Co-bots are generally manufactured as general-purpose machines, and their performance often needs to be more specified for actual use by users. In this study, Multidisciplinary Design Optimization (MDO) is used in the design process to obtain the optimal solution based on the results of analysis of assignments (a group of variables consisting of design variables, etc.) that span multiple disciplines [1]. In this study, we focused on two regions in MDO, the geometric and dynamic regions, and optimized link lengths and other parameters, minimizing the mass of the entire manipulator [2]. However, the optimization in the two regions already took a long computation time, and the computation cost must be addressed. This paper aims to speed up the computation using the DIRECT (DIvided RECTangle method) [3] optimization method.

The DIRECT method is a direct optimization method and a type of Lipschitz optimization. It is a method that compares the value of the objective function at the center point of a range divided into rectangles and repeatedly divides the rectangle with the smallest (most significant) value into further rectangles and compares them. This method can be applied to problems with multiple peaks and derive a globally optimal solution. 

The DIRECT method first trisects the Potentially Optimum Interval (POI) to create new regions. In each region, the midpoint is the representative point, and the objective function value at the representative point is assumed to be the value for the entire region. In all regions, the representative points are compared for each region of the same width, and the point with the smallest objective function is the POI for the width of the region. The termination decision is generally made by giving a threshold value to the number of iterations.

The above figure shows the architecture of the multidisciplinary design optimization applying the DIRECT method in this paper. In this paper, we aim to speed up the overall calculation by using the DIRECT method for the MDO calculation and the analysis of each region.

The above table shows the results of computation time for the different methods and processes. The round-robin method requires less computation time due to the smaller number of partitions, but the accuracy needs to be improved due to the smaller number of partitions. On the other hand, the calculation using the DIRECT method takes about 2 hours and 20 minutes in parallel computation, and the application of parallel computation and the DIRECT method has resulted in higher speed and accuracy.

The second table shows the optimization results. The optimization results for the conventional method No.0[2] and the six methods No.1~6 are shown. Compared with No.0, which is the result of the traditional method, the DIRECT method is more accurate in determining both the link length and the relative position of the trajectory.

This paper presents a method and results of applying the DIRECT method to accelerate calculations in multidisciplinary design optimization to reduce the weight of manipulators. Specifically, the DIRECT method was used not only for the optimization calculation in multidisciplinary design optimization but also for the analysis of each region. The calculation time was reduced, and the accuracy was improved.