References
- Abadi, A.S.S., Hosseinabadi, P.A., Mekhilef, S. and Ordys, A. (2020). A new strongly predefined time sliding mode controller for a class of cascade high-order nonlinear systems, Archives of Control Sciences 30(3): 599–620, DOI: 10.24425/acs.2020.134679.
- Bartoszewicz, A. and Adamiak, K. (2019). A reference trajectory based discrete time sliding mode control strategy, International Journal of Applied Mathematics and Computer Science 29(3): 517–525, DOI: 10.2478/amcs-2019-0038.
- Bishop, R.L. (1975). There is more than one way to frame a curve, The American Mathematical Monthly 82(3): 246–251, DOI: 10.2307/2319846.
- Campion, G., Bastin, G. and D’Andréa-Novel, B. (1996). Structural properties and classification of kinematic and dynamic models of wheeled mobile robots, IEEE Transactions on Robotics and Automation 12: 47–61, DOI: 10.1109/70.481750.
- Canudas de Wit, C., Bastin, G. and Siciliano, B. (1996). Theory of Robot Control, 1st edn, Springer, London.
- Carroll, D., Köse, E. and Sterling, I. (2013). Improving Frenet’s frame using Bishop’s frame, Journal of Mathematics Research 5: 97–106, DOI:10.5539/jmr.v5n4p97.
- Cichella, V., Kaminer, I., Xargay, E., Dobrokhodov, V., Hovakimyan, N., Aguiar, A.P. and Pascoal, A.M. (2012). A Lyapunov-based approach for time-coordinated 3D path-following of multiple quadrotors, Proceedings of the 51st Annual IEEE Conference on Decision and Control, Maui, Hawaii, USA, pp. 1776–1781.
- Costa, M.M. and Silva, M.F. (2019). A survey on path planning algorithms for mobile robots, 2019 IEEE International Conference on Autonomous Robot Systems and Competitions (ICARSC), Porto, Portugal, pp. 1–7, DOI: 10.1109/ICARSC.2019.8733623.
- Dulęba, I. (2000). Modeling and control of mobile manipulators, IFAC Proceedings Volumes 33(27): 447–452, DOI: 10.1016/S1474-6670(17)37970-3.
- Dyba, F. (2023). Experimental validation of the non-orthogonal Serret-Frenet parametrization applied to the path following task, Proceedings of the 20th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO, Rome, Italy, pp. 608–615, DOI: 10.5220/0012164200003543.
- Dyba, F. (2024). Parallel position and orientation control for a redundant manipulator performing the path following task, 13th International Workshop on Robot Motion and Control (RoMoCo), Poznan, Poland, pp. 199–204, DOI: 10.1109/RoMoCo60539.2024.10604337.
- Dyba, F. and Mazur, A. (2024). Comparison of curvilinear parametrization methods and avoidance of orthogonal singularities in the path following task, Journal of Automation, Mobile Robotics and Intelligent Systems 17(3): 46–64, DOI: 10.14313/JAMRIS/3-2023/22.
- Encarnação, P. and Pascoal, A. (2000). 3D path following for autonomous underwater vehicle, Proceedings of the 39th IEEE Conference on Decision and Control, Vol. 3, Sydney, NSW, Australia, pp. 2977–2982, DOI: 10.1109/CDC.2000.914272.
- Frenet, F. (1852). Sur les courbes à double courbure, Journal de Mathématiques Pures et Appliquées, 17: 437–447, http://eudml.org/doc/233946.
- Galicki, M. (2006). Adaptive control of kinematically redundant manipulator along a prescribed geometric path, in K. Kozłowski (Ed.), Robot Motion and Control, Lecture Notes in Control and Information Sciences, Vol. 335, Springer, London, pp. 129–139.
- Gonçalves, V.M., Adorno, B.V., Crosnier, A. and Fraisse, P. (2020). Stable-by-design kinematic control based on optimization, IEEE Transactions on Robotics 36(3): 644–656, DOI: 10.1109/TRO.2019.2963665.
- Gonçalves, V.M., Pimenta, L.C.A., Maia, C.A., Dutra, B.C.O. and Pereira, G.A.S. (2010). Vector fields for robot navigation along time-varying curves in n-dimensions, IEEE Transactions on Robotics 26(4): 647–659, DOI: 10.1109/TRO.2010.2053077.
- Hung, N., Rego, F., Quintas, J., Cruz, J., Jacinto, M., Souto, D., Potes, A., Sebastiao, L. and Pascoal, A. (2023). A review of path following control strategies for autonomous robotic vehicles: Theory, simulations, and experiments, Journal of Field Robotics 40(3): 747–779, DOI: 10.1002/rob.22142.
- Jafarzadeh, H. and Fleming, C. H. (2018). An exact geometry–based algorithm for path planning, International Journal of Applied Mathematics and Computer Science 28(3): 493–504, DOI: 10.2478/amcs-2018-0038.
- Kapitanyuk, Y.A., Proskurnikov, A.V. and Cao, M. (2018). A guiding vector-field algorithm for path-following control of nonholonomic mobile robots, IEEE Transactions on Control Systems Technology 26(4): 1372–1385, DOI: 10.1109/TCST.2017.2705059.
- Kozłowski, K. and Pazderski, D. (2004). Modeling and control of a 4-wheel skid-steering mobile robot, International Journal of Applied Mathematics and Computer Science 14(4): 477–496.
- Krstić, M., Kanellakopoulos, I. and Kokotović, P.V. (1995). Nonlinear and Adaptive Control Design, Wiley, New York, USA.
- Lee, J.M. (1997). Riemannian Manifolds: An Introduction to Curvature, Springer, New York.
- Li, X., Zhao, G. and Li, B. (2020). Generating optimal path by level set approach for a mobile robot moving in static/dynamic environments, Applied Mathematical Modelling 85: 210–230, DOI: 10.1016/j.apm.2020.03.034.
- Liao, Y.-L., Zhang, M.-J. and Wan, L. (2015). Serret–Frenet frame based on path following control for underactuated unmanned surface vehicles with dynamic uncertainties, Journal of Central South University 22: 214–223, DOI: 10.1007/s11771-015-2512-z.
- Liu, H. and Pei, D. (2013). Singularities of a space curve according to the relatively parallel adapted frame and its visualization, Mathematical Problems in Engineering 2013(512020): 1–12, DOI: 10.1155/2013/512020.
- Lugo-Cárdenas, I., Salazar, S. and Lozano, R. (2017). Lyapunov based 3D path following kinematic controller for a fixed wing UAV, IFAC-PapersOnLine 50(1): 15946–15951, DOI: 10.1016/j.ifacol.2017.08.1747.
- Mazur, A. (2004). Hybrid adaptive control laws solving a path following problem for non-holonomic mobile manipulators, International Journal of Control 77(15): 1297–1306, DOI: 10.1080/0020717042000297162.
- Mazur, A. (2010). Trajectory tracking control in workspace-defined tasks for nonholonomic mobile manipulators, Robotica 28(1): 57–68, DOI: 10.1017/S0263574709005578.
- Mazur, A. and Dyba, F. (2023). The non-orthogonal serret–frenet parametrization applied to the path following problem of a manipulator with partially known dynamics, Archives of Control Sciences 33(2): 339–370, DOI: 10.24425/acs.2023.146279.
- Mazur, A. and Płaskonka, J. (2012). The Serret–Frenet parametrization in a control of a mobile manipulator of (nh, h) type, IFAC Proceedings Volumes 45(22): 405–410, DOI: 10.3182/20120905-3-HR-2030.00069.
- Mazur, A., Płaskonka, J. and Kaczmarek, M. (2015). Following 3D paths by a manipulator, Archives of Control Sciences 25(1): 117–133, DOI: 10.1515/acsc-2015-0008.
- Mazur, A. and Szakiel, D. (2009). On path following control of nonholonomic mobile manipulators, International Journal of Applied Mathematics and Computer Science 19(4): 561–574.
- Micaelli, A. and Samson, C. (1993). Trajectory tracking for unicycle-type and two-steering-wheels mobile robots, Technical Report No. 2097, INRIA, Sophia-Antipolis.
- Michałek, M. and Kozłowski, K. (2009). Motion planning and feedback control for a unicycle in a way point following task: The VFO approach, International Journal of Applied Mathematics and Computer Science 19(4): 533–545, DOI: 10.1007/s10846-017-0482-0.
- Michałek, M.M. and Gawron, T. (2018). VFO Path following control with guarantees of positionally constrained transients for unicycle-like robots with constrained control input, Journal of Intelligent and Robotic Systems: Theory and Applications 89(1-2): 191 – 210.
- Oprea, J. (1997). Differential Geometry and Its Applications, Prentice Hall, Michigan University.
- Pepy, R., Kieffer, M. and Walter, E. (2009). Reliable robust path planning with application to mobile robots, International Journal of Applied Mathematics and Computer Science 19(3): 413–424, DOI: 10.2478/v10006-009-0034-2.
- Przybylski, M. and Putz, B. (2017). D* Extra Lite: A dynamic A* with search–tree cutting and frontier–gap repairing, International Journal of Applied Mathematics and Computer Science 27(2): 273–290, DOI: 10.1515/amcs-2017-0020.
- Rezende, A.M.C., Goncalves, V.M. and Pimenta, L.C.A. (2022). Constructive time-varying vector fields for robot navigation, IEEE Transactions on Robotics 38(2): 852–867, DOI: 10.1109/TRO.2021.3093674.
- Selig, J.M. and Wu, Y. (2006). Interpolated rigid-body motions and robotics, 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems, Beijing, China, pp. 1086–1091, DOI: 10.1109/IROS.2006.281815.
- Serret, J.-A. (1851). Sur quelques formules relatives à la théorie des courbes à double courbure, Journal de Mathématiques Pures et Appliquées, 16: 193–207.
- Slotine, J.-J. and Li, W. (1991). Applied Nonlinear Control, Prentice Hall, Englewood Cliffs, N.J.
- Soetanto, D., Lapierre, L. and Pascoal, A. (2003). Adaptive, non-singular path-following control of dynamic wheeled robots, Proceedings of the 42nd IEEE International Conference on Decision and Control, Vol. 2, Maui, HI, pp. 1765–1770, DOI: 10.1109/CDC.2003.1272868.
- Spong, M. and Vidyasagar, M. (1991). Robot Dynamics and Control, Wiley, New York.
- Sun, K. and Liu, X. (2021). Path planning for an autonomous underwater vehicle in a cluttered underwater environment based on the heat method, International Journal of Applied Mathematics and Computer Science 31(2): 289–301, DOI: 10.34768/amcs-2021-0019.
- Utkin, V.I. (1992). Sliding Modes in Control and Optimization, Springer, Berlin.
- Yamamoto, Y. and Yun, X. (1996). Effect of the dynamic interaction on coordinated control of mobile manipulators, IEEE Transactions on Robotics and Automation 12(5): 816–824, DOI: 10.1109/70.538986.
- Yao, W., de Marina, H.G., Lin, B. and Cao, M. (2021). Singularity-free guiding vector field for robot navigation, IEEE Transactions on Robotics 37(4): 1206–1221, DOI: 10.1109/TRO.2020.3043690.