Simulated Annealing for Distance Sensor Placement on an Obstacle-Avoiding Robot

Project info

• Field of studyRobotics and Mechatronics
• LevelMaster's thesis (S2)
• Method typeOptimisation
• Estimated build time± 5 working days
• Toolssimulannealbnd, optimoptions (Global Optimization Toolbox)
• PriceUS$28 - US$169

Research goal

Optimise the obstacle detection coverage with simulated annealing by tuning the front sensor mounting angle and the side sensor mounting angle within realistic constraints.

Variables

Example result

• 0.688Best x
• 2.031Best y
• 0.995Best objective
• 1502Iterations
• 1513Function evaluations
• 0.061Final temperature

Simulated annealing stops at Front sensor mounting angle=0.688 and Side sensor mounting angle=2.031 with best Obstacle detection coverage=0.995 after 1502 iterations; the temperature cools to 0.06 so worse moves are accepted less and less often.

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

About Simulated Annealing

simulannealbnd applies simulated annealing for global optimisation with variable bounds without needing derivatives. It suits functions with many local minima and non-smooth objectives.

Steps

1. 1Define the objective, bounds, and starting point
2. 2Set initial temperature, cooling function, and iterations with optimoptions
3. 3Run simulannealbnd
4. 4Repeat with several seeds
5. 5Check exitflag and the best objective value
6. 6Plot the trajectory or the spread of solutions

Assumptions to check

• Variable bounds are defined
• The cooling schedule is slow enough to escape local minima
• Results are stochastic, so several runs are needed

Reading and reporting the results

Report annealing settings, the best solution, objective value, and variation across runs. Compare with ga or particleswarm as other global methods.

Example MATLAB code

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

obstacle_detection_coverage = @(x) (x(1)^2 + x(2)^2)/10 + 3*(2 - cos(2*x(1)) - cos(2*x(2)));
lb = [-5 -5];  ub = [5 5];
front_sensor_mounting_angle = [4 4];                                      % starting point
opts = optimoptions('simulannealbnd', 'MaxIterations', 3000, ...
    'InitialTemperature', 50, 'Display', 'off');

nrun = 5;  best = zeros(nrun, 1);  sols = zeros(nrun, 2);
for r = 1:nrun
    rng(r);
    [sols(r,:), best(r), exitflag] = simulannealbnd(obstacle_detection_coverage, front_sensor_mounting_angle, lb, ub, opts);
end
fprintf('Best values: %s\n', mat2str(best', 4));
fprintf('Mean = %.4f, SD = %.4f, last exitflag = %d\n', mean(best), std(best), exitflag);
[~, ib] = min(best);
fprintf('Best solution: [%.4f %.4f]\n', sols(ib,1), sols(ib,2));

[g1, g2] = meshgrid(linspace(-5, 5, 200));
Z = (g1.^2 + g2.^2)/10 + 3*(2 - cos(2*g1) - cos(2*g2));
figure; contour(g1, g2, Z, 25); hold on;
plot(sols(:,1), sols(:,2), 'r*', 'MarkerSize', 10);
xlabel('x_1'); ylabel('x_2');

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