PyTrajOpt

PyTrajOpt (Python-based Trajectory Optimization) is a modern Python framework for solving complex optimal control problems (OCPs). Powered by CasADi for high-performance symbolic differentiation and Pydantic for strict runtime configuration validation, PyTrajOpt supports both single-phase and multiphase formulations via multiple shooting and direct collocation. It goes a step further by estimating state costates and performing rigorous feasibility checks to ensure the reliability of your generated solutions.

Documentation

For more details about problems supported, installation, examples and api references refer to the docs.

References

1. ally_chen.py — hen, Weifeng, and Lorenz T. Biegler. “Nested Direct Transcription Optimization for Singular Optimal Control Problems.” AIChE Journal, vol. 62, no. 10, Oct. 2016, pp. 3611–27. DOI.org (Crossref), https://doi.org/10.1002/aic.15272.
2. brachistochrone.py — Ross, I. M., et al. “Scaling and Balancing for High-Performance Computation of Optimal Controls.” Journal of Guidance, Control, and Dynamics, vol. 41, no. 10, Oct. 2018, pp. 2086–97. DOI.org (Crossref), https://doi.org/10.2514/1.G003382.
3. cart_costate.py — Conway, B. A., and K. M. Larson. “Collocation Versus Differential Inclusion in Direct Optimization.” Journal of Guidance, Control, and Dynamics, vol. 21, no. 5, Sept. 1998, pp. 780–85. DOI.org (Crossref), https://doi.org/10.2514/2.4306.
4. container_crane.py — https://archiv.ub.uni-heidelberg.de/volltextserver/24212/1/Dissertation_Bergner17.pdf
5. free_flying_robot.py — Betts, John T. Practical Methods for Optimal Control and Estimation Using Nonlinear Programming. Second, Society for Industrial and Applied Mathematics, 2010. DOI.org (Crossref), https://doi.org/10.1137/1.9780898718577.
6. hypersensitive.py — Betts, John T. Practical Methods for Optimal Control and Estimation Using Nonlinear Programming. Second, Society for Industrial and Applied Mathematics, 2010. DOI.org (Crossref), https://doi.org/10.1137/1.9780898718577.
7. lee_ramirez_reactor.py — hen, Weifeng, and Lorenz T. Biegler. “Nested Direct Transcription Optimization for Singular Optimal Control Problems.” AIChE Journal, vol. 62, no. 10, Oct. 2016, pp. 3611–27. DOI.org (Crossref), https://doi.org/10.1002/aic.15272.
8. low_thrust.py — Ross, I. Michael, et al. “Low-Thrust, High-Accuracy Trajectory Optimization.” Journal of Guidance, Control, and Dynamics, vol. 30, no. 4, July 2007, pp. 921–33. DOI.org (Crossref), https://doi.org/10.2514/1.23181.
9. moon_lander_time_dilation.py — Meditch, J.. (1964). On the problem of optimal thrust programming for a lunar soft landing. IEEE Transactions on Automatic Control, 9(4), 477–484. doi:10.1109/tac.1964.1105758 https://gpops2.com/examples/moonlander.html
10. rocket.py — https://web.casadi.org/blog/nlp-scaling/
11. rocket_multiphase.py — Ross, I. Michael, and Fariba Fahroo. Pseudospectral Knotting Methods for Solving Nonsmooth Optimal Control Problems. Journal of Guidance, Control, and Dynamics, vol. 27, no. 3, May 2004, pp. 397–405. DOI.org (Crossref), https://doi.org/10.2514/1.3426.
12. shuttle_cross_range.py — Betts, John T. Practical Methods for Optimal Control and Estimation Using Nonlinear Programming. Second, Society for Industrial and Applied Mathematics, 2010. DOI.org (Crossref), https://doi.org/10.1137/1.9780898718577.