Vibration avoidance method for flexible robotic arm manipulation. (English) Zbl 1390.93585
Summary: A new principle, run with flexible deformation, for avoiding vibration throughout trajectories of a flexible robot manipulator is proposed. It comprises the hysteretic and leading mechanisms to maintain a steady pace of flexible (neutral surface) evolution with rigid (joint axis) advance, with the surface staying on a single side of the axis for constant deformation. A simple Proportional-Derivative (PD) controller is presented to realize the mechanisms, capable of adapting deformation into an invariant set that the single-sided pace-keeping is dependable over a steady or transient period. Analytically this set is the dynamic equilibrium target, in which negativeness of the Lyapunov function’s derivative is uncertain, and is proven globally uniformly asymptotically stable via a generalized Lyapunov and LaSalle’s argument. Further, the desired deformation is same stable in the sense of Lyapunov theorem due to recursive slowdown by the controller. The theoretical work is validated by the numerical simulations, which shows that the desired performance is well achieved. Significant advantages such as vibration-free servo control of a flexible-axis-based trajectory are demonstrated.
MSC:
| 93C85 | Automated systems (robots, etc.) in control theory |
| 74H45 | Vibrations in dynamical problems in solid mechanics |
| 93D20 | Asymptotic stability in control theory |
| 93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |
| 68T40 | Artificial intelligence for robotics |
Keywords:
flexible robot manipulator; Vibration avoidance; proportional-derivative (PD) controller; negativeness of the Lyapunov function’s derivative; globally uniformly asymptotic stabilityReferences:
| [1] | Dubus, G.; David, O.; Measson, Y., Vibration control of an ivvs long-reach deployer using unknown visual features from inside the iter vessel, Fusion Eng. Des., 85, 10, 2027-2032, (2010) |
| [2] | Flores-Abad, A.; Ma, O.; Pham, K.; Ulrich, S., A review of space robotics technologies for on-orbit servicing, Progr. Aerosp. Sci., 68, 1-26, (2014) |
| [3] | Benosman, M.; Le Vey, G., Control of flexible manipulators: a survey, Robotica, 22, 05, 533-545, (2004) |
| [4] | Dwivedy, S. K.; Eberhard, P., Dynamic analysis of flexible manipulators, a literature review, Mech. Mach. Theory, 41, 7, 749-777, (2006) · Zbl 1095.70005 |
| [5] | Kiang, C. T.; Spowage, A.; Yoong, C. K., Review of control and sensor system of flexible manipulator, J. Intell. Robot. Syst., 77, 1, 187-213, (2015) |
| [6] | Zhang, W., Vibration control of multilink flexible robotic arm with impulse spectrum, Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems, Daejeon, Korea, 2622-2627, (2016) |
| [7] | Zhang, W., The impulse spectrum method for vibration suppression of a flexible multilink robot arm, J. Vibr. Control., (2018), In Press |
| [8] | Pai, M., Robust input shaping control for multi-mode flexible structures using neuro-sliding mode output feedback control, J. Frankl. Inst., 349, 3, 1283-1303, (2012) · Zbl 1273.93054 |
| [9] | Singer, N. C.; Seering, W. P., Preshaping command inputs to reduce system vibration, ASME J. Dyn. Syst., Meas. Control, 112, 1, 76-82, (1990) |
| [10] | Singhose, W., Command shaping for flexible systems: a review of the first 50 years, Int. J. Precis. Eng. Manuf., 10, 4, 153-168, (2009) |
| [11] | Wang, F.-Y.; Gao, Y., Advanced studies of flexible robotic manipulators: modeling, design, control and applications, 4, (2003), World Scientific Publishing Co. Ltd Singapore · Zbl 1030.93001 |
| [12] | Tokhi, M. O.; Azad, A. K., Flexible robot manipulators: modelling, simulation and control, 68, (2008), The Institution of Engineering and Technology London, UK · Zbl 1210.93056 |
| [13] | De Luca, A., Feedforward/feedback laws for the control of flexible robots, Proceedings of IEEE International Conference on Robotics and Automation, San Francisco, CA, USA, 233-240, (2000) |
| [14] | de Wit, C. C.; Fixot, N.; Astrom, K., Trajectory tracking in robot manipulators via nonlinear estimated state feedback, IEEE Trans. Robot. Autom., 8, 1, 138-144, (1992) |
| [15] | Marino, R.; Tomei, P., Robust adaptive state-feedback tracking for nonlinear systems, IEEE Trans. Autom. Control, 43, 1, 84-89, (1998) · Zbl 0904.93025 |
| [16] | Ozgoli, S.; Taghirad, H., A survey on the control of flexible joint robots, Asian J. Control, 8, 4, 332-344, (2006) |
| [17] | Cao, F.; Liu, J., An adaptive iterative learning algorithm for boundary control of a coupled ODE-PDE two-link rigid-flexible manipulator, J. Frankl. Inst., 354, 1, 277-297, (2016) · Zbl 1355.93094 |
| [18] | Nicosia, S.; Tomei, P., Robot control by using only joint position measurements, IEEE Trans. Autom. Control, 35, 9, 1058-1061, (1990) · Zbl 0724.93056 |
| [19] | Arteaga, M. A., Tracking control of flexible robot arms with a nonlinear observer, Automatica, 36, 9, 1329-1337, (2000) · Zbl 0966.93078 |
| [20] | Masoud, M.; Mostafa, G.; Mostafa, S. N., Observer based tip tracking control of two-link flexible manipulator, Proceedings of IEEE International Conference on Control Automation and Systems, Gyeonggi-do, South Korea, 9-13, (2010) |
| [21] | Loria, A.; Ortega, R., On tracking control of rigid and flexible joints robots, Appl. Math. Comput., 5, 2, 101-113, (1995) |
| [22] | Tomei, P., A simple pd controller for robots with elastic joints, IEEE Trans. Autom. Control, 36, 10, 1208-1213, (1991) |
| [23] | De Luca, A.; Siciliano, B.; Zollo, L., Pd control with on-line gravity compensation for robots with elastic joints: theory and experiments, Automatica, 41, 10, 1809-1819, (2005) · Zbl 1087.93044 |
| [24] | De Luca, A.; Flacco, F., A pd-type regulator with exact gravity cancellation for robots with flexible joints, Proceedings of IEEE International Conference on Robotics and Automation, Shanghai, China, 317-323, (2011) |
| [25] | De Luca, A.; Siciliano, B., Regulation of flexible arms under gravity, IEEE Trans. Robot. Autom., 9, 4, 463-467, (1993) |
| [26] | Zollo, L.; Siciliano, B.; De Luca, A.; Guglielmelli, E., Pd control with on-line gravity compensation for robots with flexible links, Proceedings of European Control Conference, Kos, Greece, 4365-4370, (2007) |
| [27] | Pereira, E.; Aphale, S. S.; Feliu, V.; Moheimani, S. R., Integral resonant control for vibration damping and precise tip-positioning of a single-link flexible manipulator, IEEE/ASME Trans. Mechatron., 16, 2, 232-240, (2011) |
| [28] | Su, Y.; Muller, P. C.; Zheng, C., A global asymptotic stable output feedback pid regulator for robot manipulators, Proceedings of IEEE International Conference on Robotics and Automation, Roma, Italy, 4484-4489, (2007) |
| [29] | Su, Y.; Muller, P. C.; Zheng, C., Global asymptotic saturated pid control for robot manipulators, IEEE Trans. Control Syst. Technol., 18, 6, 1280-1288, (2010) |
| [30] | Aguiñaga-Ruiz, E.; Zavala-Río, A.; Santibáñez, V.; Reyes, F., Global trajectory tracking through static feedback for robot manipulators with bounded inputs, IEEE Trans. Control Syst. Technol., 17, 4, 934-944, (2009) |
| [31] | Malki, H. A.; Misir, D.; Feigenspan, D.; Chen, G., Fuzzy pid control of a flexible-joint robot arm with uncertainties from time-varying loads, IEEE Trans. Control Syst. Technol., 5, 3, 371-378, (1997) |
| [32] | Tomei, P., Adaptive pd controller for robot manipulators, IEEE Trans. Robot. Autom., 7, 4, 565-570, (1991) |
| [33] | Mahamood, R. M.; Pedro, J. O., Hybrid pd/pid controller design for two-link flexible manipulators, Proceedings of 8th Asian Control Conference, Kaohsiung, Taiwan, 1358-1363, (2011) |
| [34] | Ahmad, M.; Suid, M.; Ramli, M.; Zawawi, M.; Ismail, R. R., Pd fuzzy logic with non-collocated pid approach for vibration control of flexible joint manipulator, Proceedings of 6th International Colloquium on Signal Processing and Its Applications, Malacca City, Malaysia, 53-57, (2010) |
| [35] | Tokhi, M.; Azad, A., Collocated and non-collocated feedback control of flexible manipulator systems, Mach. Vibr., 5, 3, 170-178, (1996) |
| [36] | Rao, S. S., Mechanical vibrations, (2010), Prentice Hall Upper Saddle River, NJ · Zbl 0714.73050 |
| [37] | Martins, J.; Mohamed, Z.; Tokhi, M.; da Costa, J. S.; Botto, M., Approaches for dynamic modelling of flexible manipulator systems, IEE Proc.-Control Theory Appl., 150, 4, 401-411, (2003) |
| [38] | Mishra, N.; Singh, S.; Nakra, B., Dynamic analysis of a single link flexible manipulator using Lagrangian-assumed modes approach, Proceedings of IEEE International Conference on Industrial Instrumentation and Control, Pune, India, 1144-1149, (2015) |
| [39] | De Luca, A.; Siciliano, B., Closed-form dynamic model of planar multilink lightweight robots, IEEE Trans. Syst., Man, Cybern., 21, 4, 826-839, (1991) |
| [40] | Gere, J. M.; Goodno, B. J., Mechanics of Materials, (2008), CENGAGE Learning Toronto, Canada |
| [41] | Meirovitch, L., Analytical methods in vibration, 16, (1967), Macmillan, New York · Zbl 0166.43803 |
| [42] | Sunar, M.; Toker, O., Substructural control of fuzzy nonlinear flexible structures, J. Frankl. Inst., 344, 5, 646-657, (2007) · Zbl 1269.93057 |
| [43] | Khalil, H., Nonlinear systems, (2002), Prentice Hall Upper Saddle River, NJ · Zbl 1003.34002 |
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.
