Prototype/Request: Dynamic parameters in CppAD cost functions

[PPeltzer]

This PR results from a conversation I had with Michael Neunert back in May via the CT Devs mail group. Sorry for the delay, I finally found the time to open a PR.

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This is only a prototype, i.e. no merge is desired! I hope the problem and my workaround can help to develop a proper implementation in the future.

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• Problem: I'm running a MPC with a custom cost function where I want CppAD to generate the derivatives for me. However, in this cost function, environment data must be considered. This data is passive w.r.t. differentiation - CppAD does not need to actually generate derivative code for these variables but only use it in its generated code in such a way that it can be updated between optimization calls. However, this is currently not supported by CppADCodeGen.

• Ideal solution: I was pointed to this issue over at CppADCodeGen's git repo by Michael. The feature itself appears to be available in CppAD; however, it's not yet available for code generation.

• Workaround: As suggested by Michael, I've implemented a workaround which you can find in this PR. I've added a new CostFunctionADParams class which extends the state vector by the passive parameters. This addition is ignored by 1st and 2nd derivative extraction functions - therefore the parameters are passive as desired. They can be updated using the new setCurrentParameters function.

• Drawbacks: This workaround has some rather big drawbacks:

  • Although no derivative information is extracted later, CppADCodeGen still generates the corresponding code. This results in larger executables and in very poor JIT-compilation times.
  • Since the control toolbox currently only uses Eigen static matrices, the total size of the parameters is limited by the stack size.
  • The resulting interface is very ugly, i.e. custom datatypes can not be used and everything must be mapped to a CppAD Scalar.

Although my workaround did the job for me on a smaller project, using it in the long-term is no option due to these drawbacks. I would really like to see this problem addressed at some point as I really enjoy using AD for the cost functions as it makes rapid-prototyping way easier.

Best regards,

Patrick

[markusgft]

@neunertm, fyi!