Closed-Form Solution of Algebraic Riccati Equation and Its Application to Optimal and Smooth Motion Planning
نویسنده
چکیده
This paper suggests a closed-form solution of particular case of an algebraic Riccati equation and its application example to optimal and smooth motion planning for a given linear quadratic performance index. Actually, the algebraic Riccati equation can be changed into Moser-Veselov equation by deriving both symmetric and skew-symmetric conditions from an algebraic Riccati equation itself. Also, the symmetric condition is changed into orthonormal one by finding an adequate transformation matrix. Finally, the closed-form solution of algebraic Riccati equation is suggested by using an orthonormal solution of Moser-Veselov equation, and its applicability and effectiveness are shown through the optimal and smooth motion planning example.
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