三輪移動体の最適制御問題と障害物回避問題に対する粘性解の数値解法

抄録

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.