Page 234 - 2024-Vol20-Issue2

230 | Abdul Zahra & Wali

Fig. 2. Structure of 2 – DOF Robot Manipulator controlled via Optimal STSMC

V. CHAOTIC PSO ALGORITHM behavior [27]. In the present paper, chaotic PSO algorithm is

The efficiency and the stability requirements must be achieved applied for finding the optimum values of the STSMC strategy
to the closed loop designed STSMC method to track the de- to achieve the best performance of (2-DOF) robot manipulator.
sired path of robot manipulator, three gains of the proposed In the Chaotic PSO algorithm, the parameters (a1, a2) will
controller (c, k as well as b) at each link of the robotic system be modified by employing the logistic map depending on the
musted be optimized. The trial and error method to adjust equation:

the controller parameters is not practical method, so, it is im- L(t + 1) = µ × L(t) × (1 - l(t)) 0 = M(t) = 1 (20)
proper to obtain the controller optimal values. The traditional

(PSO) algorithm is generally used a random sequence values Where L(t) generated randomly and µ =4 [26]. Then, the

to tune the parameters. First, the population solutions are new modification of velocity has been given as:

initialized using PSO algorithm which is known a particle. vi(t + 1) = r1(pbesti(t) - xi(t)) × wvi(t)L(t) (21)
+(1 - L(t) × r2(gbesti(t) - xi(t))
Assume, the search space with D-dimension and N particles.
For (ith) iteration, the position (xi(t)) and velocity (vi(t)) of

particle is denoted respectively as [25]: The objective function depends on decreasing the cost func-
xi(t) = xi1, xi2, xi3, . . . , xiD tion which is given in:
vi(t) = vi1, vi2, vi3, . . . , viD

The best position which is reached by the (ith) particle and 1? ?CostFunction =ne21+1ne22 (22)
n i=1 n i=1
denoted as (pi = pi1, pi2, pi3, . . . , piD), called (pbest ). The all
swarm then reaches to the global best position (gbest ) and Where, the (e1, e2) are the errors at each link of manipulator.
defines as (pg = pg1, pg2, pg3, . . . , pgD). The position and ve- The chaotic PSO algorithm is characterized with many advan-
locity of particle are computed in the next iteration as the tages such as the easy implementation, the superior speed of
search and the shortest time for running. The steps of chaotic
following:

xi(t + 1) = xi(t) + vi(t) (18) PSO algorithm can be represented in the flowchart given in
Fig. 4.

vi(t + 1) = a1r1(pbesti(t) - xi(t)) (19) VI. SIMULATION RESULTS
+a2r2(gbesti(t) - xi(t)) + wvi(t)
The computer results for designing the optimal STSMC
Where (w) represents the weight factor of inertia, w = 0.9 [26], scheme depending on the FPGA in Xilinx block sets are
presented to track the desired path of the robot manipula-
(a1, a2) are the coefficients of acceleration and the random tor system. The quality of the proposed controller is verified
values are (r1, r2) within the range [0,1]. The values of (w, r1 within the MATLAB/SIMLINK toolboxes environment and
and r2) are the main factors that influnced the convergence ISE (14.7) software.