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Trajectory Planning Based on Optimal Control and Exact Derivatives

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Intelligent Robotics and Applications (ICIRA 2019)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11745))

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Abstract

To solve the trajectory planning problem, a path constrained optimal control model is established and is solved by gradient-based numerical method. Since it is very computationally expensive for the adjoint equation method to calculate the gradients of path constraints, an exact derivative method is used to calculate the gradients of objective and path constraints accurately and efficiently. The method is achieved by regarding the objective and path constraints as explicit functions of the parametrized controls. Then the gradient can be calculated in reverse mode of automatic differentiation which requiring Jacobian information of the integrator for solving state equation. The Jacobian matrix of the new states with respect to current states and controls is analytically derived for the 4th-order Runge-Kutta method and is calculated and stored when integrating the state equation. From a study case, an OCP with inequality path constraints was discretized to nonlinear programming problem by control vector parameterization (CVP) and was solved by sequential quadratic (SQP) method. The simulation case for a differential drive robot demonstrates the efficiency of the proposed method.

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Acknowledgement

This research was supported by the National Natural Science Foundation of China (Grant No. 51604296 and 61573378) and the Fundamental Research Funds for the Central University (Grant No. 19CX02066A).

Author information

Authors and Affiliations

  1. College of Information and Control Engineering, China University of Petroleum (East China), Qingdao, 266580, China

    Xiaodong Zhang & Ling Tu

  2. Key Laboratory of Unconventional Oil & Gas Development, China University of Petroleum (East China), Ministry of Education, Qingdao, 266580, China

    Jiafeng Wu

  3. College of Automation, Beijing University of Posts and Telecommunications, Beijing, China

    Shurong Li

Authors
  1. Xiaodong Zhang
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  2. Ling Tu
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  3. Jiafeng Wu
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  4. Shurong Li
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Corresponding authors

Correspondence to Xiaodong Zhang or Jiafeng Wu .

Editor information

Editors and Affiliations

  1. Shenyang Institute of Automation, Shenyang, China

    Haibin Yu

  2. Shenyang Institute of Automation, Shenyang, China

    Jinguo Liu

  3. Shenyang Institute of Automation, Shenyang, China

    Lianqing Liu

  4. University of Portsmouth, Portsmouth, UK

    Zhaojie Ju

  5. Shenyang Institute of Automation, Shenyang, China

    Yuwang Liu

  6. University of Portsmouth, Portsmouth, UK

    Dalin Zhou

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Zhang, X., Tu, L., Wu, J., Li, S. (2019). Trajectory Planning Based on Optimal Control and Exact Derivatives. In: Yu, H., Liu, J., Liu, L., Ju, Z., Liu, Y., Zhou, D. (eds) Intelligent Robotics and Applications. ICIRA 2019. Lecture Notes in Computer Science(), vol 11745. Springer, Cham. https://doi.org/10.1007/978-3-030-27529-7_49

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  • DOI: https://doi.org/10.1007/978-3-030-27529-7_49

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-27528-0

  • Online ISBN: 978-3-030-27529-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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