Numerical simulation of collision-free near-shortest path generation for Dubins vehicle via Hamilton–Jacobi–Bellman equation: A case study
| Autor: | Wen-Chieh Tung, Jing-Sin Liu, Han-Jung Chou |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
0209 industrial biotechnology
General Computer Science semi-lagrange scheme 020209 energy General Chemical Engineering Hamilton–Jacobi–Bellman equation 02 engineering and technology Curvature Computer Science::Robotics obstacle avoidance 020901 industrial engineering & automation dubins path hjb equation Computer Science::Systems and Control Obstacle avoidance 0202 electrical engineering electronic engineering information engineering godunov hamiltonian scheme Mathematics Computer simulation Plane (geometry) Mathematical analysis General Engineering Dubins path Engineering (General). Civil engineering (General) Computer Science::Multiagent Systems Shortest path problem unmanned aerial vehicles TA1-2040 Constant (mathematics) |
| Zdroj: | Cogent Engineering, Vol 7, Iss 1 (2020) |
| ISSN: | 2331-1916 |
| DOI: | 10.1080/23311916.2020.1782710 |
| Popis: | Motivated by modeling an unmanned aerial vehicle at a constant altitude plane above ground level as Dubins vehicle with signed upper-bounded curvature as constrained input and the flight path as Dubins path, the class of flight paths we study is restricted to the paths composed by path segments with zero or constant curvature satisfying the curvature constraint. We start with time-optimal control formulation incorporating mixed constraints for Dubins vehicle in cluttered planar environment and derive the associated Hamilton-Jacobi-Bellman (HJB) equation for the value function from the necessary time-optimality condition. The Kruzkov transform is used to modify the HJB equation for scaling of the solution to be bounded near the obstacles. Numerical solutions based on the fast-sweeping methods with consistent, monotone upwind Godunov Hamiltonian and semi-Lagrange methods are implemented for solving the two-point boundary value problem of modified HJB equation. Comparative validation simulations suggest the appropriateness of both schemes for the numerical collision-free shortest path via Kruzkov transformed HJB equation but with different convergence rate. Two schemes both perform satisfactory path planning, while Godunov Hamiltonian scheme provides more accurate in order of convergence. It is also found by example simulations that the grid resolution and time-step size required for switching structure is finer than that of the convergence criterion. |
| Databáze: | OpenAIRE |
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