How do you represent a multi-link robot manipulator in MATLAB?

In MATLAB, you represent a multi-link robot manipulator using the rigidBodyTree object from the Robotics System Toolbox. You construct the manipulator kinematics by defining individual rigid bodies (rigidBody), attaching joints (rigidBodyJoint), specifying spatial transformations between links, and assembling them into a tree structure using addBody(). You can also define kinematics via standard Denavit-Hartenberg (DH) parameter matrices or import existing URDF models using importrobot().

Method 1: Building a Multi-Link Arm with rigidBodyTree (Recommended)

The rigidBodyTree class creates a tree-structured kinematic and dynamic model supporting forward kinematics, inverse kinematics, and 3D rendering.

% Step 1: Initialize an empty Rigid Body Tree
robot = rigidBodyTree('DataFormat', 'row');

% Step 2: Create Link 1 and its Revolute Joint
body1 = rigidBody('link1');
joint1 = rigidBodyJoint('joint1', 'revolute');
setFixedTransform(joint1, trvec2tform([0, 0, 0])); % Attached to base origin
body1.Joint = joint1;
addBody(robot, body1, 'base');

% Step 3: Create Link 2 (Length: 1.0 m along X-axis)
body2 = rigidBody('link2');
joint2 = rigidBodyJoint('joint2', 'revolute');
setFixedTransform(joint2, trvec2tform([1.0, 0, 0]));
body2.Joint = joint2;
addBody(robot, body2, 'link1');

% Step 4: Create Link 3 (Length: 0.8 m along X-axis)
body3 = rigidBody('link3');
joint3 = rigidBodyJoint('joint3', 'revolute');
setFixedTransform(joint3, trvec2tform([0.8, 0, 0]));
body3.Joint = joint3;
addBody(robot, body3, 'link2');

% Step 5: Add End-Effector
endEffector = rigidBody('end_effector');
setFixedTransform(endEffector.Joint, trvec2tform([0.6, 0, 0]));
addBody(robot, endEffector, 'link3');

% Step 6: Compute Forward Kinematics for Joint Angles [q1, q2, q3]
q = [deg2rad(30), deg2rad(45), deg2rad(-20)];
tform = getTransform(robot, q, 'end_effector', 'base');
disp('End-Effector Transformation Matrix:');
disp(tform);

% Step 7: Visualize the Multi-Link Manipulator in 3D
figure('Name', '3-DOF Multi-Link Robot Manipulator');
show(robot, q, 'Visuals', 'on', 'Collisions', 'off');
title('3-DOF Multi-Link Robot Configuration');
grid on;
axis equal;

Method 2: Representing Multi-Link Manipulators via DH Parameters

If your robot model uses standard Denavit-Hartenberg parameters [a, alpha, d, theta], configure each joint transformation using the dh flag:

% Define DH parameters: [a, alpha, d, theta_offset]
dh_params = [
    0,     pi/2,  0.5,  0;  % Link 1
    1.0,   0,     0.0,  0;  % Link 2
    0.8,   0,     0.0,  0   % Link 3
];

robotDH = rigidBodyTree('DataFormat', 'row');
numLinks = size(dh_params, 1);
parentName = 'base';

for i = 1:numLinks
    bodyName = sprintf('link%d', i);
    jointName = sprintf('joint%d', i);
    
    body = rigidBody(bodyName);
    joint = rigidBodyJoint(jointName, 'revolute');
    
    % Apply DH parameters directly
    setFixedTransform(joint, dh_params(i,:), 'dh');
    body.Joint = joint;
    
    addBody(robotDH, body, parentName);
    parentName = bodyName;
end

Key MATLAB Functions for Multi-Link Robots

Practical Engineering Applications

• Forward & Inverse Kinematics: Calculate exact end-effector coordinates and solve joint displacements for pick-and-place trajectories.
• Trajectory Generation: Create smooth polynomial profiles using trapveltraj and quinticpolytraj.
• Simscape Multibody Co-Simulation: Export the robot model to Simscape to simulate actuator torques, joint friction, and closed-loop PID control dynamics.