A New Adaptive Robust Sliding Mode Control for High-Precision PKMs: Design, Stability Analysis, and Experiments

This paper proposes a novel adaptive feedback sliding mode control for parallel kinematic manipulators (PKMs), built on the conventional model-based sliding mode control. This structure was chosen for its robustness towards uncertainties and external disturbances. The contribution of this research is the inclusion of a feedforward term based on the dynamic model of the PKM in the control design. This feedforward term compensates for high nonlinear dynamics, as well as avoids measurement noise in control inputs. Additionally, the fixed feedback gains of the sliding mode controller are redesigned as adaptive gains, which provide better correction actions for larger tracking errors. A stability analysis of the proposed control solution, based on Lyapunov’s method, is provided. The effectiveness of the proposed controller is demonstrated through its application to a Gough-Stewart platform (MISTRAL parallel robot) in various real-time experimental scenarios. The proposed approach is compared with various controllers demonstrating its superiority. It ensures nominal root mean square tracking errors of (i) about <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$22\,\mu m$ </tex-math></inline-formula> in joint space, and (ii) about <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$27\,\mu m$ </tex-math></inline-formula> in traveling plate Cartesian position. Note to Practitioners—This paper was motivated by the problem of robustness towards uncertainties and operating conditions for PKMs and especially in industry. The literature contains some control solutions to deal with these issues by designing robust or adaptive nonlinear controllers. Indeed, despite their success, for the first type, large uncertainties may degrade the tracking performance and the robustness is not always guaranteed. Adaptive controllers can be more robust, but their tuning can be difficult and especially in the case of real-time estimation of dynamic parameters. In this paper, a new robust-based sliding mode control with adaptive feedback gains is proposed to ensure the robustness towards uncertainties and external disturbances. The idea is to design adaptive feedback gains for a model-based sliding mode control, resulting in an improved robustness, while ensuring an easy tuning of its parameters. The proposed solution is validated through real-time experiments on an industrial parallel robot, and compared with some model-based controllers. The obtained results show clearly the benefits of the proposed control design and its effectiveness and robustness. In future work, the proposed controller can be endowed with a real-time estimation of the dynamic parameters, as well as, a redesign based on the super-twisting algorithm.