Linear-time quasi-static stability detection for modular self-reconfigurable robots

We address the problem of detecting potential instability in the planned motion of modular self-reconfigurable robots. Previous research primarily focused on determining the system's unique physical state but overlooked the mutual compensation effects of connection constraints. We introduce a linear-time quasi-static stability detection method for modular self-reconfigurable robots. The internal connections, non-connected contacts, and environmental contacts are considered, and the problem is modeled as a second-order cone program problem, whose solving time linearly increases with the number of modules. We aim to determine the critical stable state of the system and that is achieved by finding the required minimum characteristic connection strength. By analyzing the critical stable state, we can assess the system's stability and identify potential broken connection points. Furthermore, the internal stability margin is defined to evaluate the configuration's stability level. The suspension and object manipulation configurations are first demonstrated in simulation to analyze the effectiveness of the proposed algorithm. Subsequently, a series of physical experiments based on FreeSN were carried out. The calculated stable motion ranges of manipulator configurations are highly consistent with the actual sampling boundaries. Moreover, the proposed algorithm successfully predicts stability and identifies broken connections in diverse configurations, encompassing quadruped and closed-chain configurations on both even and uneven terrains. The load experiment further demonstrates that the impacts from unmodeled factors and input errors under normal conditions can be on a small scale. By combining the proposed detection method and stability margin, we open the door to realizing real-time motion planning on modular self-reconfigurable robots.