Motion and force control is an issue of great practical importance to the mechanical industry. This paper investigates the problem of modeling and position/force tracking for nonholonomic dynamic systems with affine constraints (NDSAC). The rigorous derivation of the dynamic model is given and a reduced dynamic model, which is suitable for control design, is developed. We consider two cases: (i) the reference signal and its time derivative are zero and (ii) the time derivative of reference signal is varying. In the first case, a continuous estimator and an adaptive control law to account for parametric uncertainties are proposed. In the second case, another adaptive control algorithm is developed. In both cases, the motion tracking error and its time derivative converge to zero, and the tracking error of Lagrangian multiplier is bounded with a controllable bound. The efficiency of the controller is demonstrated by a mechanics system: a boat on a running river.
AltafiniCSperanzonAWahlbergB (2001) A feedback control scheme for reversing a truck and trailer vehicle. IEEE Transactions on Robotics and Automation17(6): 915–922.
2.
BerkemeierMDFearingRS (1999) Tracking fast inverted trajectories of the underactuated acrobot. IEEE Transactions on Robotics and Automation15(4): 740–750.
3.
BulloFLewisAD (2004) Geometric control of mechanical systems. New York: Springer-Verlag.
4.
ChangYCChenBS (2000) Robust tracking designs for both holonomic and nonholonomic constrained mechanical systems: adaptive fuzzy approach. IEEE Transactions on Fuzzy Systems8(1): 46–66.
5.
ChenHWangCLZhangBW. (2013) Saturated tracking control for nonholonomic mobile robots with dynamic feedback. Transactions of the Institute of Measurement and Control35(2): 105–116.
6.
DongWJXuWL (2001) Adaptive tracking control of uncertian nonholonomic dynamic system. IEEE Transactions on Automatic Control46(3): 450–454.
7.
FuJChaiTYSuCY. (2013) Motion/force tracking control of nonholonomic mechanical systems via combining cascaded design and backstepping. Automatica49(12): 3682–3686.
8.
GaoFZWuYQYuanFS (2014) Semi-global finite-time stabilization of uncertain nonholonomic systems via output feedback. Transactions of the Institute of Measurement and Control DOI: 10.1177/0142331214535018.
9.
GeXSChenLQ (2004) Attitude control of a rigid spacecraft with two momentum wheel actuators using genetic algorithm. Acta Astronautica55(1): 3–8.
JiangZP (2000) Robust exponential regulation of nonholonomic systems with uncertainties. Automatica36(2): 189–209.
12.
KaiT (2006) Extended chained forms and their applications to nonholonomic kinematic systems with affine constraints: control of a coin on a rotating table. In: Proceedings of the 45th IEEE conference on decision and control, San Diego, CA, pp. 6104–6109.
13.
KaiT (2012) Mathematical modelling and theoretical analysis of nonholonomic kinematic systems with a class of rheonomous affine constraints. Applied Mathematical Modelling36(7): 3189–3200.
14.
KaiTKimuraH (2004) Theoretical analysis on nonholonomic dynamic systems with affine constraints. In: Proceedings of the SICE Annual Conference, Sapporo, Japan, pp. 2361–2366.
15.
KaiTKimuraH (2006) Theoretical analysis of affine constraints on a configuration manifold—part II: accessbility of kinematic asymmetic affine control systems with affine constraints. Transactions of the Society of Instrument and Contorl Engineer42(3): 222–231.
16.
KaiTKimuraHHaraS (2005) Nonlinear control analysis on kinematically asymmetrically affine control systems with nonholonomic affine constraints. In: Proceedings of 16th IFAC World congress, Prague, Czech.
17.
LiZJGeSSMingAG (2007) Adaptive Robust motion/force control of holonomic-constrained nonholonomic mobile manipulators. IEEE Transactions on Systems, Man and Cybernetics37(3): 607–616.
18.
LiZJGeSSWijesomaWS (2008) Robust adaptive contorl of uncertain force/motion constrained nonholonomic mobile manipulators. Automatica44(3): 776–784.
19.
MarkusM (2008) Robust tracking control of nonholonomic dynamic systems with application to the bi-steerable mobile robot. Automatica44(10): 2588–2592.
20.
MeiFXWuHB (2009) Dynamics of constrained mechanical systems. Beijing: Beijing Institute of Technology Press.
21.
MeiJRenWMaGF (2011) Distributed coordinated tracking with a dynamic leader for multiple Euler–Lagrange systems. IEEE Transactions on Automatic Control56(6): 1415–1421.
22.
MurrayRMSastryS (1993) Nonholonomic motion planning: Steering using sinusoids. IEEE Transactions on Automatic Control38(5): 700–716.
23.
OyaMSuCYKatohR (2003) Robust adaptive motion/force control of uncertain nonholonomic mechanical systems. IEEE Transactions on Robotics and Automation19(1): 175–181.
24.
SuCYStepanenkoY (1994) Robust motion/force control of mechanical systems with classical nonholonomic constraints. IEEE Transactions on Automatic Control39(3): 609–614.
25.
SunWWuYQSunZY (2014) Tracking control design for nonholonomic mechanical systems with affine constraints. International Journal of Automation and Computing11(3): 328–333.
26.
SunWWuYQ (2014) Adaptive motion/force control of nonholonomic mechanical systems with affine constraints. Nonlinear Analysis: Modelling and Control19(4): 646–659.
27.
WangZPGeSSLeeTH (2004) Robust motion/force control of uncertain holonomic/nonholonomic mechanical systems. IEEE/ASME Transactions on Mechatronics9(1): 118–123.
28.
WuYQZhaoYYuJB (2013) Global asymptotic stability controller of uncertain nonholonomic systems. Journal of the Franklin Institute350(5): 1248–1263.
29.
ZhangDKWangCLChenH. (2013) Adaptive stabilization of stochastic non-holonomic systems with non-homogeneous uncertainties. Transactions of the Institute of Measurement and Control35(5): 648–663.
30.
ZhaoYYuJBWuYQ (2011) State-feedback stabilization for a class of more general high order stochastic nonholonomic systems. International Journal of Adaptive Control and Signal Processing25(8): 687–706.
