Infinitely many two-variable generalisations of the Alexander-Conway polynomial

We show that the Alexander-Conway polynomial Delta is obtainable via a particular one-variable reduction of each two-variable Links-Gould invariant LG^{m,1}, where m is a positive integer. Thus there exist infinitely many two-variable generalisations of Delta. This result is not obvious since in the reduction, the representation of the braid group generator used to define LG^{m,1} does not satisfy a second-order characteristic identity unless m=1. To demonstrate that the one-variable reduction of LG^{m,1} satisfies the defining skein relation of Delta, we evaluate the kernel of a quantum trace.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-18.abs.htm

QUANDLE TWISTED ALEXANDER INVARIANTS

We establish a quandle version of the twisted Alexander polynomial. We also develop a theory that reduces the size of a twisted Alexander matrix with column relations. The reduced matrix can be used to refine invariants derived from the twisted Alexander matrix

Simultaneous Optimization of a Wheeled Mobile Robot Structure and a Control Parameter

A wheeled mobile mechanism with a passive and/or active linkage mechanism for traveling in the outdoor environment is developed and evaluated. In our previous research, we developed a wheeled mobile robot which has six wheels and a passive linkage mechanism, and its maneuverability was experimentally verified. The ability to climb over a 0.20 [m] high bump, which is twice height of the wheel diameter of 0.10 [m], was achieved, and the mobile robot can climb up continuous steps of 0.15 [m] high. In this research, we optimized the mobile robot linkage mechanisms and a controller parameter by evolutionary algorithm and dynamics engine in numerical simulations. The evolutionary algorithm employed in this research is Genetic Algorithm, and Open Dynamics Engine is used for dynamics calculation. To optimize the linkage mechanism and a controller parameter, we investigated outdoor environment for the mobile robot, for example obstacles, steps, and stairs. And, we selected typical three kinds of outdoor environments, 0.20 [m] high bump, right angle stairs of 0.15 [m] high, and angled stairs of 0.15 [m] high. In the numerical simulations, though the mobile robot using parameters which express our existing robot could climb up/down the 0.20 [m] high bump, but it could not achieve climbing up/down the two kinds of stairs. On the other hand, the optimized parameter mobile robot could climb up/down the three kinds of typical environments