Matrix Structure Driven Interior Point Method for Quadrotor Real-Time Trajectory Planning
Sequential convex programming (SCP) has been recently employed in various trajectory planning problems, including entry flight, planetary landing, and aircraft formation. In SCP, convex programming subproblems are sequentially solved to obtain the optimum of original nonconvex problems. For SCP-base...
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doaj-97c604566ee04c3dad879e907bc52e662021-03-29T23:37:02ZengIEEEIEEE Access2169-35362019-01-017909419095310.1109/ACCESS.2019.29267828755844Matrix Structure Driven Interior Point Method for Quadrotor Real-Time Trajectory PlanningGuangtong Xu0https://orcid.org/0000-0003-0683-5992Teng Long1Zhu Wang2Yan Cao3School of Aerospace Engineering, Beijing Institute of Technology, Beijing, ChinaSchool of Aerospace Engineering, Beijing Institute of Technology, Beijing, ChinaSchool of Aerospace Engineering, Beijing Institute of Technology, Beijing, ChinaSchool of Aerospace Engineering, Beijing Institute of Technology, Beijing, ChinaSequential convex programming (SCP) has been recently employed in various trajectory planning problems, including entry flight, planetary landing, and aircraft formation. In SCP, convex programming subproblems are sequentially solved to obtain the optimum of original nonconvex problems. For SCP-based quadrotor trajectory planning, this paper proposes a matrix-structure-driven interior point method (MSD-IPM) to improve the efficiency of solving search directions in convex programming. In MSD-IPM, primal-dual systems for solving search directions are derived from the Karush-Kuhn-Tucher (KKT) conditions of quadrotor trajectory planning subproblems. Then, the successive elimination technique is used to solve the inverse of large-scale coefficient matrices of primal-dual systems by more efficient operations on small-scale matrices. In successive elimination, the positive definiteness of several small-scale matrices is used to enhance the numerical stability of computing search directions, and the specific diagonal structures of small-scale matrices are exploited to efficiently compute the search directions. The complexity analysis shows that the efficiency of the proposed method is about one order of magnitude higher than that of the standard IPM. The comparative studies on simulation experiments demonstrate that the MSD-IPM generally outperforms several well-known optimizers (e.g., MOSEK, SDPT3, and SeDuMi) in terms of efficiency and robustness. Finally, the indoor trajectory tracking experiments indicate that the proposed method can generate smooth trajectories for real-world applications.https://ieeexplore.ieee.org/document/8755844/Quadrotor trajectory planningsequential convex programminginterior point methodmatrix structure exploitation |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Guangtong Xu Teng Long Zhu Wang Yan Cao |
spellingShingle |
Guangtong Xu Teng Long Zhu Wang Yan Cao Matrix Structure Driven Interior Point Method for Quadrotor Real-Time Trajectory Planning IEEE Access Quadrotor trajectory planning sequential convex programming interior point method matrix structure exploitation |
author_facet |
Guangtong Xu Teng Long Zhu Wang Yan Cao |
author_sort |
Guangtong Xu |
title |
Matrix Structure Driven Interior Point Method for Quadrotor Real-Time Trajectory Planning |
title_short |
Matrix Structure Driven Interior Point Method for Quadrotor Real-Time Trajectory Planning |
title_full |
Matrix Structure Driven Interior Point Method for Quadrotor Real-Time Trajectory Planning |
title_fullStr |
Matrix Structure Driven Interior Point Method for Quadrotor Real-Time Trajectory Planning |
title_full_unstemmed |
Matrix Structure Driven Interior Point Method for Quadrotor Real-Time Trajectory Planning |
title_sort |
matrix structure driven interior point method for quadrotor real-time trajectory planning |
publisher |
IEEE |
series |
IEEE Access |
issn |
2169-3536 |
publishDate |
2019-01-01 |
description |
Sequential convex programming (SCP) has been recently employed in various trajectory planning problems, including entry flight, planetary landing, and aircraft formation. In SCP, convex programming subproblems are sequentially solved to obtain the optimum of original nonconvex problems. For SCP-based quadrotor trajectory planning, this paper proposes a matrix-structure-driven interior point method (MSD-IPM) to improve the efficiency of solving search directions in convex programming. In MSD-IPM, primal-dual systems for solving search directions are derived from the Karush-Kuhn-Tucher (KKT) conditions of quadrotor trajectory planning subproblems. Then, the successive elimination technique is used to solve the inverse of large-scale coefficient matrices of primal-dual systems by more efficient operations on small-scale matrices. In successive elimination, the positive definiteness of several small-scale matrices is used to enhance the numerical stability of computing search directions, and the specific diagonal structures of small-scale matrices are exploited to efficiently compute the search directions. The complexity analysis shows that the efficiency of the proposed method is about one order of magnitude higher than that of the standard IPM. The comparative studies on simulation experiments demonstrate that the MSD-IPM generally outperforms several well-known optimizers (e.g., MOSEK, SDPT3, and SeDuMi) in terms of efficiency and robustness. Finally, the indoor trajectory tracking experiments indicate that the proposed method can generate smooth trajectories for real-world applications. |
topic |
Quadrotor trajectory planning sequential convex programming interior point method matrix structure exploitation |
url |
https://ieeexplore.ieee.org/document/8755844/ |
work_keys_str_mv |
AT guangtongxu matrixstructuredriveninteriorpointmethodforquadrotorrealtimetrajectoryplanning AT tenglong matrixstructuredriveninteriorpointmethodforquadrotorrealtimetrajectoryplanning AT zhuwang matrixstructuredriveninteriorpointmethodforquadrotorrealtimetrajectoryplanning AT yancao matrixstructuredriveninteriorpointmethodforquadrotorrealtimetrajectoryplanning |
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1724189221891080192 |