Adaptive global prescribed performance tracking control of uncertain robotic systems with unknown control directions

Abstract In this article, we develop an adaptive global prescribed performance tracking control scheme for nonlinear multiple‐input multiple‐output (MIMO) robotic systems in the presence of unknown control directions and nonparametric uncertainties, in which the proposed solution mainly includes the following steps. Firstly, by constructing a global prescribed performance function, together with a series of transformations, the corresponding control guarantees the position tracking error evolves strictly within the prespecified region for all time, which is independent of initial conditions; Secondly, in order to cope with the problem of multiple unknown control directions, we make use of a symmetric matrix lemma to convert the underlying problem from matrix form to scalar form, so that the Nussbaum‐gain lemma for SISO systems becomes effective for MIMO systems with multiple inputs; In addition, we employ the integrable function to handle the nonparametric uncertainties, enabling the control scheme with the capability to drive the tracking error toward zero asymptotically. The effectiveness of the proposed control is validated via a two‐link rigid robotic manipulator.