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Multi-objective optimization of 6-DOF deposition trajectories using NSGA-II

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Abstract

In fused filament fabrication, an emerging challenge lies in assuring heightened performance during material deposition, being an objective that trajectory optimization techniques can achieve. A study of the trajectory planning techniques used for material deposition and their challenges and benefits are presented. Trajectory planning focuses on movements of six degrees of freedom, carried out by a designed Hexa parallel manipulator. These layered paths are linked through proximate spatial connections, generating a continuous trajectory for the printing process. The problem of multi-objective optimization arises with decision variables that modify the fill line distance, the corner smoothing, and the layers. Also, metrics to evaluate the trajectories are defined, focused on motors’ consumption, movements’ precision, surface quality, printing time, and material used. The non-dominated sorting genetic algorithm (NSGA-II) solves this problem, and the linear programming technique for multidimensional analysis of preference (LINMAP) fixes the trajectory selection. Finally, on a gallery of parts, the trajectory optimization algorithm is implemented, and the performance of the optimal trajectories is compared against trajectories generated by free commercial software, improving its performance above 70% on superficial underfilling and coated volume error, and without control effort generated by travel movements.

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Abbreviations

% Infill:

Infill percentage

a :

Acceleration of the end-effector for printing

\(A_{123}\) :

Coordinates in the local frame

\(A_{XYZ}\) :

Coordinates in the global frame

\(C\text {-} E\) :

Control effort

d :

Diameter of the nozzle

\(D_{i+}\) :

LINMAP value of ith individual

DOF :

Degrees of freedom

\(e_{123}\) :

Unit vectors of local frame

\(e_{xyz}\) :

Unit vectors of global frame

\(F_{ij}\) :

Value of jth objective function for ith individual

\(f_{i}\) :

ith objective function

\(F_{j}^{ideal}\) :

Desired value of jth objective function

\(ISE_{L}\) :

Integral square error of linear position signals

\(ISE_{R}\) :

Integral square error of rotational position signals

\(L_{mat}\) :

Material deposited lenght

\(l_{n}\) :

Distance of the linear movement in section n

LINMAP:

Linear programming technique for multidimensional analysis of preference

NSGA:

Non-dominated sorting genetic algorithm

\(\vec {p_d}\) :

Desired linear position

\(\vec {p_r}\) :

Real linear position

RUS:

R stands for revolute joint, U universal joint and S spherical joint

\(t_{n}\) :

Printing time in section n

\(t_{rise}\) :

Rise time for printing

TOPSIS:

Technique for order of preference by similarity to ideal solution

\(\uptau _{i}\) :

Control signal of motor i

U :

Search space of optimization problem

v :

Maximum linear velocity for printing

\(Vol_{error}\) :

Absolute coated volume error

\(Vol_{total}\) :

Total volume of the part

\(\chi _{i}\) :

ith decision variable

\(\dot{\vec {x_d}}\) :

Desired linear and angular velocity

\(\dot{\vec {x_r}}\) :

Real linear and angular velocity

\(\vec {x_d}\) :

Desired linear and angular position

\(\vec {x_r}\) :

Real linear and angular position

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Acknowledgements

This work is a research product from the IMP-ING-3122 high-impact project and was supported and funded by the Research Vice-Chancellor of Universidad Militar Nueva Granada–2022.

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Author notes

  1. D. A. Nunez, M. S. Dutra, M. Mauledoux and O. F. Aviles authors contributed equally to this work.

Authors and Affiliations

  1. Robotics Laboratory, Mechanical Engineering Department, Universidade Federal do Rio de Janeiro, Av. Horácio Macedo, 2030, Rio de Janeiro, 21941-914, Brazil

    Juan C. Guacheta-Alba & Max Suell Dutra

  2. Davinci Research Group, Mechatronics Engineering Department, Universidad Militar Nueva Granada, Carrera 11, No 101-80, Bogotá, 111071, Colombia

    Diego A. Nunez, Mauricio Mauledoux & Oscar F. Aviles

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  1. Juan C. Guacheta-Alba
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Corresponding author

Correspondence to Juan C. Guacheta-Alba.

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The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Replication of results

The.mat files containing the optimal paths obtained in the MATLAB software are attached to the paper submission. In addition, these trajectories are also presented in.fig files, interactive figures that allow rotating, zooming, and other options. Finally, videos have also been attached that express the printing process of the selected pieces with the optimal trajectories.

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Technical Editor: Adriano Almeida Gonçalves Siqueira.

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Guacheta-Alba, J.C., Nunez, D.A., Dutra, M.S. et al. Multi-objective optimization of 6-DOF deposition trajectories using NSGA-II. J Braz. Soc. Mech. Sci. Eng. 45, 610 (2023). https://doi.org/10.1007/s40430-023-04495-1

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