The quest to the minimum of overlapped local minima in the parameter spaces of the steepest descent MRAC robotic manipulator
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This research presents an adaptive control scheme which can be implemented in an off-the-shelf microprocessor to eliminate the nonlinearities generated by the interactions of the two-link robotic manipulator. A new concept of parameter space is developed as a part of this thesis. This concept enhances a researcher’s ability to understand and investigate the complex dynamics of a robotic manipulator. The adaptive control scheme comprises a steepest descent regulator and a regulation adjustor in a model-referenced adaptive controller (MRAC). The inherent coupled nonlinearities which are a major burden to conventional control methods can be eliminated by the steepest descent model-referenced adaptive control with precalculated weighting factors. These factors are estimated off-line and loaded as computation-saving mechanism. The robustness, stability, and global convergence is achieved when the manipulator has gear ratios of one. In eliminating the nonlinearities of a general manipulator, the weighting factors of adaptive regulators can be found in the minimum of overlapped local minima of the suggested multi-dimension parameter space of the general robotic manipulator. The multi-dimension parameter space consists of a combined tracking error and several weighting factors. The idea of the parameter space, which comes from the utilization of the downhill simplex parameter minimization, provides an insight into choosing the best parameter set. The concept of the parameter space has been proven to be helpful in understanding the complex nonlinear dynamics of the multi-link robotic manipulator and in finding the minimum of overlapped local minima for most control schemes whose parameters must be empirically adjusted.