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Problem Formulation and Examples
Published in Sabiha Wadoo, Pushkin Kachroo, Autonomous Underwater Vehicles, 2017
The simplest example of a nonholonomic system can be a wheel that rolls on a lane surface, such as a unicycle. The constraints here arise due to the roll without a slip condition. The configuration or the generalized coordinate vector is q = (x, y, θ). The coordinates x and y are the position coordinates of the wheel, and θ is the angle that the wheel makes with the x axis. The unicycle is shown in Figure 2.2. The constraint here is that the wheel cannot slip in the lateral direction.
Finite-time stabilisation for a class of output-constrained nonholonomic systems with its application
Published in International Journal of Systems Science, 2018
Fangzheng Gao, Yuqiang Wu, Hongsheng Li, Yanhong Liu
As an important nonlinear system, nonholonomic system has attracted extensive attention during the past decades because it can model many practical systems, such as mobile robots, car-like vehicle, under-actuated satellites and so on. However, from the Brockett sabilisation theorem (Brockett, 1983), it is well known that no smooth (or even continuous) time-invariant static state feedback exists for the stabilisation of nonholonomic systems. To give this difficulty a solution, a number of control approaches have been proposed, which mainly are discontinuous time-invariant stabilisation (Astolfi, 1996; Xu & Huo, 2000), smooth time-varying stabilisation (Jiang, 1996; Samson, 1995; Tian & Li, 2002) and hybrid stabilisation (Hespanha, Linberzon, & Morse, 1999; Kolmanovsky & McClamroch, 1996), refer to the survey paper (Liang & Wang, 2011) for more details. Mainly thanks to these valid approaches, a number of interesting results on asymptotic stabilisation have been established over the last years, see, e.g. Gao, Yuan, and Yao (2010), Ge, Wang, and Lee (2003), Huang, Liu, and Wu (2017), Jiang (2000), Liu and Zhang (2005), Wu, Zhao, and Yu (2013), Wu and Liu (2015), Xi, Feng, Jiang, and Cheng (2007), Zuyev (2016) and the references therein.