Self-assembly of modular robots from finite number of modules using graph grammars

Abstract

A passive compass gait consists of the stance and collision phases. The author clarified that the former is unstable and the latter is marginally stable, and that the state error norm tends to increase during the stance phases and decreases during the collision phases. The convergence property is, however, complicated and the overall self-stabilization mechanism is still unclear. This paper then investigates it from the mechanical energy point of view. First, we introduce the linearized mechanical energy that leads to the linearized dynamic equation of the compass-like biped robot, and numerically show that its error norm almost monotonically converges to zero. Second, we numerically show that the monotonic convergence comes from the fact that the error of the angular positions is one digit smaller than that of the angular velocities by using approximate difference functions that varies depending on the slope.