Multidisciplinary Design Optimization for Weight Reduction of Six DoF Manipulator using Directional Manipulability Index

Kaho Hibino, Mitsuru Endo, Yukio Tsutsui

3rd International Conference of IFToMM for SDG I4SDG2025

Background

Industrial robots consume significant material and energy resources during their manufacture and operation. Reducing the weight of robot manipulators can cut energy consumption (SDG7, SDG13), conserve material resources (SDG12, SDG15), and improve collaborative safety (SDG8, SDG9).

Past lightweight designs focused on individual components (e.g., composite materials, modular actuators) [2] [3] [4] [5]. However, comprehensive optimization across disciplines remains limited in robotics. Multidisciplinary Design Optimization (MDO), proven in aerospace, offers a systematic framework for this [9], but its application to robots is still rare.

This study aims to reduce the weight of a 6 DoF manipulator through MDO, introducing new indices—the Directional Manipulability Index (DMI) and the Directional Energy Index (DEI)—to account for path direction in the optimization [6] [7].

Method

The proposed approach uses a sequential MDO architecture with:

System-Level Optimizer (SLO): Minimizes total mass by selecting link lengths.
Sub-Optimizer 1 (SO1): Optimizes the manipulator’s base location to maximize a specified index (Manipulability, DMI, or DEI).
Sub-Optimizer 2 (SO2): Selects motors and reducers minimizing joint weight while ensuring torque/speed capacity.

Key new indices:

DMI (Directional Manipulability Index): Evaluates manipulability along the task path direction, capturing directional ease of movement [1] [6].
DEI (Directional Energy Index): Estimates kinetic energy considering the path direction, supporting energy-efficient design [7].

spaces

Fig.2 Relationship between operational space, joint space, and parametric variable Space

The overall optimization architecture integrates these indices to better evaluate the manipulator’s relative location to the path (see Fig. 3). Optimization problems were formulated for each level, with bounds for link lengths and base position. The DIRECT algorithm was used for optimization [9].

MDO

Fig.3 Architecture of Multidisciplinary Design Optimization used in this study. It is composed of a system-level optimizer and two sub-optimizers

A pick-and-place path was used as the target task, with travel times in three cases.

Result

The manipulability measure alone led to heavier designs, failing to account for path direction [1].
Incorporating DMI reduced weight by ~16–17% compared to manipulability-based optimization [6].
Using DEI achieved even greater reductions of ~35–54%, especially effective in slower motion scenarios requiring less kinetic energy [7].
Results demonstrated that considering directionality prevents over-design in unnecessary directions and allows for shorter link lengths and lighter actuators.

Conclusion

This study applied MDO to minimize the weight of a 6 DoF manipulator by introducing DMI and DEI. These indices account for path direction, improving design efficiency compared to conventional manipulability measures.

Key outcomes:

Up to 17% weight reduction with DMI [6].
Up to 54% weight reduction with DEI [7].
Enhanced energy efficiency and task-specific optimization.

Future work will expand MDO to more design disciplines, integrate advanced optimization methods, and validate the approach through physical experiments.

References

[1] T. Yoshikawa: Manipulability of robotic mechanisms, The International Journal of Robotics Research 4(2), pp.3–9 (1985).

[2] R. Citalan-Lara, C. A. Cruz-Villar: Multidisciplinary Optimization of Servodrives for Robot Manipulators, 2014 IEEE/ASME International Conference on Advanced Intelligent Mechatronics, pp.38–43 (2014).

[3] J. Zhang, B. Li, Y. Liu: Multidisciplinary collaborative optimization design of robots, International Technology and Innovation Conference 2009 (ITIC 2009), Xi’an, China, pp.1–5 (2009).

[4] J. Zhang, J. Liu, C. Wang, Y. Song, B. Li: Study on multidisciplinary design optimization of a 2-degree-of-freedom robot based on sensitivity analysis and structural analysis, Advances in Mechanical Engineering. 2017;9(4) (2017).

[5] T. Chen, C. Yang: Multidisciplinary design optimization of mechanisms, Advances in Engineering Software, Vol.36, Issue 5, pp.301–311 (2005).

[6] K. Hibino, M. Endo, H. Nakamura, S. Tanaka: Elementary Multidisciplinary Optimization of Workspace and Driving Mechanism to Reduce Weight of Industrial Robots, ROBOMECH2023, 2P2-A20 (2023) (IN JAPANESE).

[7] K. Hibino, M. Endo, Z. Shan, Y. Tsutsui: Location Optimization of Manipulator to Minimize Energy Considering the Path Direction, SII2025, 2925 (ACCEPTED).

[8] J. Hickel: Less is More - How degrowth will save the world, Windmill Books (2021).

[9] Donald R. Jones, Joaquim R. R. A. Martins: The DIRECT Algorithm: 25 Years Later, Journal of Global Optimization, 79, pp.521–566 (2021).

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