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Rocket Landing with Trajectory Optimization- Image by Author

Hello and welcome back 😎!

This blog would provide an interesting summary of an idea I worked on in my research for most of the previous year — Trajectory optimization. I personally learned about trajectory optimization by binge-watching videos of MIT Professor Russ Tedrake on YouTube, who is an expert in this area and has applied this to many problems in robotics. In reality, trajectory optimization has been applied in solving numerous other problems, including spacecraft missions, controlling quadrotors, and landing rockets-which we will explore in this blog 👌🏼.

As the name implies, Trajectory optimization involves optimizing for a set of control inputs to perform a given task over a certain time frame (horizon or trajectory). In our case, that would be optimizing for a set of control inputs to land our rocket model from an initial condition. The setup for most trajectory optimization problems is usually framed as solving for a set of optimal control inputs that minimize a certain cost or objective function (J) subject to the dynamics that describe the evolution of the system and additional constraints. In our case, that cost could be the fuel the rocket uses during landing, the time it takes for the rocket to reach a landing position, or even a mix of both 👍🏻. Just to mention, the extra constraints could be constraints…