This article formulates the control problem of underactuated mobile robot as servo constraint-following, and develops a novel constraint-following servo control approach for underactuated mobile robot under both servo soft and hard constraints. Servo soft constraints are expressed as equalities, which may be holonomic or non-holonomic. Servo hard constraints are expressed as inequalities. It is required that the underactuated mobile robot motion eventually converges to servo soft constraints, and satisfies servo hard constraints at all times. Diffeomorphism is employed to incorporate hard constraints into soft constraints, yielding new soft constraints to relax hard constraints. By this, we design a constraint-following servo control based on the new servo soft constraints, which drives the system to strictly follow the original servo soft and hard constraints. The effectiveness of the proposed approach is proved by rigorous proof and simulations.
KlancarGMatkoDBlaiS. A control strategy for platoons of differential drive wheeled mobile robot. Robot Autonom Syst2011; 59(2): 57–64.
5.
YueMHuPSunW. Path following of a class of non-holonomic mobile robot with underactuated vehicle body. IET Control Theory Appl2010; 4(10): 1898–1904.
6.
FukaoTNakagawaHAdachiN. Adaptive tracking control of a nonholonomic mobile robot. IEEE Trans Robot Autom2000; 16(5): 609–615.
7.
KhanpoorAKhalajiAKMoosavianSAA. Modeling and control of an underactuated tractor–trailer wheeled mobile robot. Robotica2017; 35: 1–22.
8.
ChwaD. Sliding-mode tracking control of nonholonomic wheeled mobile robots in polar coordinates. IEEE Trans Control Syst Tech2004; 12(4): 637–644.
9.
HamerlainFAchourKFloquetT, et al. Higher order sliding mode control of wheeled mobile robots in the presence of sliding effects. In: Proceedings of the 44th IEEE conference on decision and control, Seville, 15 December 2005, pp.1959–1963. New York: IEEE.
10.
LiZGeSMingA. Adaptive robust motion/force control of holonomic-constrained nonholonomic mobile manipulators. IEEE Trans Syst Man Cyb Part B2007; 37(3): 607–616.
11.
ChenYHZhangX. Adaptive robust approximate constraint-following control for mechanical systems. J Frank Inst2010; 347(1): 69–86.
12.
LiZLiJYuK. Adaptive robust coordinated control of multiple mobile manipulators interacting with rigid environments. Automatica2010; 46(12): 2028–2034.
13.
UdwadiaFEKalabaRE. Analytical dynamics: a new approach. Cambridge: Cambridge University Press.
14.
KalabaRUdwadiaF. Analytical dynamics with constraint forces that do work in virtual displacements. Appl Math Comput2001; 121(2): 211–217.
15.
UdwadiaFEKalabaRE. On the foundations of analytical dynamics. Int J Non Line Mech2002; 37(6): 1079–1090.
16.
XuJXuJChenYH, et al. A new approach to control design for constraint-following for fuzzy mechanical systems. J Optim Theory Appl2015; 165(3): 1022–1049.
17.
RosenbergR. Analytical dynamics of discrete systems. New York: Plenum Press, 1977.
18.
BraunDJGoldfarbM. A control approach for actuated dynamic walking in biped robots. IEEE Trans Robot2009; 25(6): 1292–1303.
19.
SunHChenYHXiongY, et al. Configuring tasks as constraints for coordinated mechanical systems: a Udwadia–Kalaba theory based adaptive robust control. J Frank Inst2020; 357: 3387–3418.
20.
UdwadiaFE. Optimal tracking control of nonlinear dynamical systems. Proc Math Phys Eng Sci2008; 464(2097): 2341–2363.
21.
UdwadiaFE. A new perspective on the tracking control of nonlinear structural and mechanical systems. P R Soc London Ser A: Math Phys Eng Sci2003; 459(2035): 1783–1800.
22.
SicilianoBValavanisKP. Control problems in robotics and automation. Springer: Berlin, 1998, pp. 135–150.
23.
YinHChenYHYuDJ. Controlling an underactuated two-wheeled mobile robot: a constraint-following approach. J Dyn Syst Meas Control2019; 141: 071002.
24.
El-HawwaryMIElshafeiAEmaraH, et al. Adaptive fuzzy control of the inverted pendulum problem. IEEE Trans Control Syst Tech2006; 14(6): 1135–1144.
25.
Aguilar-AvelarCMoreno-ValenzuelaJ. New feedback linearization-based control for arm trajectory tracking of the Furuta pendulum. IEEE/ASME Trans Mech2016; 21(2): 638–648.
26.
Montoya-VillegasLMoreno-ValenzuelaJPérez-AlcocerR. A feedback linearization-based motion controller for a UWMR with experimental evaluations. Robotica2019; 37(6): 1–17.
27.
LiZZhangYYangY. Support vector machine optimal control for mobile wheeled inverted pendulums with unmodelled dynamics. Neurocomputing2010; 73(13-15): 2773–2782.
28.
AbramovaILatyshevS. Using the fundamental equation of constrained motion with inequality constraints. Appl Math Comput2009; 215(8): 2858–2876.
29.
PajakGPajakI. Sub-optimal trajectory planning for mobile manipulators. Robotica2015; 33(06): 1181–1200.
30.
YinHChenYHYuDJ. Vehicle motion control under equality and inequality constraints: a diffeomorphism approach. Nonlin Dynam2019; 95(1): 175–194.
31.
ChenYH. Constraint-following servo control design for mechanical systems. J Vib Control2009; 15(3): 369–389.
32.
KogantiPBUdwadiaFE. Unified approach to modeling and control of rigid multibody systems. J Guid Control Dynam2016; 39: 272.
