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
Four different position control algorithms are compared with each other
- P controller
- PI controller
- PID controller
- Lyapunov controller
These are analyzed on three different paths
- Circular Path
- Eight-shaped Path
- Rectangular Path

Summary of important numerical values of controller test on circular trajectory

Results Circular Path¶
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

Summary of important numerical values of controller test on eight-shaped trajectory

Results Eight-shaped Path¶
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

Summary of important numerical values of controller test on square trajectory

Results Square Path¶
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

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.