forward kinematics in matlab

Forward kinematics is the process of calculating the position and orientation of the end-effector of a robotic arm given the joint angles. In Matlab, the forward kinematics can be calculated using the following steps:

1. Define the Denavit-Hartenberg (DH) parameters of the robot arm. The DH parameters are a set of four parameters defining each link of the robotic arm.

2. Compute the transformation matrix for each link using the DH parameters.

3. Multiply the transformation matrices to compute the homogeneous transformation matrix from the base to end-effector.

4. Extract the position and orientation of the end-effector from the homogeneous transformation matrix.

Here’s an example code to calculate the forward kinematics of a 3-link robotic arm:

main.m
% Define the DH parameters
d1 = 0.1; a1 = 0.2; alpha1 = pi/2;
d2 = 0.1; a2 = 0.2; alpha2 = 0;
d3 = 0; a3 = 0.1; alpha3 = pi/2;

% Define the joint angles
q1 = pi/4; q2 = pi/3; q3 = pi/2;

% Compute the transformation matrices
T01 = compute_dh_matrix(d1, a1, alpha1, q1);
T12 = compute_dh_matrix(d2, a2, alpha2, q2);
T23 = compute_dh_matrix(d3, a3, alpha3, q3);

% Compute the homogeneous transformation matrix
T03 = T01 * T12 * T23;

% Extract the position and orientation of the end-effector
position = T03(1:3,4);
orientation = tform2quat(T03);
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The compute_dh_matrix() function computes the transformation matrix for each link using the DH parameters. The tform2quat() function extracts the orientation of the end-effector in quaternion form.