Abstract
Reach-avoid problems compute control laws under which a dynamic system can reach a desired set of states while avoiding another set. They are used in solving a variety of problems, such as goal-seeking and obstacle avoidance. Hamilton-Jacobi analysis provides a method for solving reach-avoid problems, through a corresponding Hamilton-Jacobi (HJ) equation. Although the HJ equation can be utilized for a general class of problems, computing the solution of the HJ equation by grid-based methods has exponential complexity in the dimension of the continuous state. To alleviate this complexity, this letter presents a generalized version of the Hopf-Lax formula and proves its correctness for solving the reach-avoid problem. The method does not rely on discretization of the state space. A numerical algorithm for the proposed Hopf-Lax formula is presented, and demonstrated using a 12D vehicle example.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
