Modeling and Control for Wheeled Mobile Robots with Nonholonomic Constraints
Date Issued
2006
Date
2006
Author(s)
Tsai, Pu-Sheng
DOI
en-US
Abstract
Based on the decoupling feature arises from the Appell equations, this dissertation fo-cuses on the design of the following three hierarchical control architectures: fuzzy com-pensator for tri-wheeled mobile robots, backstepping controller for car-like mobile robots, and Lyapunov synthesis method for four-wheeled vehicle with steering wheel system. The problem to be attacked here is the tracking of a desired trajectory for three types of mobile robots moving on a horizontal plane. The reduced Appell equation in matrix form is first established to deal with the modeling problem of nonholonomic systems by a systematic and structural procedure. By appropriately choosing a set of privileged variable, the re-duced Appell equations are decoupled from the kinematics such that the system design may be separated into three levels: motion planning, kinematic, and dynamic. In motion planning level, the proposed algorithm is an integrated application of the constrained opti-mization method and B-spline function to generate a feasible path that the kinematic con-straints and curvature restrictions are satisfied. In addition, the matrix form of divided B-spline curve is derived, which makes it possible to realize the constrained optimization programming. Three types of the compensator, fuzzy inference engine, backstepping in chained form and Lyapunov synthesis method, in the kinematic level are respectively de-signed to update the desired trajectory computed in the motion planning level. The updated privileged variables are then fed into the dynamic controller in the bottom level. To deal with the uncertainties in the system parameters, an adaptive sliding mode controller is then adopted to track the new reference values of privileged variables assured by the skew-symmetric property in the dynamical level, which subsequently drives all system variables to the desired values by natural mechanism. The decoupling paves the way for the structure of hierarchical control which simultaneously takes kinematic equation and dynamic equation into consideration indeed gives rise to an effective methodology for the trajectory tracking problem. Furthermore, the effects of external disturbances and interac-tions between kinematics and dynamics will appear gradually while the initial condition is significantly away from the desired configuration. Two robust control compensations, switching function and saturation function, are investigated to guarantee the performance of developed hierarchical tracking control systems. As to what we expect, simulation re-sults demonstrate the success of the proposed systematic design of the hierarchical tracking control scheme.
Subjects
非完整約束系統
階層式追蹤控制
路徑規劃
動力模型
運動模型
B樣條曲線
特權變數
鏈狀模型
後退式控制器
滑動模式控制器
nonholonomic constrained systems
hierarchical tracking control
path planning
kinematics
dynamics
B-spline curve
privileged variable
chained form system
backstepping controller
reduced Appell equation
sliding mode controller
Type
thesis
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