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Solving non-linear equations symbolicaly

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Caio Vinicius do Carmo
Caio Vinicius do Carmo on 15 Jun 2021
Hi,
I'm trying find the solution for the equations system of 12 equation and 6 variables for a robotic manipulator 6-DOF.
However, the matlab stays in busy and don't find the solution
%MATLAB 2015
%symbolic variables
symstheta1 theta2 theta3 theta4 theta5 theta6 a1 a2 d3 d4 d5
symsnx ny nz ox oy oz ax ay az px py pz py
%%Forward Kinematic ---------
% Transformation matrices
T1 = [cos(theta1) -sin(theta1) 0 0;sin(theta1) cos(theta1) 0 0 ; 0 0 1 0; 0 0 0 1]*[1 0 0 a1;0 1 0 0;0 0 1 0; 0 0 0 1]*[1 0 0 0; 0 0 -sin(deg2rad(90)) 0; 0 sin(deg2rad(90)) 0 0 ; 0 0 0 1]
T2 = [cos(theta2) -sin(theta2) 0 0;sin(theta2) cos(theta2) 0 0 ; 0 0 1 0; 0 0 0 1]*[1 0 0 a2;0 1 0 0;0 0 1 0; 0 0 0 1]
T3 = [cos(theta3) -sin(theta3) 0 0;sin(theta3) cos(theta3) 0 0 ; 0 0 1 0; 0 0 0 1]*[1 0 0 d3;0 1 0 0;0 0 1 0; 0 0 0 1]*[1 0 0 0; 0 0 -sin(deg2rad(-90)) 0; 0 sin(deg2rad(-90)) 0 0 ; 0 0 0 1]
T4 = [cos(theta4) -sin(theta4) 0 0;sin(theta4) cos(theta4) 0 0 ; 0 0 1 0; 0 0 0 1]*[1 0 0 0;0 1 0 0;0 0 1 -d4; 0 0 0 1]*[1 0 0 0; 0 0 -sin(deg2rad(-90)) 0; 0 sin(deg2rad(-90)) 0 0 ; 0 0 0 1]
T5 = [cos(theta5) -sin(theta5) 0 0;sin(theta5) cos(theta5) 0 0 ; 0 0 1 0; 0 0 0 1]*[1 0 0 d5;0 1 0 0;0 0 1 0; 0 0 0 1]*[1 0 0 0; 0 0 -sin(deg2rad(-90)) 0; 0 sin(deg2rad(-90)) 0 0 ; 0 0 0 1]
T6 = [cos(theta6) -sin(theta6) 0 0;sin(theta6) cos(theta6) 0 0 ; 0 0 1 0; 0 0 0 1]
T06 = T1*T2*T3*T4*T5*T6;
RHS = T06;
%initial reference matrix
T = [nx ox ax px;ny oy ay py;nz oz az pz;0 0 0 1]
%% Inverse Kinematics
%T06 == T
eq1 = T06(1,1)==nx;
eq2 = T06(1,2)==ox;
eq3 = T06(1,3)==ax;
eq4 = T06(1,4)==px;
eq5 = T06(2,1)==ny;
eq6 = T06(2,2)==oy;
eq7 = T06(2,3)==ay;
eq8 = T06(2,4)==py;
eq9 = T06(3,1)==nz;
eq10 = T06(3,2)==oz;
eq11 = T06(3,3)==az;
eq12 = T06(3,4)==pz;
eqns = [eq1 eq2 eq3 eq4 eq5 eq6 eq7 eq8 eq9 eq10 eq11 eq12];
[solt1,solt2,solt3,solt4,solt5,solt6] = solve(eqns,[theta1 theta2 theta3 theta4 theta5 theta6])

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