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Robot path optimization based on adaptive weight pseudospectral method

Published online by Cambridge University Press:  06 August 2025

Wenzhi Zhou Open the ORCID record for Wenzhi Zhou [Opens in a new window] ,
Zhiwei Gao ,
Xin Sun  and
Licheng Fan
Wenzhi Zhou
Affiliation:
School of Mechanical and Electrical Engineering, Soochow University, Suzhou, China
Zhiwei Gao
Affiliation:
School of Mechanical and Electrical Engineering, Soochow University, Suzhou, China
Xin Sun
Affiliation:
School of Mechanical and Electrical Engineering, Soochow University, Suzhou, China
Licheng Fan*
Affiliation:
School of Mechanical and Electrical Engineering, Soochow University, Suzhou, China
*
Corresponding author: Licheng Fan; Email: fanlicheng@suda.edu.cn
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Abstract

In complex work environments, improving efficiency and stability is an important issue in robot path planning. This article proposes a new path optimization algorithm based on pseudospectral methods. The algorithm includes an adaptive weighting factor in the objective function, which automatically adjusts the quality of the path while satisfying the performance indicators of the shortest time. It also considers kinematic, dynamic, boundary, and obstacle constraints, and applies the Separating Axis Theorem collision detection method to improve computational efficiency. To discretize the continuous path optimization problem into a nonlinear programming problem, the algorithm utilizes Chebyshev polynomials for the interpolation of state and control variables, along with the adoption of the Lagrange interpolation polynomial to approximate the curve. Finally, it solves the nonlinear programming problem numerically using CasADi, which supports automatic differentiation. The results of the simulation demonstrate that the path optimized by the adaptive-weight pseudospectral method can satisfy various constraints and optimization objectives simultaneously. Experimental verification confirms the efficiency and feasibility of the proposed algorithm.

Keywords

roboticpseudospectral methodadaptive weightingpath optimizationoptimal control

Information

Type
Research Article
Information
Robotica , Volume 43 , Issue 8 , August 2025 , pp. 3011 - 3029
Copyright
© The Author(s), 2025. Published by Cambridge University Press

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References

Kim, J. and Croft, E. A., “A Benchmark Study on the Planning and Control of Industrial Robots with Elastic Joints,” In: 2015 IEEE International Conference on Advanced Intelligent Mechatronics (AIM) (2015) pp. 1378–1383.Google Scholar
Sun, Y., Wang, Y., Li, J., Qi, B. and Zhang, D., “Research on Path Tracking Optimal Control of Two-Wheel Mobile Robot Based on Adaptive Dynamic Programming,” In: 2024 36th Chinese Control and Decision Conference (CCDC) (2024) pp. 1391–1395.Google Scholar
Wu, H., Yang, J., Huang, S., Ning, X. and Zhang, Z., “Multi-objective adaptive trajectory optimization for industrial robot based on acceleration continuity constraint,” Robot Cim.-INT Manuf. 84, 102597 (2023).CrossRefGoogle Scholar
Howell, T. A., Cleac’h, S. L., Singh, S., Florence, P., Manchester, Z. and Sindhwani, V., “Trajectory optimization with optimization-based dynamics,” IEEE Robot. Autom. Lett. 7(3), 6750–6757 (2022).CrossRefGoogle Scholar
Schulman, J., Duan, Y., Ho, J., Lee, A., Awwal, I., Bradlow, H., Pan, J., Patil, S., Goldberg, K. and Abbeel, P., “Motion planning with sequential convex optimization and convex collision checking,” Int. J. Robot. Res. 33(9), 1251–1270 (August 2014).CrossRefGoogle Scholar
Li, S., Wang, J., Zhang, H., Feng, Y., Lu, G. and Zhai, A., “Incremental accelerated gradient descent and adaptive fine-tuning heuristic performance optimization for robotic motion planning,” Expert Syst. Appl. 243, 122794 (2024).CrossRefGoogle Scholar
Mukadam, M., Dong, J., Yan, X., Dellaert, F. and Boots, B., “Continuous-time gaussian process motion planning via probabilistic inference,” Int. J. Robot. Res. 37(11), 1319–1340 (2018).CrossRefGoogle Scholar
Elgindy, K. T., “Numerical solution of nonlinear periodic optimal control problems using a fourier integral pseudospectral method,” J. Process Control 144, 103326 (2024).CrossRefGoogle Scholar
Chen, R., Bai, Y., Zhao, Y., Wang, Y., Yao, W. and Chen, X., “Closed-loop optimal control based on two-phase pseudospectral convex optimization method for swarm system,” Aerosp. Sci. Technol. 143, 108704 (2023).CrossRefGoogle Scholar
Gao, D., Gong, Y., Li, C., Guo, Y., Fadda, E. and Brandimarte, P., “Adaptive pseudospectral successive convex optimization for six-degree-of-freedom powered descent guidance,” Aerosp. Sci. Technol. 155, 109544 (2024).CrossRefGoogle Scholar
Zhao, Y., Lin, H.-C. and Tomizuka, M., “Efficient Trajectory Optimization for Robot Motion Planning,” In: 2018 15th International Conference on Control, Automation, Robotics and Vision (ICARCV) (2018) pp. 260–265.Google Scholar
Moreno-Martín, S., Ros, L. í. and Celaya, E., “A Legendre-Gauss Pseudospectral Collocation Method for Trajectory Optimization in Second Order Systems,” In: 2022 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (2022) pp. 13335–13340.Google Scholar
Crain, A. and Ulrich, S., “Experimental validation of pseudospectral-based optimal trajectory planning for free-floating robots,” J. Guid., Control, Dyn. 42(8), 1726–1742 (2019).CrossRefGoogle Scholar
Zhang, X. and Shi, G., “Multi-objective optimal trajectory planning for manipulators in the presence of obstacles,” Robotica 40(4), 888–906 (2022).CrossRefGoogle Scholar
Teo, K. L., Li, B., Yu, C. and Rehbock, V., “Chapter 9 - Optimal Control Problems with State and Control Constraints,” In: Applied and Computational Optimal Control (2021) pp. 315–369.Google Scholar
Peng, H. A. N., Jia-yuan, S. H. A. N. and Xiu-yun, M. E. N. G., “Re-entry trajectory optimization using a multiple-interval radau pseudospectral method,” J. Beijing Inst. Tech. 22(1), 20–27 (2013).Google Scholar
Chang, J.-W. and Kim, M.-S., “Efficient triangle–triangle intersection test for obb-based collision detection,” Comput. Graph. 33(3), 235–240 (2009).CrossRefGoogle Scholar
Prasanth, D. R. and Shunmugam, M. S., “Collision detection during planning for sheet metal bending by bounding volume hierarchy approaches,” Int. J. Comput. Integr. Manuf. 31(9), 893–906 (2018).CrossRefGoogle Scholar
Kalantari, B., “An algorithmic separating hyperplane theorem and its applications,” Discrete Appl. Math. 256, 59–82 (2019). Distance Geometry Theory and Applications (DGTA 16).CrossRefGoogle Scholar
Chang, J.-W., Wang, W. and Kim, M.-S., “Efficient collision detection using a dual obb-sphere bounding volume hierarchy,” Comput. Aided Des. 42(1), 50–57 (2010).CrossRefGoogle Scholar
Gan, B. and Dong, Q., “An improved optimal algorithm for collision detection of hybrid hierarchical bounding box,” Evolut. Intell. 15(4), 2515–2527 (2022).CrossRefGoogle Scholar
Wang, T., Wang, L., Li, D., Cai, J. and Wang, Y., “Monte carlo-based improved ant colony optimization for path planning of welding robot,” J. King Saud Univer. - Comput. Inf. Sci. 35(7), 101603 (2023).CrossRefGoogle Scholar
Riboli, M., Jaccard, M., Silvestri, M., Aimi, A. and Malara, C., “Collision-free and smooth motion planning of dual-arm cartesian robot based on b-spline representation,” Robot. Auton. Syst. 170, 104534 (2023).CrossRefGoogle Scholar
Abdelkhalik, O., Zou, S., Robinett, R., Bacelli, G., Wilson, D. and Coe, R., “Controlof three degrees-of-freedom wave energy converters using pseudo-spectralMethods,” J. Dyn. Syst., Meas., Control 140(7), 01 (2018).CrossRefGoogle Scholar
Keil, R. E., Kumar, M. and Rao, A. V., “Warm start method for solving chance constrained optimal control problems using biased kernel density estimators,” J. Dyn. Syst., Meas., Control 143(12), 09 (2021).CrossRefGoogle Scholar
Trefethen, L. N., “Barycentric interpolation formula,” In: Approximation Theory and Approximation Practice, Extended Edition, vol. 128, Other Titles in Applied Mathematics. SIAM (2019) pp. 33–41.CrossRefGoogle Scholar
Liu, H., Huang, J. and Zhang, W., “Numerical algorithm based on extended barycentric lagrange interpolant for two dimensional integro-differential equations,” Appl. Math. Comput. 396, 125931 (2021).Google Scholar
Waldvogel, J., “Fast construction of the fejér and clenshaw–curtis quadrature rules,” Bit 46(1), 195–202 (2006).CrossRefGoogle Scholar
Nazmara, M. M. F. G. and Ahmadi, S. M., “Exponentially convergence for the regressor-free adaptive fuzzy impedance control of robots by gradient descent algorithm,” Int. J. Syst. Sci. 51(11), 1883–1904 (2020).CrossRefGoogle Scholar
Elhesasy, M., Dief, T. N., Atallah, M., Okasha, M., Kamra, M. M., Yoshida, S. and Rushdi, M. A., “Non-linear model predictive control using casadi package for trajectory tracking of quadrotor,” Energies 16(5), 2143 (2023).CrossRefGoogle Scholar
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