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This paper aims to address robot/environment interacting problems by designing an adaptive finite-time impedance controller. To deal with crucial issues regarding these sorts of problems, namely interacting with unknown environments and the system's uncertain nonlinearity, a backstepping control structure accompanied by an adaptive Taylor series system is developed. By designing a sliding surface term, two new variables are defined to form the backstepping controller to guarantee that the sliding surface converges to zero in a finite time. Also, impedance parameters are tuned adaptively using the gradient-descent algorithm inspired by a well-designed control literature. The designed controller has several useful features, such as being capable of implementing on n-DOF (degree-of-freedom) industrial manipulators, a guaranteed finite-time stability analysis, a regressor-free design, and dealing with uncertainties. Finally, a numerical simulation applied on a six-DOF manipulator and also a comparison with an impedance control are provided to show the efficiency of the designed controller.

Adaptive finite-time impedance backstepping control for uncertain robotic systems interacting with unknown environments