Low Thrust Trajectory Optimization w/ Dr. Francesco Topputo | Space Engineering Podcast Clips 9

Dr. Francesco Topputo shares how set up and solve low thrust trajectory optimization problems from Sun-Earth L2 halo orbit to asteroids. Link to full episode: • Dr. Francesco Topputo,...
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#trajectoryoptimization #lowthrusttrajectoryoptimization #optimalcontrol

[@stevenverwer6074]

Exactly what I am looking for now, but it is so hard to solve this problem. No clue how they actually set up the two-point boundary condition solver.

[@alfonsogonzalez-astrodynam2207]

I'm currently working on learning more about shooting methods and boundary value problems, but I'm not quite at the point where I'm ready to teach them, so I'll have to get back to you on this. However, you've likely already encountered simple shooting methods without knowing it. Newton's root solver method is a shooting method. You "shoot" an initial guess at the root of a function, then use the function value and its derivative to update your guess so at the next step your new "shot" will be closer to the actual root of the function. kzbin.info/www/bejne/sH_HXqaIr6ZqmJo Lambert's problem is also a two point boundary value problem. You know the initial and final position vectors, and you are solving for the initial velocity vector (by iteration) that will reach the final velocity vector after some amount of time. So again you shoot some initial guess and use the error in the final position to adjust your next shot and continue iterating. The next level of complexity (which I still have lots to learn on) comes from the continuous thrust portion of the trajectory, which is optimal control. I'm currently working through the book called "Practical Methods for Optimal Control Using Nonlinear Programming" by John T. Betts so once I make enough progress and am able to write these shooting methods and optimization programs I will be making videos on them Also, there are "multiple shooting methods", which will set up boundary conditions at multiple stages of the trajectory, and then converge at them propagating from both sides. So say for an Earth to Jupiter trajectory, the initial boundary is Earth's position, the final boundary is Jupiter's position (at arrival), and then there will be a boundary somewhere in the middle of the trajectory. So in this scenario you shoot starting from Earth going forward in time, and then you shoot starting from Jupiter going backwards in time, and iterate until the forward and backward shots meet at the middle boundary condition. Also in this case, a discontinuity in the velocity vectors at the boundary condition is allowed, since that is then considered a delta V maneuver at that point (deep space / trajectory correction maneuver). Here's a paper that my boss Juan Arrieta co-authored on that kind of analysis: www.researchgate.net/publication/330533150_The_Low-thrust_Interplanetary_EXplorer_A_Medium-Fidelity_Algorithm_for_Multi-Gravity_Assist_Low-Thrust_Trajectory_Optimization