Keywords: Extremely Modular System, Pipe-Z, Arm-Z, discrete optimization, dihedral rotation, “snakebot”, reconfiguration.

Pipe-Z (PZ) is a parametric design system which comprised of a congruent modules (PZM) allows the creation of complex three-dimensional, single-branch structures which can be represented by mathematical knots. Once the geometrical parameters are set for the PZM, the shape of PZ is controlled solely by relative twists of the PZMs in a sequence. Therefore each PZM has one degree of freedom (1DOF). This paper presents the preliminary optimization of PZ reconfiguration from a “straight tube” to a half-torus. Here the displacement of PZMs transverse to the “bending direction” is to be minimized. In other words, it resembles “truing” of a wheel. In the considered case, the PZ is comprised of eight hexagonal PZMs. Thus every PZM can have six possible positions relative to the previous module. The initial (PZI) and target (PZT) configurations are given. Since the time-steps and relative twists are discrete, it is a discrete optimization and has combinatorial nature. The number of possible configurations grows astronomically with the assumed number of time-steps from one position to another and the number of PZMs. However, the optimization algorithm can be naturally parallelized. At first the concept of PZ is outlined, followed by the experiment. The results are illustrated and discussed.

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