The stabilizing problem of stochastic nonholonomic mobile robots with uncertain parameters is addressed in this paper. The nonholonomic mobile robots with kinematic unknown parameters are extended to the stochastic case. Based on backstepping technique, adaptive state-feedback stabilizing controllers are designed for nonholonomic mobile robots with kinematic unknown parameters whose linear velocity and angular velocity are subject to some stochastic disturbances simultaneously. A switching control strategy for the original system is presented. The proposed controllers that guarantee the states of closed-loop system are asymptotically stabilized at the zero equilibrium point in probability. 1. Introduction In the past decades, the control of nonholonomic systems has been widely pursued. By the results of Brockett [1], the nonholonomic system cannot be stabilized at a single equilibrium point by any static smooth pure state-feedback controller. To solve this problem, lots of novel approaches have been considered: discontinuous feedback control [2–4], smooth time-varying feedback controller [5], and the method of LMI [6]. The control of nonholonomic mobile robots plays an important role in that of nonholonomic systems because they are a benchmark for these systems. There is much attention devoted to the control of nonholonomic mobile robots. The nonholonomic mobile robots were classified into four types, which were characterized by generic structures of the model equations [7]. Based on the backstepping technique, the control for nonholonomic mobile robots was discussed: tracking problems [8] and stabilizing problems [9, 10]. Hespanha et al. introduced the mobile robot with parametric uncertainties [11], which were further discussed [12, 13]. But all the above articles discussed the nonholonomic systems in the deterministic case, which was not considered a stochastic disturbance. In recent years, stochastic nonlinear systems have received much attention [14, 15], especially for stochastic control when backstepping designs were firstly introduced [16, 17]. For stochastic nonholonomic systems, there were a few papers. The almost global adaptive asymptotical controllers of stochastic nonholonomic chained form systems were discussed by using discontinuous control [18]. The adaptive stabilization problem of stochastic nonholonomic systems with nonlinear drifts was considered [19–21]. By using state-scaling method, backstepping controllers were proposed to deal with exponential stabilization for nonholonomic mobile robots with stochastic disturbance [22, 23].
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