Robot Navigation in Complex Workspaces Employing Harmonic Maps and Adaptive Artificial Potential Fields
Abstract
:1. Introduction
1.1. Contributions
1.2. Preliminaries
2. Problem Formulation
3. Harmonic Maps for Planar Navigation
- maps the outer boundary to the unit circle ;
- maps the boundary of each obstacle to a distinct point ;
- is a diffeomorphism for all .
4. Control Design
4.1. Artificial Harmonic Potential Fields
4.2. Adaptive Laws
4.3. Stability Analysis
5. Extensions
5.1. Unicycle Robot Kinematics
5.2. Atlas of Harmonic Maps
Algorithm 1 Altas-based motion planning scheme for a holonomic robot |
Require: , , |
6. Simulations and Experimental Results
6.1. Simulations—Full Workspace Transformation
6.2. Simulations—Atlas of Harmonic Maps
6.3. Comparative Study—Workspace Transformation
6.4. Comparative Study—Control Law
6.4.1. APF-Based Schemes
6.4.2. Sampling-Based Scheme
6.5. Experiments
7. Conclusions and Future Work
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A
Appendix A.1. Proof of Proposition 1
Appendix A.2. Proof of Proposition 2
Appendix A.3. Proof of Proposition 3
Appendix A.4. Proof of Proposition 4
Appendix A.5. Proof of Proposition 5
Appendix A.6. Proof of Theorem 1
Appendix A.7. Proof of Theorem 2
Appendix A.8. Proof of Theorem 3
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Geometry Representation | Global | Analytic | |
---|---|---|---|
HM | Points on the boundary | Yes | Yes |
SST | Trees of Stars | Yes | Yes |
NT | -manifolds | No | No |
MANT | Trees of -manifolds | No | No |
Convergence | Collision Avoidance | Computational Cost | |
---|---|---|---|
AHPF | By design | By design | Cheap |
HPF | By design | By design | Expensive |
RKNF | Requires tuning | By design | Cheap |
HNF | By design | Requires tuning | Cheap |
a | b | c | d | |
---|---|---|---|---|
SST | 3.63 | 4.18 | 2.12 | 4.09 |
MANT | 4.26 | 4.69 | 2.34 | 4.45 |
NT | 3.35 | 4.30 | 2.18 | 4.22 |
HM | 3.19 | 4.21 | 2.05 | 4.32 |
a | b | c | d | |
---|---|---|---|---|
SST | 4.22 | 5.43 | 86.93 | 2.16 |
MANT | 1.23 | 1.47 | 13.56 | 2.06 |
NT | 66.97 | 25.23 | 14.89 | 6.92 |
HM | 2.47 | 2.49 | 14.76 | 2.77 |
a | b | c | d | |
---|---|---|---|---|
SST | 0.0303 | 0.0283 | 0.0159 | 0.0063 |
MANT | 0.0644 | 0.1253 | 0.1870 | 0.0648 |
NT | 0.1386 | 0.0506 | 0.0915 | 0.0058 |
HM | 0.0335 | 0.0377 | 0.0103 | 0.0181 |
Red | Green | Blue | Yellow | |
---|---|---|---|---|
NF | 19.781 | 20.427 | 22.090 | 18.397 |
HNF | 18.224 | 22.538 | 26.959 | 20.062 |
AHNF | 17.874 | 19.419 | 23.364 | 18.595 |
Red | Green | Blue | Yellow | |
---|---|---|---|---|
NF | 0.1158 | 0.0102 | 0.1210 | 0.1103 |
HNF | 0.3347 | 0.2135 | 0.2591 | 0.2166 |
AHPF | 0.1310 | 0.0352 | 0.2043 | 0.1854 |
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Vlantis, P.; Bechlioulis, C.P.; Kyriakopoulos, K.J. Robot Navigation in Complex Workspaces Employing Harmonic Maps and Adaptive Artificial Potential Fields. Sensors 2023, 23, 4464. https://doi.org/10.3390/s23094464
Vlantis P, Bechlioulis CP, Kyriakopoulos KJ. Robot Navigation in Complex Workspaces Employing Harmonic Maps and Adaptive Artificial Potential Fields. Sensors. 2023; 23(9):4464. https://doi.org/10.3390/s23094464
Chicago/Turabian StyleVlantis, Panagiotis, Charalampos P. Bechlioulis, and Kostas J. Kyriakopoulos. 2023. "Robot Navigation in Complex Workspaces Employing Harmonic Maps and Adaptive Artificial Potential Fields" Sensors 23, no. 9: 4464. https://doi.org/10.3390/s23094464