Analysis of Various Manipulator Configurations

Design of Various Manipulator Configurations Based on Multi-Objective Black-Box Optimization

This study parametrizes joint types and link lengths, automatically generates URDFs, and performs multi-objective optimization from the perspectives of end-effector reachability and joint torque to discuss the structures of various manipulators.

Design parameters handled in this study: The joint type J_i and link length L_i are varied as design parameters.

Objective functions for multi-objective optimization: The left image shows end-effector reachability, while the right image shows necessary joint torque.

Experiments: Multi-Objective Optimization of 6-DOF Manipulator

Optimization results for a 6-DOF manipulator: The upper figure visualizes the sampling results, color-coded based on differences in the first four joint types. The lower figure presents a subset of the solutions, showing end-effector reachability, joint torque, and four postures generated by assigning random joint angles.

A general trend observed is that, even within the same joint structure, increasing reachability often results in placing two DOFs near the origin (shoulder), one Pitch or Roll joint at the intermediate position (elbow), and three DOFs at the end-effector (wrist). The specific joint configurations are discussed below. PRRY exhibits both high overall reachability and low required torque. In particular, PRRY has low torque around the y-axis, while RPPY has low torque around the x-axis. RPYP places the Yaw joint in the middle, allowing the end-effector to achieve various postures. However, its reachability is reduced in positions close to the body. This structure reflects a conflict between two motives, resulting in an indecisive configuration. One aims to determine the 3D orientation with the initial RPY and place a Pitch joint in the middle. The other seeks to allocate all three RPY degrees of freedom to the end-effector. YPPY has two consecutive Pitch joints after a Yaw joint, making it susceptible to gravitational effects. However, its overall reachability remains quite high. This configuration is used in manipulators such as ALOHA, COBOTTA, and xArm 6. Manipulators mounted on quadruped robot platforms like Boston Dynamics' Spot also share this structure. YPPP is the configuration adopted by ARX and myCobot. Similar to YPPY, it is directly influenced by gravitational effects. With three consecutive Pitch joints, its reachability is relatively low, but it offers the simplest and most intuitive kinematics.

Experiments: Multi-Objective Optimization of 7-DOF Manipulator

Optimization results for a 7-DOF manipulator: The upper figure visualizes the sampling results, color-coded based on differences in the first four joint types. The lower figure presents a subset of the solutions, showing end-effector reachability, joint torque, and four postures generated by assigning random joint angles.

Overall, the trends observed in the 7-DOF case are somewhat different from those in the 6-DOF case. While two degrees of freedom are concentrated near the origin (shoulder) and three degrees of freedom at the end-effector (wrist), as in the 6-DOF case, there are two distinct approaches for distributing the remaining two degrees of freedom: one where they are grouped around the elbow, dividing the entire linkage into a 1:1 ratio, and another where they are distributed more evenly in a 1:1:1 ratio. The specific joint configurations are discussed below. PRRY exhibits both high reachability and low required torque, consistent with the results from the 6-DOF case. As the degrees of freedom at the end-effector increase, reachability improves, but the required torque also increases. YPRR is a modification of the 6-DOF PRRY with an additional Yaw joint at the base. Since the first Yaw joint does not experience significant torque, the required torque remains nearly the same as in the 6-DOF PRRY, while reachability is improved. YPPP, YPPY, and YPYP have simple and intuitive joint structures, but as in the 6-DOF case, are more directly affected by gravitational effects. All three exhibit similar performance, but among them, YPYP has the lowest torque requirements. YPYP is one of the most common structures in industrial robots, and manipulators such as Franka Emika Panda, Sawyer, and Kinova Gen3 adopt similar configurations. Additionally, a robot with the YPRP structure is the Robai Cyton Gamma.

Bibtex

@article{kawaharazuka2025manip,
  author={K. Kawaharazuka and K. Yoneda and T. Hattori and S. Inoue and K. Okada},
  title={Analysis of various manipulator configurations based on multi-objective black-box optimization},
  journal={Advanced Robotics},
  publisher={Taylor \& Francis},
  doi={10.1080/01691864.2025.2607670},
  year={2025},
}