Abstract
The tracking performance of mobile robot is often affected by uncertainties from the deviation of initial conditions, external disturbances and varying loads, etc. An Udwadia-Kalaba based adaptive robust control is proposed for the trajectory tracking of an omnidirectional mobile robot in the presence of uncertainties. The proposed control includes nominal control part based on Udwadia-Kalaba theory and adaptive robust control part. The desired trajectory is considered as a virtual servo constraint applied to the robot system and converted into the second order standard form. So that the analytical form of constraint force could be obtained via Udwadia-Kalaba Fundamental Equation (UKFE). The system will precisely obey the given constraint (i.e., the desired trajectory) under the obtained constraint force in ideal cases. No auxiliary variables are required and it is effective whether the constraints are holonomic or nonholonomic. The designed adaptive law is in leakage type and the adaptive parameters are adjusted according to the performance of the system in order to compensate for the effect caused by uncertainty in the system. No extra information of uncertainty is needed except for the existence of uncertainty bound. Comparing with PID control, it can be found that the proposed control has better performance and can realize higher precision trajectory tracking control.
Highlights
Benefitting from its characteristics of moving in any direction, omnidirectional mobile robots have more advantages than traditional mobile platforms
According to [13], a real-time navigation and trajectory tracking controller for nonholonomic mobile robot based on biological excitation was proposed by combining back-stepping technology with neural dynamics.In addition, fuzzy theory is a popular method to deal with uncertainty, such as [14], [15]
An adaptive robust controller based on Udwadia-Kalaba Fundamental Equation (UKFE) is designed and applied to the trajectory tracking of an omnidirectional wheeled mobile robot
Summary
Benefitting from its characteristics of moving in any direction, omnidirectional mobile robots have more advantages than traditional mobile platforms. F. Dong et al.: Adaptive Robust Constraint Following Control for Omnidirectional Mobile Robot: An Indirect Approach. In reference [8], an adaptive controller was designed based on UKFE for constraint tracking of differential mobile robot. According to [13], a real-time navigation and trajectory tracking controller for nonholonomic mobile robot based on biological excitation was proposed by combining back-stepping technology with neural dynamics.In addition, fuzzy theory is a popular method to deal with uncertainty, such as [14], [15]. Suppose the mechanical system (8) is subjected to the constraints (14), the controller has the following performance under the assumptions 1-4: (i) Uniform boundedness: For any r > 0, there exists a finite positive real number d(r), if ψ(t0) ≤ r, ψ(t) ≤ d(r) for all t ≥ t0.
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