Trajectory Optimization Problem

Trajectory optimization aims to find the best possible path for a system, considering factors like efficiency, safety, and constraints. Current research focuses on developing efficient algorithms, such as those based on differential dynamic programming, sequential convex programming, and various neural network architectures (including diffusion models and transformers), to solve these often complex, non-convex problems across diverse applications. These advancements are crucial for improving the autonomy and performance of robots, autonomous vehicles, and spacecraft, enabling more sophisticated control and planning in challenging environments. The field is also seeing increased use of hybrid approaches combining optimization with sampling and learning techniques to improve both speed and robustness.