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3D Matrix Multiplication using a Series

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Mark Dawson
Mark Dawson 2020-10-18
评论： Ameer Hamza 2020-10-18
So I've got an issue in regards to multiplying out 3 4x4 matricies that i need to obtain my final transformation matrix. They're contained within a 4 x 4 x 3 matirx, as three distinct 4 x 4 "slices". The 3D matrix is probably the neatest way i can store the data, the numeric data is obained from a few arbitrary functions, for all intents and purposes, assume its just random numbers.
So i need to multiply them out to obtain "T" my overal transforation matrix, but for the sake of making my program more versatile I cant merely multiply out the slices. I need to do it as part of a series, say use N, for a 4 x 4 x N matrix. I.e. I kinda want my program to be universal.
Edit: I shouls add, it's required for the 4 x 4 matricies to be multiplied in order, i.e. Ast(:,:,n)*Ast(:,:,n+1)*...*Ast(:,:,n+m)
% 4 x 4 Homogeneous Translation Matricies
TransX = @(a)[1 0 0 a; 0 1 0 0; 0 0 1 0; 0 0 0 1];
TransY = @(b)[1 0 0 0; 0 1 0 b; 0 0 1 0; 0 0 0 1];
TransZ = @(c)[1 0 0 0; 0 1 0 0; 0 0 1 c; 0 0 0 1];
% 4 x 4 Homogeneous Rotational Matricies
RotX =@(theta)[1 0 0 0; 0 cos(theta) -sin(theta) 0; 0 sin(theta) cos(theta) 0; 0 0 0 1];
RotY =@(theta)[cos(theta) 0 sin(theta) 0; 0 1 0 0; -sin(theta) 0 cos(theta) 0; 0 0 0 1];
RotZ =@(theta)[cos(theta) -sin(theta) 0 0; sin(theta) cos(theta) 0 0; 0 0 1 0; 0 0 0 1];
%%%%%%%%%%%%%%%%%%%Physical System Parameters%%%%%%%%%%%%%%%%%%%%
%Link Numbers - Kinda Important for Making application more universal
n = 3;
%Denevit Hartenberg 'Table'
%User Can set these to whatever, but must be n entries
a= [2,3,4];
alpha = [0,0,0];
d = [0,0,0];
theta_l = [pi/12,pi/12,pi/12];
theta = cumsum(theta_l);
%Anonymous Numeric Denavit Hartenberg Function
A=@(a_i,alpha_i,d_i,theta_i)RotZ(theta_i)*TransZ(d_i)*TransX (a_i)*RotX(alpha_i);
A_i= @(i)A(a(i),alpha(i),d(i),theta(i));
%Create 4 x 4 x n 3D Transformation Matricies
for j = [1:1:n]
Ast(:,:,j)= A_i(j);
end
%Overall Transformation Matrix
T = Ast(:,:,1)*Ast(:,:,2)*Ast(:,:,3);

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Ameer Hamza
Ameer Hamza 2020-10-18
A for-loop might be the simpliest solution
A = rand(4,4,10);
n = 2;
m = 4;
A_result = eye(size(A,1));
for i = n:n+m
A_result = A_result*A(:,:,i);
end

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