The contact force between the polishing tool and the workpiece is crucial in determining the surface quality in robotic polishing. Different from rigid end-effectors, this paper presents a novel compliant end-effector (CEE) for robotic polishing using flexible beams. The flexibility of the CEE helps to suppress the excessive displacement caused by the inertia of the polishing robot and avoids damaging the polishing tool and workpiece surface. In addition, the contact force can also be precisely estimated via the measurement of the CEE’s displacement using a capacitive position sensor. The design, modeling and experimental validation of the CEE are presented. Firstly, the analytical model of the CEE is established using the stiffness matrix method. Subsequently, the analytical model is verified by finite element analysis. Further, a prototype is manufactured, and its characteristics and performance are experimentally tested. The equivalent stiffness is measured to be 0.335 N/μm, and the first natural frequency along its working direction is 42.1 Hz. Finally, the contact force measurement using the CEE is compared with a force sensor. Under open-loop condition, the resolution of the contact force measurement is found to be 0.025 N, which makes the fine tuning of the contact force possible in robotic polishing.

Traditional industrial robots often face challenges in achieving a perfectly polished surface on a workpiece because of their high mechanical rigidity. The active compliance force control device installed at the robotic arm’s end enables high-precision contact force control between the grinding tool and the workpiece. However, the complex hysteresis nonlinearity between cylinder air pressure and output force, as well as various random disturbances during the grinding process, can affect the accuracy of the contact force and potentially impact the grinding effect of the workpiece, even causing irreversible damage to the surface of the workpiece. Given the complex random variation of cylinder output force in the actual grinding process, a rate-dependent hysteresis model based on diagonal recurrent neural network and Pradtl–Ishlinskii models named dRNN-PI is designed to compensate for the complex nonlinear hysteresis of the cylinder and calculate the desired air pressure to maintain a steady contact force on the workpiece. The proxy-based sliding mode control (PSMC) is utilized to quickly track the desired air pressure without overshooting. This paper also proves the controller’s stability using the Lyapunov-based methods. Finally, the accuracy of the proposed hysteresis compensation model and the effectiveness and robustness of the PSMC are verified by experiment results.

This paper proposes a “planning and control” scheme for a compliant mechanism (CM) based on a pneumatic actuator (PAC) with hysteresis nonlinearity and full-state constraints. In the planning part, a novel direct inverse model is presented to compensate for hysteresis nonlinearity, enabling more accurate planning of the desired air pressure based on the desired contact force. In the control part, by fusing fuzzy logic systems (FLSs) and an extended state observer (ESO), a fuzzy ESO is developed to observe the external disturbance and the rate of change of the air pressure. Additionally, the challenges in the controller design caused by full-state constraints are overcome by constructing barrier Lyapunov functions (BLFs). It is proved that all signals of the closed-loop system are bounded, and the tracking error of the air pressure can converge to a small neighborhood of the origin. Finally, the effectiveness and robustness of the proposed method are verified by hardware experiments, which also show that the root mean square errors of force control accuracies are within 2N, achieving satisfactory force control effects.