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An algorithm to resolve the optimal locomotion problem of modular robots

Mencek, Hakan
In this study, a novel optimal motion planning algorithm is developed for the locomotion of modular robots. The total energy consumption of the robot is considered to be the optimization criteria. In order to determine the energy consumption of the system, the kinematic and dynamic analyses of the system are performed. Due to the variable number of modules in the system, a recursive formulation is developed for both kinematic and dynamic analyses. Coulomb's static and dynamic friction models are used to model the frictional forces at the contact points. In modular robot locomotion, the number of contact points and the positions of the contact points vary with time. As a result, the structure of the dynamic equilibrium equations changes. Depending upon the number and type of contacts (i.e., contact with static or dynamic friction), the dynamic equilibrium equations may lead to an overdetermined, regular or underdetermined system of equations. The last case implies that the system is statically indeterminate. A novel solution method, which takes into account the deflections of the flexible links in the modular robot, is introduced to resolve this statical indeterminacy problem. Another important contribution is the identification of the singularities associated with the dynamic equilibrium equations. It is shown that these equations become singular when all tangential contact point velocities are in the same direction. The developed optimal motion planning algorithm ensures that such singularities are avoided. The procedure is illustrated via a modular, self reconfigurable robot called MTRAN. However, the method may be easily extended to other modular robots by changing the structural parameters. In order to display the resulting motion, a visual simulation program is developed for MTRAN using the commercial software Mathematica.