日本ロボット学会誌
Online ISSN : 1884-7145
Print ISSN : 0289-1824
ISSN-L : 0289-1824
Hamilton-Jacobi偏微分方程式の粘性解を用いた三輪移動体の制御
今福 啓山下 裕西谷 紘一
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1999 年 17 巻 5 号 p. 689-695

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To construct an optimal regulator for nonlinear systems, we need to solve a Hamilton-Jacobi partial differential equation (HJ-PDE) . However, if the system has nonholonomic constraints, the HJ-PDE has a nonsmooth solution because of the nonsmoothness of the optimal cost function. In such a case, the viscosity solution, a nonsmooth weak solution of the HJ-PDE, is obtained.
In this paper, we deal with a wheeled vehicle, which is a nonholonomic system, and propose a numerical method to achieve a viscosity solution of the HJ-PDE using the dynamic programming principle (DPP) . The DPP can be applied to acquire a nonsmooth solution of the HJ-PDE. We also construct an optimal control law using derivatives of the viscosity solution of the HJ-PDE. The effectiveness of the proposed method is shown through simulations.

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