Hybrid crawling–jumping dynamics of a vibration-driven bristle robot

Vibration-driven bristle robots are widely treated as pure crawlers because their propulsion relies on asymmetric friction. However, when the excitation is strong, the robot can intermittently lose ground contact and jump. In this regime, a crawling-only model not only fails to capture jumping events, but also underestimates the locomotion performance gains enabled by jump-induced flight phases. Therefore, this study establishes a hybrid dynamics model of a vibration-driven bristle robot, which describes consecutive crawling and flying stages with jumping and landing events. This event-triggered hybrid model is nonlinear and non-smooth, and it yields diverse gaits ranging from period-1 to multi-period and irregular motions. Numerical analysis, dynamics simulation and prototype experiments are then used to characterize the hybrid gaits and locomotion performance. Numerical results identify two jumping mechanisms, leg lifting and push-off, and show that appreciable jumping height and average speed occur in a parameter region where push-off jumps coexist with periodic motion. Dynamics simulations provide a quantitative check of the theoretical results. Experiments on the prototype further confirm hybrid crawl–jump gaits, achieving a maximum average speed of 24 cm/s and a maximum jump height of 6 mm. The results of this study provide a more complete theoretical description of vibration-driven bristle robots by incorporating jump-induced flight phases.