Multirepresentations and Multiconstraints Approach to the Numerical Synthesis of Serial Kinematic Structures of Manipulators

Abstract

This paper presents a set of algorithms for the synthesis of kinematic structures of serial manipulators using multiple constraint formulation and provides a performance comparison of different kinematic representations, the Denavit-Hartenberg notation, the Product of Exponentials (screws), and Roll-Pitch-Yaw angles with translation parameters. Synthesis is performed for five given tasks, and both revolute and prismatic joints can be synthesized. Two different non-linear programming optimization algorithms were used to support the findings. The results are compared and discussed. Data show that the choice of the constraint design method has a significant impact on the success rate of optimization convergence. The choice of representation has a lower impact on convergence, but there are differences in the optimization time and the length of the designed manipulators. Furthermore, the best results are obtained when multiple methodologies are used in combination. An arbitrary manipulator was designed and assembled based on a trajectory in the collision environment to demonstrate the advantages of the proposed methodology. The input/output data and synthesis methodology algorithms are provided through an open repository. INDEX TERMS robot design, serial manipulator synthesis, numerical optimization, kinematic representations I. INTRODUCTIONThe synthesis of a kinematic structure of a robot manipulator 1 is the process of finding kinematic parameters with which 2 the structure fulfills a given task. As a task, one can imagine 3 a path or trajectory that goes through the previously specified 4 poses, i.e., a predefined translation and orientation of the end-5 effector. In industry, a typical manipulator has the so-called 6 angular kinematic structure with 6 degrees of freedom (DoF), 7 and it can universally serve in various tasks. A synthesized 8 (customized) manipulator can overcome the angular robot in 9 ways such as providing the possibility of avoiding collisions 10 due to its task-specific design, reducing the cost when fewer 11 joints (motors) are needed, or even the ability to change its 12 kinematic structure during the working process as presented 13 by Brandstötter et al. [1], where increased temperature of