The authors have developed five kinds of biped locomotive robots so far. They are named BIPER-1, 2, 3, 4, and 5. All of them are statically unstable but can perform a dynamically stable walk with suitable control. BIPER-1 and BIPER-2 walk only sideways. BIPER-3 is a stilt-type robot whose foot contacts occur at a point and who can walk sideways, back ward, and forward. BIPER-4's legs have the same degrees of freedom as human legs. BIPER-5 is similar to BIPER-3, but in the case of BIPER-5 all apparatus, such as the computer, are mounted on it. This paper deals with the control theory used for BIPER-3 and BIPER-4. In both cases, basically the same control method is applied. The most important point is that the mo tion of either robot during the single-leg support phase can be approximated by the motion of an inverted pendulum. Ac cordingly, in this paper, dynamic walk is considered to be a series of inverted-pendulum motions with appropriate condi tions of connection.

In this article, we propose a new analyzing method for self-assembling systems. Its initial purpose was to predict the yield—the final amount of desired product—of our original self-assembling mechanical model. Moreover, the method clarifies the dynamical evolution of the system. In this method, the quantity of each intermediate product is adopted as state variables, and the dynamics that dominates the state variables is derived. The behavior of the system is reduced to a set of difference equations with a small degree of freedom. The concept is the same as in chemical kinetics or in population dynamics. However, it was never applied to self-assembling systems. The mathematical model is highly abstracted so that it is applicable to other self-assembling systems with only small modifications.

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