired trajectories taken are: (1) sin(t) (2) 0.15cos((pi/2)t), for which the whole data have been recorded. Dissimilar trajectories and dissimilar robot parameters have been employed to get 18 observations. The performance of all the 446 H. CHAUDHARY ET AL. Figure 4. Comparison plot for trajectory tracking of joint angle q1. Figure 5. Comparison plot for trajectory tracking of joint angle q3. Figure 6. Comparison plot for trajectory tracking of joint angle q4. ANFISPD + I controller with ICA, PSO and GA optimisation techniques can be checked through their output responses also, which are shown in Figures 4–8. The controller tuned with ICA optimisation technique is able to deal with the continuous and discontinuous frictions, gravity and other external disturbances, while successfully following the desired trajectory with minimum errors. The NMSE and MAPE values of path errors for joint angles, q1 to q6 except q2, are calcu- lated for each experiment, but due to space limitation, results are discussed for 10 s only, as given in Tables 3–7. Tables 3–7 show that the performance index of the ANFISPD + I controller is better with the ICA optimisation technique rather than PSO and GA optimisation techniques. The force tracking error response of ANFISPD + I controller with various optimisation techniques mentioned above is shown in Figures 9–11. FUZZY INFORMATION AND ENGINEERING 447 Figure 7. Comparison plot for trajectory tracking of joint angle q5. Figure 8. Comparison plot for trajectory tracking of joint angle q6. Table 3. Parameters used in tuning of algorithms. Algorithm Parameters Values ICA Number of initial Countries 50 No. of parameters to be optimised 18 Number of Initial Imperialists 8 Revolution Rate 0.3 β 2 ζ 0.02 λ 0.5 zarib 1.05 α 0.1 Number of Decades (iterations) 100 PSO Size of the swarm 100 C 1.2 C 0.12 W 0.9 Birds steps (iterations) 100 GA Population Size 20 Stall Generation Limit 20 iterations 100 In Figure 9, the force error signal is settled down to zero after 0.028 s and the maxi- mum and minimum overshoot is 0.0295 pu and −0.015 pu, whereas in Figure 10, it is 0.39 and −0.04, respectively. The maximum and minimum overshoot in Figure 11 is 0.39 pu and −0.04, respectively. The settling time in the case of all three controllers is 0.028, 0.053 and 0.089 s approximately. The mean square errors of joint force error signal are 3.87e-08, 4.95e-05 and 0.0423 for ICA-ANFISPD + I, PSO-ANFISPD + I and GA-ANFISPD + I controller, 448 H. CHAUDHARY ET AL. Table 4. Performance Index for q1 (10 s). MAPE NMSE Controller C WF WG WTAU C WF WG WTAU GA-ANFISPD + I 1.22E-06 1.22E-06 1.31E-06 2.16E-05 2.42E-05 2.34E-05 2.43E-05 1.29E-05 PSO-ANFISPD + I 1.22E-06 1.22E-06 1.31E-06 1.75E-05 1.63E-05 1.59E-05 1.62E-05 1.34E-06 ICA-ANFISPD + I 1.21E-06 1.20E-06 1.29E-06 1.72E-05 1.98E-07 1.91E-07 1.98E-07 1.19E-07 Table 5. Performance Index for q3 (10 s). NMSE MAPE Controller C WF WG WTAU C WF WG WTAU GA-ANFISPD + I 1.46E-06 1.47E-06 3.41E-06 1.75E-06 5.11E-06 3.88E-05 3.37E-05 3.65E-06 PSO-ANFISPD + I 1.47E-06 1.47E-06 3.48E-06 1.79E-06 4.37E-06 3.06E-06 3.60E-06 2.85E-06 ICA-ANFISPD + I 1.45E-06 1.45E-06 3.27E-06 1.75E-06 2.64E-07 2.98E-07 2.43E-07 2.52E-07 Table 6. Performance Index for q4 (10 s). NMSE MAPE Controller C WF WG WTAU C WF WG WTAU GA-ANFISPD + I 2.53E-06 2.54E-06 2.53E-06 2.32E-06 2.59E-06 2.69E-06 2.75E-06 2.55E-06 PSO-ANFISPD + I 2.45E-06 2.46E-06 2.46E-06 2.35E-07 2.26E-06 2.27E-06 2.24E-06 2.21E-06 ICA-ANFISPD + I 2.46E-06 2.46E-06 2.45E-06 2.32E-05 2.34E-07 2.40E-07 2.30E-07 2.36E-07 Table 7. Performance Index for q5 (10 s). NMSE MAPE Controller C WF WG WTAU C WF WG WTAU GA-ANFISPD + I 2.87E-06 2.87E-06 2.78E-06 2.46E-07 2.85E-05 2.87E-05 2.90E-05 2.84E-05 PSO-ANFISPD + I 2.83E-06 2.84E-06 2.76E-06 2.33E-07 1.38E-05 1.39E-05 1.37E-05 1.38E-05 ICA-ANFISPD + I 2.81E-06 2.80E-06 2.71E-06 2.30E-07 1.27E-06 1.44E-06 1.44E-06 1.50E-06 Figure 9. ICA-based ANFISPD + I controller joint force error. respectively. The fitness values found after optimisation process are 0.0125, 0.0159 and 0.0255 for ICA-ANFISPD + I, PSO-ANFISPD + I and GA-ANFISPD + I controller, respectively (Table 8). Table 8. Performance Index for q6 (10 s). NMSE MAPE Controller C WF WG WTAU C WF WG WTAU GA-ANFISPD + I 3.52E-06 3.52E-06 3.52E-06 2.51E-05 3.81E-05 3.83E-05 3.87E-05 3.79E-05 PSO-ANFISPD + I 3.50E-06 3.51E-06 3.51E-06 2.58E-06 2.50E-05 2.52E-05 2.49E-05 2.50E-05 ICA-ANFISPD + I 3.58E-06 3.57E-06 3.57E-06 2.48E-06 1.10E-06 1.14E-06 1.41E-05 1.41E-05 FUZZY INFORMATION AND ENGINEERING 449 Figure 10. PSO-based ANFISPD + I controller joint force error. Figure 11. GA-based ANFISPD + I controller joint force error. With the above observations, the ANFISPD + I controller tuned with ICA optimisation technique gives better performance than the other techniques. 6. Conclusions A hybrid ICA-ANFISPD + I force/position controller has been proposed for the trajectory control of a robot manipulator arm with unspecified robot dynamics. Various optimisation techniques have been applied to estimate the unknown parameters of the said controller. The fitness value for the proposed hybrid ICA-ANFISPD + I force/position controller is min- imum. In order to know the controller performance, it was subjected to different tests with or without external disturbances in real constraint environment. The system performance of PUMA 560 robot manipulator has been investigated extensively through simulation out- comes for trajectory control and the force exerted by the manipulator on the surface. It has been demonstrated, via simulations, that the proposed model yields good results for handling uncertain dynamics while following the desired trajectory. Disclosure statement No potential conflict of interest was reported by the author(s). Notes on contributors Dr. Himanshu Chaudhary received his M.E. degree in Automatic Controls & Robotics in 2000 from the Electrical Engineering Department of Maharaja Sayajirao University, Baroda, Gujarat, India. He has completed his PhD from the Department of Electrical Engineering from IIT Roorkee in 2014 in Robotics. He has around 20 years of teaching and industry experience in Electronics and Communi- cation Engineering. Currently he is working as Associate Professor (Sr. Scale) in Manipal University Jaipur, Rajasthan, India where he has been working since 2016. He has published various research papers in SCI Indexed Journals and he is Certified Peer Reviewer of IEEE, Elsevier and various Interna- tional journals of repute. His research interests include Soft Computing, Intelligent control, Artificial Intelligence, Fuzzy Control, Automation, Robotic and MEMS Sensors. 450 H. CHAUDHARY ET AL. Dr. Vikas Panwar received his PhD from the Department of Mathematics, IIT Roorkee in 2006 in Robotics. He is currently Assistant Professor at the School of Vocational Studies and Applied Sciences, Gautam Buddha University, Greater Noida (U.P.), India. He has published various research papers in SCI Indexed Journals such as Applied Mathematics and Computation, Journal of Mechanical Science and Technology, Applied Soft Computing etc. He is Certified Peer Reviewer of Elsevier, and various International journals of repute. His research interests include Robotics and control, Neural Networks and intelligent control. Dr. N. Sukavanam is currently working as Professor and Head, Mathematics Engineering Department, IIT Roorkee where he has been working since 2018. He worked as Research Scientist in IIT, Bombay during 1987–90. He was a Scientist-B in Naval Science and Technological Laboratory, DRDO, Vizag during 198486. He has published more than 100 research papers in various SCI Indexed journals. He has guided more than 19 PhD students for the completion of their PhD. His research interests include Nonlinear Analysis, Control Theory and Robotics and Control. Dr. Bhawna Chahar is Associate Professor in School of Business and Commerce, Manipal University Jaipur. She has rich experience in corporate and in academics. She has publications in ABDC, Web of Science, SCOPUS and UGC listed journals. She has written chapters in books and presented research papers in international and national level conferences and seminars in India and abroad. She is Cer- tified Peer Reviewer of Elsevier, Scopus indexed journals and UGC listed international journals. She has chaired sessions as concurrent chairperson and as Keynote/Invited Speaker in several interna- tional and national conferences in India and abroad. She has won various awards for her contribution in research and academics. She has Government of India sanctioned projects in her account. Her research interests include Emotional Intelligence, Emotional Intelligence and Robotics, Performance Appraisal/Management, Entrepreneurship, Training and Development and HRM Practices. 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Fuzzy Information and Engineering – Taylor & Francis
Published: Oct 1, 2020
Keywords: Adaptive neuro fuzzy control; evolutionary computation; force control; imperialist competitive algorithm (ICA); position control; PUMA robot manipulator
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