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In parallel mechanisms with redundant actuators, actuator forces are underspecified because of redundancy. In this paper, the method to minimize a maximum actuator force was proposed. At first, parallel mechanism with two redundant actuators and Stewart platform model using the linear shaft motor were developed. This redundant parallel mechanism was consists of Stewart platform and additional 2 redundant actuators. Inverse dynamics of each mechanisms were formulated. Secondly, effectiveness of dynamic control of Stewart platform was experimentally confirmed. Finally, the method to minimize a maximum actuator force using Linear Matrix Inequality (LMI) was proposed. And the effectiveness of the proposed method was confirmed by simulation.

This paper deals with the global optimization algorithm of the Bilinear Matrix Inequalities (BMIs) based on the Unimodal Normal Distribution Crossover (UNDX) GA. First, analyzing the structure of the BMIs, the existence of the typical difficult structures is confirmed. Then, in order to improve the performance of algorithm, based on results of the problem structures analysis and consideration of BMIs characteristic properties, we proposed the algorithm using primary search direction with relaxed Linear Matrix Inequality (LMI) convex estimation. Moreover, in these algorithms, we propose two types of evaluation methods for GA individuals based on LMI calculation considering BMI characteristic properties more. In addition, in order to reduce computational time, we proposed parallelization of RCGA algorithm, Master-Worker paradigm with cluster computing technique.