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Hi @afossa, I somehow missed this post, I am very sorry for the late reply. To better help you, could you please provide the complete script? From the above it is not clear how the infinite parameter is being defined. |
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Hi @afossa, this is a cool model and there is a lot to unpack. One problem likely at play here is the equation scaling. It seems that there are some very large difference in the values of the variables involved in different operations which it often problematic for numerical solvers to handle. I would suggest scaling the variables/equations such the orders-of-magnitude are similar. |
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Hi @pulsipher, The optimization variables are already scaled in the problem formulation, and are all of order one in the You can check the range of values for the optimization variables by looking at the JSON file I attached above. After solving the scaled problem, you can recover their values in metric units by multiplying the outputs of the optimization by the values in the |
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What is the scaling factor for the position vector? A key thing to keep in mind is that the default tolerance for the Ipopt solver is 1e-8, whereas your integration is using a tolerance of 1e-14. Also, |
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The components of the positions are scaled by 1 AU, such that the initial radius is approximately 1 (the Earth's orbit radius in AU) and the final radius is approximately 1.5 (the Mars' orbit radius in AU). Velocities are scaled such that the period of the Earth orbit is 2pi. For the discretization I am using 400 nodes and a third-order orthogonal collocation. I am also setting these tolerances for IPOPT And this is the output I obtain for the QSW case: the outputs for the other two simulations are very similar. Finally, the explicit integration uses a piecewise-constant control that matches the solution to the NLP. |
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Given the relative scales involved. The discrepancy between the optimization solution and the integrator could simply be explained by the relative order of the methods used for integration (9th order instead of 3rd order). In other words, I suspect the error can just be attributed to truncation error. The formulation itself looks reasonable. A tolerance of |
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Hello,
I am using
InfiniteOptto solve optimal control problems in trajectory optimization. These type of problems frequently have complicated nonlinear expressions in both the dynamics and the constraints, and they rely a lot on operations like matrix-vector products, cross products, norms, etc.I was able to successfully solve an optimal transfer between the Earth and Mars, but I am looking for suggestions on how I can improve my implementation, specifically how to avoid recomputing quantities that appear in more than one constraint, such as the distance from the Sun. Should I add a variable for each of them, or is there a better way to achieve this?
I am also experimenting with different problem formulations, in particular I want to express the control variables for the three components of the thrust vector in either the inertial frame or in a rotating frame defined by the spacecraft position and velocity vectors. In the second case, I need to compute the rotation matrix from the rotating to the inertial frame, but I am getting an error that seems to be related to the normalization of the angular momentum vector (computed as the cross product between position and velocity):
So I modified the problem formulation to avoid it, however, the accuracy of the solution with the thrust expressed in rotating frame is much lower than that of the solution with the thrust expressed directly in inertial frame. My guess is that the rotation matrix, as I am computing it now, is not perfectly orthogonal. This is the working code I came up with:
Do you have any suggestion on how I can improve it, both in terms of accuracy and efficiency as discussed above?
The results I obtain in inertial frame are:
and in QSW frame:
finally, in TNW frame:
Attached is the full script and input data to reproduce these results. I am using the version of
InfiniteOptchecked out from themasterbranch to use theconstant_over_collocationmethod that enforces a piecewise-constant control.earth_mars_input.json
earth_mars_script.txt
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