Stochastic Optimal Trajectory Planning: Harnessing Dynamical Indicators and Perron-Frobenius

What is it about?

This study delves into the complex domain of stochastic trajectory planning. Leveraging state-of-the-art techniques, the research introduces a novel approach that efficiently minimizes uncertainties via entropy minimization methods based on the Perron-Frobenius operator and stochastic dynamical indicators. The study focuses on the most crucial aspects of the system, providing a robust means of handling uncertainties, especially in scenarios dominated by non-Gaussian uncertainties. By integrating sparse-grid based pseudospectral optimal control and the stochastic indicators, the research aims to develop a precise numerical approach for optimal control under stochastic and nonlinear dynamics, contributing to more reliable and effective trajectory planning strategies in astronautics.

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Photo by FlyD on Unsplash

Photo by FlyD on Unsplash

Why is it important?

This study stands out for its unique contributions in addressing the complexities of stochastic trajectory planning by integrating advanced concepts like Stochastic Finite-Time Lyapunov Exponent (sFTLE), Pseudo-diffusion Exponents and Perron-Frobenius operator. The exploration of concepts based on Lagrangian Coherent Structures and Entropy, specifically sFTLE and Pseudo-diffusion Exponents, introduces a fresh perspective and not only adds a layer of robustness to the trajectory planning process but also aligns with the broader trend in computational efficiency and accuracy under non-gaussian uncertainties. These dynamical indicators contribute valuable insights into the way trajectory planning challenges are approached in astronautics.

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