MATLAB Code Implementation for Trajectory Optimization

In this article, we present trajectory optimization source code and demonstrate how to solve optimal control problems using the Chebyshev method. We will provide detailed explanations of the underlying concepts and mathematical principles, including Chebyshev polynomial approximations, collocation point selection, and transcription methods for converting continuous optimal control problems into nonlinear programming formulations. The implementation features key MATLAB functions for polynomial differentiation matrices, constraint handling, and numerical optimization using built-in solvers like fmincon. Practical examples and demonstrations will be included to help readers better understand the subject, showcasing implementation techniques for path constraints, boundary conditions, and performance index optimization. Finally, we will explore real-world applications of trajectory optimization and its potential future impacts in fields such as aerospace trajectory planning, robotic motion control, and autonomous systems. Through this article, readers will gain comprehensive understanding of trajectory optimization and optimal control problems, along with practical knowledge for applying these techniques to solve engineering challenges.