Adaptive planar curve tracking control and robustness analysis under state constraints and unknown curvature. (English) Zbl 1351.93080
Summary: We provide adaptive controllers for curve tracking in the plane, under unknown curvatures and control uncertainty, which is a central problem in robotics. The system dynamics include a nonlinear dependence on the curvature, and are coupled with an estimator for the unknown curvature, to form the augmented error dynamics. We prove input-to-state stability of the augmented error dynamics with respect to an input that is represented by additive uncertainty on the control, under polygonal state constraints and under suitable known bounds on the curvature and on the control uncertainty. When the uncertainty is zero, this gives tracking of the curve and convergence of the curvature estimate to the unknown curvature. Our curvature identification result is a significant improvement over earlier results, which do not ensure parameter identification, or which identify the control gain but not the curvature.
MSC:
| 93C40 | Adaptive control/observation systems |
| 93B35 | Sensitivity (robustness) |
| 93C10 | Nonlinear systems in control theory |
| 93D25 | Input-output approaches in control theory |
| 93C41 | Control/observation systems with incomplete information |
| 93C85 | Automated systems (robots, etc.) in control theory |
Keywords:
adaptive systems; constrained parameters; curve tracking; robotics; robustness; uncertaintyReferences:
| [1] | Aguiar, A.; Hespanha, J., Trajectory-tracking and path-following of underactuated autonomous vehicles with parametric modeling uncertainty, IEEE Transactions on Automatic Control, 52, 8, 1362-1379 (2007) · Zbl 1366.93393 |
| [3] | Bresch-Pietri, D.; Krstic, M., Delay-adaptive predictor feedback for systems with unknown long actuator delay, IEEE Transactions on Automatic Control, 55, 9, 2106-2112 (2010) · Zbl 1368.93621 |
| [4] | Bresch-Pietri, D.; Krstic, M., Delay-adaptive control for nonlinear systems, IEEE Transactions on Automatic Control, 59, 5, 1203-1218 (2014) · Zbl 1360.93342 |
| [5] | Do, K.; Jiang, Z. P.; Pan, J., Robust adaptive path following of underactuated ships, Automatica, 40, 6, 929-944 (2004) · Zbl 1096.93021 |
| [6] | Do, K.; Pan, J., Robust path-following of underactuated ships: theory and experiments on a model ship, Ocean Engineering, 33, 10, 1354-1372 (2006) |
| [8] | Khalil, H., Nonlinear systems (2002), Prentice Hall: Prentice Hall Upper Saddle River, NJ · Zbl 1003.34002 |
| [9] | Krstic, M., Delay compensation for nonlinear, adaptive, and PDE systems (2009), Birkhauser: Birkhauser Boston, MA · Zbl 1181.93003 |
| [10] | Lenain, R.; Thuilot, B.; Cariou, C.; Martinet, P., High accuracy path tracking for vehicles in presence of sliding: application to farm vehicle automatic guidance for agricultural tasks, Autonomous Robots, 21, 1, 79-97 (2006) |
| [11] | Lumelsky, V.; Stepanov, A., Path planning strategies for a point mobile automaton moving amidst unknown obstacles of arbitrary shape, Algorithmica, 2, 2, 403-430 (1987) · Zbl 0643.68150 |
| [12] | Malisoff, M.; Mazenc, F.; Zhang, F., Stability and robustness analysis for curve tracking control using input-to-state stability, IEEE Transactions on Automatic Control, 57, 5, 1320-1326 (2012) · Zbl 1369.93217 |
| [13] | Malisoff, M.; Zhang, F., Adaptive control for planar curve tracking under controller uncertainty, Automatica, 49, 5, 1411-1418 (2013) · Zbl 1319.93041 |
| [14] | Malisoff, M.; Zhang, F., Robustness of adaptive control under time delays for three-dimensional curve tracking, SIAM Journal on Control and Optimization, 53, 4, 2203-2236 (2015) · Zbl 1317.93228 |
| [16] | Micaelli, A.; Samson, C., Trajectory tracking for unicycle-type and two-steering-wheels mobile robots. INRIA Report 2097 (1993) |
| [17] | Morin, P.; Samson, C., Motion control of wheeled mobile robots, (Springer handbook of robotics (2008), Springer: Springer Berlin, Germany), 799-826 |
| [18] | Mukhopadhyay, S.; Wang, C.; Patterson, M.; Malisoff, M.; Zhang, F., Collaborative autonomous surveys in marine environments affected by oil spills, (Cooperative robots and sensor networks (2014), Springer: Springer New York), 87-113 |
| [19] | Woolsey, C.; Techy, L., Cross-track control of a slender, underactuated AUV using potential shaping, Ocean Engineering, 36, 1, 82-91 (2009) |
| [21] | Zhang, F.; Fratantoni, D.; Paley, D.; Lund, J.; Leonard, N., Control of coordinated patterns for ocean sampling, International Journal of Control, 80, 7, 1186-1199 (2007) · Zbl 1119.93014 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
