Neural Network fitnet Estimation of Planar Robot Arm Inverse Kinematics from End-Effector Position

Project info

• Field of studyRobotics and Mechatronics
• LevelDoctoral dissertation (S3)
• Method typeMachine Learning
• Estimated build time± 7 working days
• Toolsfitnet, train, perform (Deep Learning Toolbox)
• PriceUS$38 - US$228

Research goal

Build a fitnet neural network model to predict the first joint angle from the end-effector x position and end-effector y position features on synthetic data.

Variables

Example result

• 0.987Test R
• 0.171Test RMSE
• 0.02Best val. MSE
• 28Epochs
• 12Hidden neurons
• 300Samples

A neural network with 12 hidden neurons predicts First joint angle from End-effector x position and End-effector y position with a test correlation of R=0.987 and RMSE 0.171 after 28 epochs; the best validation MSE is 0.0202.

Computed from illustrative synthetic data, not from a real study.

About Neural Network (fitnet)

fitnet builds a feedforward neural network for regression or nonlinear function approximation. It suits modelling complex input-output relations when the equation form is unknown and enough data are available.

Steps

1. 1Prepare data with features as rows and samples as columns
2. 2Create the network with fitnet and set the hidden neuron count
3. 3Set train, validation, and test division and the training algorithm
4. 4Train with train and monitor performance
5. 5Evaluate RMSE and R on the test data
6. 6Plot predictions against actuals and training history

Assumptions to check

• There are enough data relative to the number of weights
• Features are normalised (fitnet does this automatically)
• Training is stochastic so results depend on the seed and initialisation

Reading and reporting the results

Report the architecture, algorithm, data division, and test RMSE and R. Compare with linear regression to show the need for a nonlinear model.

Example MATLAB code

A short starting script with this project's variable names. The delivered version is adapted to your data and fully commented.

rng(10);
n = 500;
end_effector_x_position = [10*rand(1, n); 5*rand(1, n)];            % features x samples
first_joint_angle = sin(end_effector_x_position(1, :)) .* end_effector_x_position(2, :) + 0.2*randn(1, n);

net = fitnet(10, 'trainlm');
net.divideParam.trainRatio = 0.7;
net.divideParam.valRatio = 0.15;
net.divideParam.testRatio = 0.15;
net.trainParam.showWindow = false;
[net, tr] = train(net, end_effector_x_position, first_joint_angle);

pred = net(end_effector_x_position);
te = tr.testInd;
rmse = sqrt(mean((pred(te) - first_joint_angle(te)).^2));
R = corrcoef(pred(te), first_joint_angle(te));
fprintf('Test RMSE = %.3f, R = %.3f, epochs = %d\n', rmse, R(1, 2), tr.num_epochs);
b = [ones(numel(te), 1) end_effector_x_position(:, te)'] \ first_joint_angle(te)';
lin = [ones(numel(te), 1) end_effector_x_position(:, te)'] * b;
fprintf('Linear baseline RMSE = %.3f\n', sqrt(mean((lin - first_joint_angle(te)').^2)));

figure;
subplot(1,2,1); plot(first_joint_angle(te), pred(te), '.'); hold on; refline(1, 0);
xlabel('Actual'); ylabel('Predicted');
subplot(1,2,2); semilogy(tr.perf); hold on; semilogy(tr.vperf); semilogy(tr.tperf);
legend('Train', 'Validation', 'Test'); xlabel('Epoch'); ylabel('MSE');

Packages and prices

Choose how much help you need. Each higher package includes everything in the lower ones. Prices exclude 11% VAT.

• Payment: 50% down payment before work starts, balance after the deliverables are handed over
• Tax: Prices exclude 11% VAT
• Data and academic integrity: Results are computed from your own research data; you write and stand behind your manuscript, we help with the analysis and your understanding of it
• Revisions: Up to 2 revisions are included in the price (Package 3: 3 rounds)

Frequently asked questions