In this article, we study the problem of trajectory planning for a class of nonlinear systems with convex state/control constraints and nonconvex state constraints with concave constraint functions. This corresponds to a challenging nonconvex optimal control problem. We present how to convexify the nonlinear dynamics without any approximation via a combination of variable redefinition and relaxation. We then prove that the relaxation is exact by designing an appropriate objective function. This exact relaxation result enables us to further convexify the nonconvex state constraints simply by linearization. As a result, an algorithm is designed to iteratively solve the obtained convex optimization problems until convergence to get a solution of the original problem. A unique feature of the proposed approach is that the algorithm is proved to converge and it does not rely on any trust-region constraint. High performance of the algorithm is demonstrated by its application to trajectory planning of UAVs and autonomous cars with obstacle avoidance requirements.


    Access

    Check access

    Check availability in my library

    Order at Subito €


    Export, share and cite



    Title :

    Convergence-Guaranteed Trajectory Planning for a Class of Nonlinear Systems With Nonconvex State Constraints


    Contributors:
    Liu, Xinfu (author)


    Publication date :

    2022-06-01


    Size :

    1136147 byte




    Type of media :

    Article (Journal)


    Type of material :

    Electronic Resource


    Language :

    English




    Multi-UAV Trajectory Planning for Guaranteed Search

    Kolling, Andreas / Kleiner, Alexander | BASE | 2013

    Free access


    A guaranteed collision‐free trajectory planning method for autonomous parking

    Zhiming Zhang / Shan Lu / Lei Xie et al. | DOAJ | 2021

    Free access

    A guaranteed collision‐free trajectory planning method for autonomous parking

    Zhang, Zhiming / Lu, Shan / Xie, Lei et al. | Wiley | 2021

    Free access