Birkhoff擬スペクトル法を用いた最適軌道生成

抄録

A variety of numerical methods have been developed to solve nonlinear optimal control problems for dynamic systems. A pseudospectral-based method quickly obtains a converged solution that satisfies feasibility, and it can verify optimality through a joint application of Pontryagin’s and Covector-Mapping Principles. In such circumstances, a novel pseudospectral method approach has recently been developed based on Birkhoff interpolation concepts instead of the conventional Lagrange interpolation; however, the method has only a few applications. This study applies the Birkhoff pseudospectral (BPS) method to solve the optimal trajectory generation problem of the quadrotor. To evaluate the performance of the BPS method, numerical examples are provided for comparison with the legacy Legendre pseudospectral (LPS) method. The results demonstrate that the BPS method is more practical than the legacy LPS method.