Research on the Static Stability of a Climbing Robot with a Vacuum Gripper

The paper presents a static model for estimating the minimum required vacuum pressure in the suction gripper of a climbing robot when it is held on an inclined surface by a single supporting gripper. The system configuration is described by the surface inclination angle β , the platform rotation angle γ , as well as the geometric parameters and the position of the center of mass. An analytical expression Δ P_min( β , γ ) is obtained, taking into account three limiting mechanisms of stability loss: detachment, slippage, and overturning. The minimum vacuum is determined as the maximum of the corresponding

force and moment constraints with the introduction of a safety factor that accounts for atmospheric pressure reduction, variations in the friction coefficient, and dynamic disturbances. To consider the spatial orientation of the center of mass, a quaternion-based rotation formalism is employed. An experimental test bench with an adjustable inclination angle and a pneumatic system enabling controlled variation of vacuum pressure and detection of the critical onset of motion is developed. An algorithm for determining the critical vacuum level based on pressure and platform rotation angle measurements is proposed. А comparison of theoretical and experimental Δ P values for several configurations ( β , γ ) is performed. The discrepancy is shown to remain within a few percent; the mean absolute percentage error for absolute pressure is 2.26 %, while the mean absolute error in vacuum pressure is about 2.2 kPa. The results confirm the adequacy of the proposed model and its applicability to the design of vacuum holding systems, selection of gripper geometry, and synthesis of control algorithms for robot operation near the boundaries of static stability. The proposed approach provides a unified analytical expression for analyzing various robot configurations and can be extended to multi-gripper systems and optimization of center-of-mass placement and vacuum system parameters.

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