Robust Constraint Following Stabilization for Mechanical Manipulators Containing Uncertainty: An Adaptive <inline-formula> <tex-math notation="LaTeX">$\varphi$ </tex-math> </inline-formula> Approach

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The constraint following stabilization problem of aerospace mechanical manipulators containing uncertainty is investigated. Due to the inevitable modeling error and external disturbance, there always exists uncertainty. To guarantee that the mechanical system follows prescribed constraints (holonomic or non-holonomic), two classes of adaptive robust controls are proposed. The system performance is represented based on a $\varphi $ -measure. The control scheme consists of two parts: the nominal control part and the adaptive robust control part. By the Udwadia–Kalaba theory, the nominal control is proposed to force the nominal mechanical system to meet the constraints. Furthermore, the adaptive robust control is proposed to address the uncertainty issue, while the adaptation law is proposed to estimate the bounding information of the uncertainty. Under the control, the system is guaranteed to follow the constraint regardless of the uncertainty.