Position Control of Mobile Robots for Laser Material Processing
Features
- The aim of this paper is to investigate and to compare different position control algorithms that have been designed for and implemented in a mobile robot
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- Four different position control algorithms are compared with each other
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- P controller
- PI controller
- PID controller
- Lyapunov controller
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- These are analyzed on three different paths
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- Circular Path
- Eight-shaped Path
- Rectangular Path
Results
- The results are shown for each of the thee different paths
Circular Path

Results Circular Path
Summary of important numerical values of controller test on circular trajectory
metric | P controller | PI controller | PID controller | Lyapunov controller |
---|---|---|---|---|
mean absolute error in mm | 1.45 | 1.76 | 0.997 | 1.196 |
median absolute error in mm | 1.443 | 1.558 | 0.908 | 1.032 |
share of points above 2 mm target in % | 27.866 | 34.076 | 9.554 | 13.535 |
minimal error in mm | 0.029 | 0.045 | 0.014 | 0.012 |
maximal error in mm | 4.19 | 8.284 | 4.734 | 6.43 |
Eight-shaped Path

Results Eight-shaped Path
Summary of important numerical values of controller test on eight-shaped trajectory
metric | P controller | PI controller | PID controller | Lyapunov controller |
---|---|---|---|---|
mean absolute error in mm | 2.101 | 2.791 | 3.445 | 3.175 |
median absolute error in mm | 1.966 | 2.116 | 2.648 | 2.306 |
share of points above 2 mm target in % | 49.535 | 53.753 | 64.618 | 58.756 |
minimal error in mm | 0.029 | 0.014 | 0.035 | 0 |
maximal error in mm | 7.237 | 42.218 | 39.812 | 13.155 |
Rectangular Path

Results Square Path
Summary of important numerical values of controller test on square trajectory
metric | P controller | PI controller | PID controller | Lyapunov controller |
---|---|---|---|---|
mean absolute error in mm | 1.588 | 1.314 | 1.781 | 1.095 |
median absolute error in mm | 1.311 | 1.172 | 1.604 | 0.971 |
share of points above 2 mm target in % | 23.81 | 13.874 | 39.348 | 9.774 |
minimal error in mm | 0.02 | 0.018 | 0 | 0.04 |
maximal error in mm | 14.78 | 11.321 | 11.077 | 8.237 |
Acknowledgements
- Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germanys Excellence Strategy – EXC-2023 Internet of Production – 390621612
- The authors acknowledge the financial support by the Federal Ministry of Education and Research of Germany in the framework of Research Campus Digital Photonic Production (project number: 13N15423)
- The authors would like to thank Prof. Jeremy Witzens and Dr. Florian Merget from the Institute and Chair of Integrated Photonics at RWTH Aachen University for their support.

