State-Space Basins for Monopedal Jumping With Stable Landing

Abstract Maintaining stability in jumping robots remains a challenge due to their hybrid dynamics. Despite recent advances, existing research lacks a clear definition and comprehensive criteria for jumping stability. To address this gap, the definition of a post-landing stable state is presented and used to formulate state-space partitions, or post-landing stable state basins, that serve as general stability criteria for flight-to-stance tasks. A hybrid-phase approach is applied to solve the flight and stance phases as separate sub-problems through analytical and optimization-based methods, subject to nonlinear system dynamics, environmental contact constraints, and task requirements. Post-landing stable state basins are constructed for a monoped jumping robot, Salto-1P, for two tasks, targeted jumping and cat-like righting, to demonstrate the use of the basins as comprehensive criteria for jumping stability. The stance-phase sub-problem solution, or landing state basin, is analyzed to determine the effect of and identify safe sets of landing state variables for balance after landing. This basin is also validated against simulated controller-specific basins of attraction. The basins obtained reveal the relationships between stability, task requirements, initial state variables such as body orientation and velocity, and landing state variables such as body angle at landing.