D =
Hi Juan,
The error you're encountering is due to an incorrect use of the "simplify" function. The "simplify" function simplifies expressions, not matrices, with respect to a variable. In your code, instead of trying to simplify matrices 'U11', 'U12', 'U21', and 'U22' with respect to 'q1' and 'q2', you should simply call "simplify" on the matrix without specifying a variable.
The correct MATLAB code using simplify function is as follows:
clc
close all
clear all
%Declaración de Variables Simbólicas longitudes, masas, pos, vel y acel.
syms L1 L2 m1 m2 g
syms q1 q2 qd1 qd2 qdd1 qdd2
%Definicion de vectores de posición para las articulaciones
r11 = [0;0;0;1];
r22 = [0;0;0;1];
g0 = [0,0,-g,0];
%Hallar matrices de transformación
A01 = [cos(q1),-sin(q1), 0, L1*cos(q1);
sin(q1), cos(q1), 0, L1*sin(q1);
0, 0, 1, 0;
0, 0, 0, 1];
A12 = [cos(q2),-sin(q2), 0, L2*cos(q2);
sin(q2), cos(q2), 0, L2*sin(q2);
0, 0, 1, 0;
0, 0, 0, 1];
A02 = A01*A12;
%Obtener matrices parciales Uij
U11 = simplify(A01);
U12 = simplify(A01);
U21 = simplify(A02);
U22 = simplify(A02);
%Obtener matrices Uijk
U111 = simplify(diff(U11,q1));
U112 = simplify(diff(U11,q2));
U121 = simplify(diff(U12,q1));
U122 = simplify(diff(U12,q2));
U211 = simplify(diff(U21,q1));
U212 = simplify(diff(U21,q2));
U221 = simplify(diff(U22,q1));
U222 = simplify(diff(U22,q2));
%Obtener Matrices Ji (Tomadas desde el origen de las coordenadas).
J1 = [0,0,0,0;
0,0,0,0;
0,0,0,0;
0,0,0,m1];
J2 = [0,0,0,0;
0,0,0,0;
0,0,0,0;
0,0,0,m2];
%Obtener la matriz de inercias i=1 j=1 k=1:2
d11 = trace(U11*J1*transpose(U11)) + trace(U21*J2*transpose(U21));
%i=1 j=2 k=2
d12 = trace(U22*J2*transpose(U21));
%i=2 j=1 k=2
d21 = trace(U22*J1*transpose(U12));
%i=2 j=2 k=2
d22 = trace(U22*J2*transpose(U22));
D=[d11,d12;
d21,d22];
D=simplify(D)
%Obterner los términos hikm
%i=1 k=1 m=1 j=1:2
h111 = trace(U111*J1*transpose(U11)) + trace(U211*J2*transpose(U21));
%i=1 k=1 m=2 j=2
h112 = trace(U212*J2*transpose(U21));
%i=1 k=2 m=1 j=2
h121 = trace(U221*J2*transpose(U12));
%i=1 k=2 m=2 j=2
h122 = trace(U212*J2*transpose(U12));
%i=2 k=1 m=1 j=2
h211 = trace(U211*J2*transpose(U21));
%i=2 k=1 m=2 j=2
h212 = trace(U212*J2*transpose(U21));
%i=2 k=2 m=1 j=2
h221 = trace(U221*J2*transpose(U22));
%i=2 k=2 m=2 j=2
h222 = trace(U222*J2*transpose(U22));
%Matriz Coriolis y Centrípeta
%i=1 k=1:2 m=1:2
h1 = (h111*qd1*qd1 + h112*qd1*qd2) + (h121*qd2*qd1 + h122*qd2*qd2);
%i=1 k=1:2 m=1:2
h2 = (h211*qd1*qd1 + h212*qd1*qd2) + (h221*qd2*qd1 + h222*qd2*qd2);
H = simplify([h1;h2])
%Hallar la matriz de fuerzas de gravedad
%i=1 j=1:2
c1 = (-m1*g0*U11*r11) + (-m2*g0*U21*r22);
%i=2 j=1:2
c2 = (-m1*g0*U12*r11) + (-m2*g0*U22*r22);
C = simplify([c1;c2])
%Hallar el torque o ecuación dinámica del sistema
qdd = [qdd1;qdd2];
tau = D*qdd+H+C
You may refer to the following documentation links to have a better understanding on working with simplify function and MATLAB Euler-Lagrange library:
