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Computation of avoidance regions for driver assistance systems by using a Hamilton-Jacobi approach

Title data

Xausa, Ilaria ; Baier, Robert ; Bokanowski, Olivier ; Gerdts, Matthias:
Computation of avoidance regions for driver assistance systems by using a Hamilton-Jacobi approach.
In: Optimal Control Applications and Methods. Vol. 41 (2020) Issue 2 . - pp. 668-689.
ISSN 1099-1514
DOI: https://doi.org/10.1002/oca.2565


This is the latest version of this item.

Project information

Project title:
Project's official titleProject's id
Marie-Curie Initial Training Network "Sensitivity Analysis for Deterministic Controller Design" (SADCO)264735-SADCO

Project financing: 7. Forschungsrahmenprogramm für Forschung, technologische Entwicklung und Demonstration der Europäischen Union

Abstract in another language

We consider the problem of computing safety regions, modeled as nonconvex backward reachable sets, for a nonlinear car collision avoidance model with time-dependent obstacles. The Hamilton-Jacobi-Bellman framework is used. A new formulation of level set functions for obstacle avoidance is given, and sufficient conditions for granting the obstacle avoidance on the whole time interval are obtained even though the conditions are checked only at discrete times. Different scenarios, including various road configurations, different geometry of vehicle and obstacles, as well as fixed or moving obstacles, are then studied and computed. Computations involve solving nonlinear partial differential equations of up to five space dimensions plus time with nonsmooth obstacle representations, and an efficient solver is used to this end. A comparison with a direct optimal control approach is also done for one of the examples.

Further data

Item Type: Article in a journal
Refereed: Yes
Additional notes: Contents:
1. Motivation
2. Problem Setting and Modelling
2.1 Presentation of the problem
2.2 The four-dimensional point mass model
2.3 Level-set functions for target and state constraints
3. Hamilton-Jacobi-Bellman Approach
.. Minimal time function and optimal trajectory reconstruction
4. Level-Set Functions for Different Problem Data and Collision Avoidance
4.1 Road configurations
4.2 Obstacles and corresponding level-set functions
... Circular obstacles
... Rectangular obstacles
... Moving obstacles
... Collision avoidance between time steps
5. Numerical Simulations
5.1 Scenario 1: Straight road with a fixed rectangular obstacle
... Convergence test (scenario 1)
... Comparison with a direct method (scenario 1)
5.2 Scenario 2: Straight road with varying width
5.3 Scenario 3: Curved road with fix or moving obstacles
5.4 Scenario 4: Crossing road and moving obstacles
6. Conclusion
Keywords: backward reachable sets; collision avoidance; Hamilton-Jacobi-Bellman equations; high-dimensional partial differential equations; level-set approach
Subject classification: Mathematics Subject Classification Code: 93B03 (49K15 49L25 93C10)
Institutions of the University: Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Profile Fields
Profile Fields > Advanced Fields
Profile Fields > Advanced Fields > Nonlinear Dynamics
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 14 Sep 2020 08:54
Last Modified: 14 Sep 2020 08:54
URI: https://eref.uni-bayreuth.de/id/eprint/56878

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