Robotics System in MATLAB
MATLAB provides a comprehensive set of tools for robotics system design and simulation, leveraging its Robotics System Toolbox. This section covers essential concepts, common operations, and examples in robotics systems using MATLAB.
Introduction to Robotics in MATLAB
The Robotics System Toolbox in MATLAB allows users to design algorithms for mobile robots, manipulate robotic arms, and simulate their movements in 3D environments. Common tasks include trajectory planning, inverse kinematics, and control systems.
Basic Concepts
Before delving into advanced topics, here are some basic operations:
% Loading the toolbox
addpath('C:\MATLAB\toolbox\robotics'); % Replace with your toolbox path
robot = robotics.RigidBodyTree; % Create a robotic arm structure
disp(robot);
Output:
RigidBodyTree with no bodies.
Example 1: Forward Kinematics
Forward kinematics involves computing the position and orientation of the robot’s end-effector from its joint angles. Here’s how to compute it:
% Define the robotic structure
robot = robotics.RigidBodyTree;
body = robotics.RigidBody('link1');
joint = robotics.Joint('joint1', 'revolute');
setFixedTransform(joint, trvec2tform([0, 0, 1])); % Transformation
body.Joint = joint;
addBody(robot, body, 'base');
% Compute Forward Kinematics
config = homeConfiguration(robot);
T = getTransform(robot, config, 'link1');
disp(T);
Output:
1 0 0 0
0 1 0 0
0 0 1 1
0 0 0 1
Example 2: Inverse Kinematics
Inverse kinematics solves the joint angles required to position the end-effector at a specified location. Here’s an example:
% Create an inverse kinematics solver
ik = robotics.InverseKinematics('RigidBodyTree', robot);
targetPose = trvec2tform([0.5, 0.5, 0.5]); % Desired position
[configSol, solInfo] = ik('link1', targetPose, [1 1 1 1 1 1], config);
disp(configSol);
disp(solInfo);
Example 3: Trajectory Planning
Plan a smooth trajectory for the robot to move between two points:
% Define waypoints
waypoints = [0 0 0; 1 1 1; 2 0 0];
trajTimes = [0; 2; 4]; % Time at each waypoint
[q, dq, ddq] = cubicpolytraj(waypoints', trajTimes, 0:0.1:4);
plot3(q(1,:), q(2,:), q(3,:)); grid on;
title('Trajectory Path');
xlabel('X'); ylabel('Y'); zlabel('Z');
Solving Advance Problems in Robotics using MATLAB
Example 4: Path Following for a Mobile Robot
In this example, a mobile robot follows a pre-defined path using waypoints.
% Define waypoints for the robot path
waypoints = [0 0; 1 1; 2 0; 3 1];
% Visualize the waypoints
plot(waypoints(:,1), waypoints(:,2), 'ro-');
hold on;
title('Path Following for Mobile Robot');
xlabel('X'); ylabel('Y'); grid on;
% Simulate robot movement along the path
for i = 1:size(waypoints, 1)-1
current = waypoints(i,:);
target = waypoints(i+1,:);
quiver(current(1), current(2), target(1)-current(1), target(2)-current(2), 0, 'b');
pause(0.5); % Pause to animate
end
hold off;
Output:
A 2D plot showing the robot moving along the specified path.
Example 5: Workspace Analysis of a Robotic Arm
Analyze the reachable workspace of a 2-link planar robotic arm.
% Define link lengths
L1 = 1;
L2 = 1;
% Define joint angle ranges
theta1 = linspace(0, 2*pi, 50);
theta2 = linspace(0, 2*pi, 50);
% Compute reachable workspace
[X, Y] = meshgrid(theta1, theta2);
Px = L1*cos(X) + L2*cos(X+Y);
Py = L1*sin(X) + L2*sin(X+Y);
% Plot the workspace
plot(Px(:), Py(:), 'b.');
title('Workspace of 2-Link Planar Robotic Arm');
xlabel('X'); ylabel('Y'); axis equal; grid on;
Output:
A 2D scatter plot showing the reachable workspace of the robotic arm.
Example 6: PID Control of a Robotic Arm Joint
Implement a PID controller to control the position of a robotic arm’s joint.
% Define the desired angle (setpoint)
desiredAngle = pi/4;
% Initialize PID parameters
Kp = 10; Ki = 2; Kd = 1;
% Initialize variables
currentAngle = 0; error = 0; integral = 0;
dt = 0.01; % Time step
angles = []; times = 0:dt:5;
% Simulate PID control
for t = times
prevError = error;
error = desiredAngle - currentAngle;
integral = integral + error*dt;
derivative = (error - prevError)/dt;
controlSignal = Kp*error + Ki*integral + Kd*derivative;
% Update current angle (simplified model)
currentAngle = currentAngle + controlSignal*dt;
angles = [angles currentAngle];
end
% Plot the results
plot(times, angles, 'b-', times, desiredAngle*ones(size(times)), 'r--');
legend('Joint Angle', 'Desired Angle');
title('PID Control of Robotic Arm Joint');
xlabel('Time (s)'); ylabel('Angle (rad)'); grid on;
Output:
A plot showing the joint angle converging to the desired angle over time.
Example 7: Simulating a Robotic Arm in 3D
Visualize a 2-link robotic arm moving in a 3D space.
% Define link lengths
L1 = 1; L2 = 0.5;
% Define joint angles
theta1 = linspace(0, pi, 20);
theta2 = linspace(0, pi/2, 20);
% Simulate the arm movement
figure; hold on; grid on;
for i = 1:length(theta1)
% Compute joint positions
x1 = L1*cos(theta1(i)); y1 = L1*sin(theta1(i)); z1 = 0;
x2 = x1 + L2*cos(theta1(i) + theta2(i));
y2 = y1 + L2*sin(theta1(i) + theta2(i)); z2 = 0;
% Plot the arm
plot3([0 x1 x2], [0 y1 y2], [0 z1 z2], 'b-o');
pause(0.2);
end
title('3D Simulation of 2-Link Robotic Arm');
xlabel('X'); ylabel('Y'); zlabel('Z');
axis equal;
Output:
A dynamic 3D plot showing the robotic arm moving through different configurations.
Useful MATLAB Functions for Robotics
Practice Questions
Test Yourself
1. Create a robotic arm with 2 joints and compute the forward kinematics.
2. Plan a trajectory for a mobile robot moving in a square path.
3. Solve the inverse kinematics for an end-effector at (1, 2, 3).
4. Modify the path-following example to include a circular path.
5. Extend the workspace analysis to include a 3-link robotic arm.
6. Implement PID control for a 2-joint robotic arm, considering each joint independently.