aspm.rar_ASPM_Wheeled Mobile Robot_mathematica_wheeled_wheeled r

%%% This code implements varying eigenspread%%%%% function varyingeigs() clc; clear all; A1 = [-0.1950; -0.9750;-1.5955;-1.9114]; Jmin = [0.0965;0.0731;0.0322;0.0038]; count = 5; for k = 1:4 a1 = A1(k); a2 = 0.95; sigma_u = 1; jmn = Jmin(k); mu = 0.3; n = 0; v_0 = (-1/sqrt(2))*[a1+a2;a1-a2]; [la1,la2] = eigs(a1,a2,sigma_u); la1; la2; eigspread = la1/la2; n = 0; for i = 1:200; v(:,i) = [(1-mu*la1)*v_0(1);(1-mu*la2)*v_0(2)]; v_0= v(:,i); vt = v(:,i); w(:,i) = [-a1-(vt(1)+vt(2))/sqrt(2);-a2-(vt(1)-vt(2))/sqrt(2)]; J(i) = jmn+la1*vt(1)^2+la2*vt(2)^2; n = n+1; end v1 = v(1,:); v2 = v(2,:); w1 = w(1,:); w2 = w(2,:); figure(k); plot(v1,v2,'r','LineWidth',1.5); % axis ([-6 6 6 6]) hold on; grid on; for j =1:6 delJ = J(j)-jmn/la1; v_1 = -sqrt(delJ/la1):0.001:sqrt(delJ/la1); v_21 = -sqrt((1/la2)*(delJ - la1*v_1.^2)); v_22 = sqrt((1/la2)*(delJ - la1*v_1.^2)); plot(v_1,abs(v_21)); hold on; plot(v_1,-abs(v_22)); end figure(count) plot(w1,w2,'k','LineWidth',1.5); % axis([-12 6 6 6]); hold on; grid on; for j= 1:6 delJ = J(j)-jmn/la1; w_1 = -2:0.001:2; a = (la1/2 + la2/2); b = (a1*la1+a2*la1-a1*la2+a2*la2+la1*w_1-la2*w_1); c = (a1^2*la1)/2+a1*a2*la1+(a2^2*la1)/2+(a1^2*la2)/2-a1*a2*la2+(a2^2*la2)/2+a1*la1*w_1+a2*la1*w_1+a1*la2*w_1-a2*la2*w_1+(la1*w_1.^2)/2+(la2*w_1.^2)/2 -delJ; w_21 = (-b+sqrt(b.^2-4*a*c))/2*a; w_22 = (-b-sqrt(b.^2-4*a*c))/2*a; plot(w_1,real(w_21)); hold on; plot(w_1,real(w_22)); end count = count+1; figure(15) plot(J);hold on; grid on; title('Plot of J(n)'); end