Influence of the supporting surface inclination angle on the locomotion conditions of a vibration-driven system

This paper investigates the influence of supporting surface inclination angle on the locomotion of a capsule-type robot driven by an imbalanced rotor, considering dry anisotropic friction. Using Lagrange’s second-order differential equations, a mathematical model is developed, and numerical simulations are performed with Wolfram Mathematica software. The scientific novelty lies in the comprehensive analysis of how inclination angle, coupled with anisotropic friction, affects the capsule’s motion, including the derivation of analytical conditions for maintaining a “non-detachable” motion regime and preventing backward slippage. Key results include the establishment of relationships for the maximum permissible angular velocity of the imbalanced rotor as a function of surface inclination angle and friction coefficient. It is found that this velocity is maximal on horizontal surfaces and decreases with increasing inclination, while higher backward friction coefficients allow for greater rotor speeds. The practical value of these findings is significant for the design and control of vibration-driven robots, particularly for applications such as pipeline inspection, monitoring, and cleaning, where reliable navigation across varied inclinations is crucial.