×

Singularity-avoiding swing-up control for underactuated three-link gymnast robot using virtual coupling between control torques. (English) Zbl 1305.93147

Summary: An underactuated three-link gymnast robot (UTGR) is a simple model of a gymnast on a high bar. The control objective of a UTGR is to swing it up from a point near the straight-down position and to stabilize it at the straight-up position. To achieve this, we first divide the motion space into two subspaces, swing-up area and balancing area, and design a controller for each. The design of a swing-up control law that ensures that the UTGR enters the balancing area is crucial because the UTGR is subject to a nonholonomic constraint and is highly nonlinear during the swing-up motion. This study focused on how to design a swing-up control law that contains no singularities. The key concept is the introduction of a virtual coupling between control torques, which converts the problem of avoiding singularities to one of imposing constraints on the parameters of the control law and properly selecting those parameters. A swing-up control law thus designed ensures that the UTGR enters the balancing area in a natural stretched-out posture. This makes it easy to stabilize the UTGR in the balancing area.

MSC:

93C85 Automated systems (robots, etc.) in control theory
68T40 Artificial intelligence for robotics
49N10 Linear-quadratic optimal control problems
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Bullo, Controllability and motion algorithms for underactuated Lagrangian systems on Lie groups, IEEE Transactions on Automatic Control 45 (8) pp 1437– (2000) · Zbl 0990.70019 · doi:10.1109/9.871753
[2] Grizzle, Nonlinear control of mechanical systems with an unactuated cyclic variable, IEEE Transactions on Automatic Control 50 (5) pp 559– (2005) · Zbl 1365.70035 · doi:10.1109/TAC.2005.847057
[3] Qaiser, Exponential stabilization of a class of underactuated mechanical systems using dynamic surface control, International Journal of Control, Automation, and Systems 5 (5) pp 547– (2007)
[4] Xu, Sliding mode control of a class of underactuated systems, Automatica 44 (1) pp 233– (2008) · Zbl 1138.93409 · doi:10.1016/j.automatica.2007.05.014
[5] Miyazaki M Sampei M Koga M Takahashi A A control of underactuated hopping gait systems: acrobot example Proceedings of the 39th IEEE Conference on Decision and Control 2000 4797 4802
[6] Spong, The swing up control problem for the acrobot, IEEE Control Systems Magazine 15 (1) pp 44– (1995) · doi:10.1109/37.341864
[7] Xin, Analysis of the energy-based swing-up control of the acrobot, International Journal of Robust and Nonlinear Control 17 (16) pp 1503– (2007) · Zbl 1128.93375 · doi:10.1002/rnc.1184
[8] Lai, Comprehensive unified control strategy for underactuated two-link manipulators, IEEE Transactions on Systems, Man and Cybernetics, Part B 39 (2) pp 389– (2009) · doi:10.1109/TSMCB.2008.2005910
[9] Mahindrakar A Astolfi A Ortega R Viola G Further constructive results on interconnection and damping assignment control of mechanical systems: the acrobot example Proceedings of the 2006 American Control Conference 2006 5584 5589 · Zbl 1134.93346
[10] Takashima S Control of gymnast on a high bar Proceedings of IEEE/RSJ International Workshop on Intelligent and Robotic Systems 3 1991 1424 1429
[11] Oriolo G Nakamura Y Control of mechanical systems with second-order nonholonomic constraints: underactuated manipulators Proceedings of the 30th IEEE Conference on Decision and Control 1991 2398 2403
[12] Spong W The control of underactuated mechanical systems Proceedings of the 1st International Conference on Mechatronics 1994 1 21
[13] Xin, Swing-up control for a 3-DOF gymnastic robot with passive first joint: design and analysis, IEEE Transactions on Robotics 23 (6) pp 1277– (2007) · doi:10.1109/TRO.2007.909805
[14] Lai, Motion control of underactuated three-link gymnast robot based on combination of energy and posture, IET Control Theory & Applications 5 (13) pp 1484– (2011) · doi:10.1049/iet-cta.2010.0210
[15] Khalil, Nonlinear Systems, 3. ed. (2002)
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.