Numerical Methods for Viscosity Solutions of an Optimal Control Problem and an Obstacle Avoidance Problem for a Wheeled Vehicle

To construct an optimal regulator for a wheeled vehicle, we need a viscosity solution of the Hamilton-Jacobi partial differential equation (HJ-PDE). In this paper, we propose a new method to have the viscosity solution of the HJ-PDE more quickly by applying a new searching method which uses a sequen...

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Published inShisutemu Seigyo Jouhou Gakkai rombunshi Vol. 13; no. 10; pp. 458 - 469
Main Authors IMAFUKU, Kei, YAMASHITA, Yuh, NISHITANI, Hirokazu
Format Journal Article
LanguageJapanese
English
Published THE INSTITUTE OF SYSTEMS, CONTROL AND INFORMATION ENGINEERS (ISCIE) 2000
Subjects
Hamilton-Jacobi partial differential equation
nonlinear control
optimal regulator
viscosity solution
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Summary:To construct an optimal regulator for a wheeled vehicle, we need a viscosity solution of the Hamilton-Jacobi partial differential equation (HJ-PDE). In this paper, we propose a new method to have the viscosity solution of the HJ-PDE more quickly by applying a new searching method which uses a sequence of random inputs. This method reduces the number of searching points and makes calculation time faster than the previous method. Next, we propose a method to have the viscosity solution for obstacle avoidance. From the theoretical result of optimal control with state constraints, we can get the viscosity solution which avoids obstacles optimally. Then we make sure that an optimal solution can be obtained analytically by the finite difference numerical approximation of the HJ-PDE. This new result gives us an optimal solution without searching. Finally, the effectiveness of control results calculated from proposed methods are confirmed through simulations.
ISSN:1342-5668
2185-811X
DOI:10.5687/iscie.13.10_458