Global dynamics mapping and low-energy bidirectional control of a vibro-impact capsule

The nonlinear dynamics and motion control of vibro-impact capsule systems, characterized by non-smooth interactions, present critical challenges for reliable locomotion in complex engineering scenarios. This study systematically investigates the influence of multi-parameter coupling on the dynamic behavior of a vibro-impact capsule system and proposes a global dynamics-based motion regulation strategy. By constructing dynamic distribution maps within the excitation parameter plane, the evolution of periodic, chaotic, and multistable responses under variations in clearance ratio, damping ratio, stiffness ratio, and mass ratio is comprehensively revealed. It is found that structural parameter tuning exerts a great influence on the contraction or expansion of simple motion regimes and on the suppression or emergence of multistable behaviors. More importantly, to address the practical requirement of avoiding complex and unpredictable motions while maintaining maneuverability, bidirectional motion control strategy is established based on the average velocity characteristics of simple period-1 responses. It demonstrates that directional switching and speed-mode selection can be achieved either through fine adjustments of excitation frequency or solely by modulating initial perturbations, without necessitating any modification of system parameters. This work not only advances the fundamental understanding of non-smooth dynamical transitions but also offers a concrete theoretical basis and practical guidance for the design and efficient operation of vibro-impact capsule robots.