Transformers for Trajectory Optimization with Application to Spacecraft Rendezvous (2310.13831v3)
Abstract: Reliable and efficient trajectory optimization methods are a fundamental need for autonomous dynamical systems, effectively enabling applications including rocket landing, hypersonic reentry, spacecraft rendezvous, and docking. Within such safety-critical application areas, the complexity of the emerging trajectory optimization problems has motivated the application of AI-based techniques to enhance the performance of traditional approaches. However, current AI-based methods either attempt to fully replace traditional control algorithms, thus lacking constraint satisfaction guarantees and incurring in expensive simulation, or aim to solely imitate the behavior of traditional methods via supervised learning. To address these limitations, this paper proposes the Autonomous Rendezvous Transformer (ART) and assesses the capability of modern generative models to solve complex trajectory optimization problems, both from a forecasting and control standpoint. Specifically, this work assesses the capabilities of Transformers to (i) learn near-optimal policies from previously collected data, and (ii) warm-start a sequential optimizer for the solution of non-convex optimal control problems, thus guaranteeing hard constraint satisfaction. From a forecasting perspective, results highlight how ART outperforms other learning-based architectures at predicting known fuel-optimal trajectories. From a control perspective, empirical analyses show how policies learned through Transformers are able to generate near-optimal warm-starts, achieving trajectories that are (i) more fuel-efficient, (ii) obtained in fewer sequential optimizer iterations, and (iii) computed with an overall runtime comparable to benchmarks based on convex optimization.
- D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. Van Den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot et al., “Mastering the game of go with deep neural networks and tree search,” Nature, vol. 529, no. 7587, pp. 484–489, 2016.
- C. Adams, A. Spain, J. Parker, M. Hevert, J. Roach, and D. Cotten, “Towards an Integrated GPU Accelerated SoC as a Flight Computer for Small Satellites,” in 2019 IEEE Aerospace Conference, 2019, pp. 1–7.
- T. H. Park and S. D’Amico, “Online Supervised Training of Spaceborne Vision during Proximity Operations using Adaptive Kalman Filtering,” 2023. [Online]. Available: https://arxiv.org/abs/2309.11645
- N. T. Redd, “Bringing satellites back from the dead: Mission extension vehicles give defunct spacecraft a new lease on life - [news],” IEEE Spectrum, vol. 57, no. 8, pp. 6–7, 2020.
- C. J. Dennehy and J. R. Carpenter, “A summary of the rendezvous, proximity operations, docking, and undocking (RPODU) lessons learned from the defense advanced research project agency (DARPA) orbital express (OE) demonstration system mission,” Tech. Rep., 2011. [Online]. Available: https://ntrs.nasa.gov/citations/20110011506
- S. D’Amico, “Autonomous Formation Flying in Low Earth Orbit.” PhD Thesis, Delft University, 2010.
- C. D’Souza, C. Hannak, P. Spehar, F. Clark, and M. Jackson, “Orion rendezvous, proximity operations and docking design and analysis,” in AIAA guidance, navigation and control conference and exhibit, 2007, p. 6683. [Online]. Available: https://ntrs.nasa.gov/citations/20070025134
- D. Izzo, M. Märtens, and B. Pan, “A survey on artificial intelligence trends in spacecraft guidance dynamics and control,” Astrodynamics, vol. 3, pp. 287–299, 2019.
- K. Hovell and S. Ulrich, “Deep reinforcement learning for spacecraft proximity operations guidance,” Journal of Spacecraft and Rockets, vol. 58, no. 2, pp. 254–264, 2021.
- L. Federici, B. Benedikter, and A. Zavoli, “Deep learning techniques for autonomous spacecraft guidance during proximity operations,” Journal of Spacecraft and Rockets, vol. 58, no. 6, pp. 1774–1785, 2021.
- L. Federici, A. Scorsoglio, A. Zavoli, and R. Furfaro, “Meta-reinforcement learning for adaptive spacecraft guidance during finite-thrust rendezvous missions,” Acta Astronautica, vol. 201, pp. 129–141, 2022.
- S. Banerjee, T. Lew, R. Bonalli, A. Alfaadhel, I. A. Alomar, H. M. Shageer, and M. Pavone, “Learning-based Warm-Starting for Fast Sequential Convex Programming and Trajectory Optimization,” in 2020 IEEE Aerospace Conference, 2020, pp. 1–8.
- A. Cauligi, P. Culbertson, E. Schmerling, M. Schwager, B. Stellato, and M. Pavone, “Coco: Online mixed-integer control via supervised learning,” IEEE Robotics and Automation Letters, vol. 7, no. 2, pp. 1447–1454, 2021.
- L. Chen, K. Lu, A. Rajeswaran, K. Lee, A. Grover, M. Laskin, P. Abbeel, A. Srinivas, and I. Mordatch, “Decision transformer: Reinforcement learning via sequence modeling,” Advances in neural information processing systems, vol. 34, pp. 15 084–15 097, 2021. [Online]. Available: https://arxiv.org/abs/2106.01345
- M. Janner, Q. Li, and S. Levine, “Offline reinforcement learning as one big sequence modeling problem,” Advances in neural information processing systems, vol. 34, pp. 1273–1286, 2021. [Online]. Available: https://arxiv.org/abs/2106.02039
- A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez, Ł. Kaiser, and I. Polosukhin, “Attention is all you need,” Advances in neural information processing systems, vol. 30, 2017. [Online]. Available: https://arxiv.org/abs/1706.03762
- A. Radford, K. Narasimhan, T. Salimans, I. Sutskever et al., “Improving language understanding by generative pre-training,” 2018. [Online]. Available: {https://s3-us-west-2.amazonaws.com/openai-assets/research-covers/language-unsupervised/language_understanding_paper.pdf}
- A. Dosovitskiy, L. Beyer et al., “An image is worth 16x16 words: Transformers for image recognition at scale,” in International Conference on Learning Representations, 2021.
- I. Radosavovic, T. Xiao, B. Zhang, T. Darrell, J. Malik, and K. Sreenath, “Learning humanoid locomotion with transformers,” arXiv preprint arXiv:2303.03381, 2023. [Online]. Available: https://arxiv.org/abs/2303.03381
- A. Vaswani, N. Shazeer et al., “Attention is all you need,” Advances in neural information processing systems, vol. 30, p. 6000–6010, 2017. [Online]. Available: https://arxiv.org/abs/1706.03762
- A. Radford, J. Wu, R. Child, D. Luan, D. Amodei, and I. Sutskever, “Language models are unsupervised multitask learners,” 2019. [Online]. Available: https://arxiv.org/abs/1706.03762
- A. Goyal, A. Lamb, Y. Zhang, S. Zhang, A. Courville, and Y. Bengio, “Attention is all you need,” Advances in neural information processing systems, p. 4608–46160, 2016. [Online]. Available: https://arxiv.org/abs/1610.09038
- S. D’Amico, “Relative Orbital Elements as Integration Constants of Hills Equations,” TN05-08, German Space Operations Centre (GSOC), Munich, Germany, 2005.
- J. Sullivan and S. D’Amico, “Nonlinear Kalman Filtering for Improved Angles-Only Navigation Using Relative Orbital Elements,” Journal of Guidance, Control, and Dynamics, pp. 1–18, Jul. 2017.
- T. Guffanti and S. D’Amico, “Passively Safe and Robust Multi-Agent Optimal Control with Application to Distributed Space Systems,” Journal of Guidance, Control, and Dynamics, vol. 46, no. 8, pp. 1448–1469, 2023.
- A. W. Koenig, T. Guffanti, and S. D’Amico, “New State Transition Matrices for Spacecraft Relative Motion in Perturbed Orbits,” Journal of Guidance, Control, and Dynamics, vol. 40, no. 7, pp. 1749–1768, 2017.
- T. Guffanti and S. D’Amico, “Linear Models for Spacecraft Relative Motion Perturbed by Solar Radiation Pressure,” Journal of Guidance, Control, and Dynamics, vol. 42, no. 9, pp. 1962–1981, 2019.
- T. Guffanti, S. D’Amico, and M. Lavagna, “Long-Term Analytical Propagation of Satellite Relative Motion in Perturbed Orbits,” in 27th AAS/AIAA Space Flight Mechanics Meeting, San Antonio, TX, 2017, pp. 1–31.
- G. Gaias and S. D’Amico, “Impulsive maneuvers for formation reconfiguration using relative orbital elements,” Journal of Guidance, Control, and Dynamics, vol. 38, no. 6, pp. 1036–1049, 2015.
- M. Chernick and S. D’Amico, “New Closed-Form Solutions for Optimal Impulsive Control of Spacecraft Relative Motion,” Journal of Guidance, Control, and Dynamics, vol. 41, no. 2, pp. 301–319, 2018.
- P. Lu and X. Liu, “Autonomous trajectory planning for rendezvous and proximity operations by conic optimization,” Journal of Guidance, Control, and Dynamics, vol. 36, no. 2, pp. 375–389, 2013.
- D. Malyuta, T. Reynolds, M. Szmuk, B. Acikmese, and M. Mesbahi, “Fast trajectory optimization via successive convexification for spacecraft rendezvous with integer constraints,” in AIAA Scitech 2020 Forum, 2020.
- D. Malyuta, T. P. Reynolds, M. Szmuk, T. Lew, R. Bonalli, M. Pavone, and B. Açıkmeşe, “Convex Optimization for Trajectory Generation: A Tutorial on Generating Dynamically Feasible Trajectories Reliably and Efficiently,” IEEE Control Systems Magazine, vol. 42, no. 5, pp. 40–113, 2022.
- S. D’Amico and O. Montenbruck, “Proximity Operations of Formation-Flying Spacecraft Using an Eccentricity/Inclination Vector Separation,” Journal of Guidance, Control, and Dynamics, vol. 29, no. 3, pp. 554–563, May 2006.
- A. Domahidi, E. Chu, and S. Boyd, “ECOS: An SOCP solver for embedded systems,” in European Control Conference (ECC), 2013, pp. 3071–3076.
- R. H. Byrd, J. C. Gilbert, and J. Nocedal, “A Trust Region Method Based on Interior Point Techniques for Nonlinear Programming,” Mathematical Programming, vol. 89, no. 1, pp. 149–185, 2000.
- X. Liu and P. Lu, “Solving Nonconvex Optimal Control Problems by Convex Optimization,” Journal of Guidance, Control, and Dynamics, vol. 37, no. 3, pp. 750–765, 2014.
- D. Morgan, S.-J. Chung, and F. Y. Hadaegh, “Model Predictive Control of Swarms of Spacecraft Using Sequential Convex Programming,” Journal of Guidance, Control, and Dynamics, vol. 37, no. 6, pp. 1725–1740, 2014. [Online]. Available: https://doi.org/10.2514/1.G000218
- R. Bonalli, A. Cauligi, A. Bylard, and M. Pavone, “GuSTO: Guaranteed sequential trajectory optimization via sequential convex programming,” in IEEE International Conference on Robotics and Automation (ICRA), Montreal, May, 2019.
- Y. Tay, M. Dehghani, D. Bahri, and D. Metzler, “Efficient transformers: A survey,” ACM Computing Surveys, vol. 55, pp. 0360–0300, 2022. [Online]. Available: https://doi.org/10.1145/3530811
- A. Paszke, S. Gross, S. Chintala, G. Chanan, E. Yang, Z. DeVito, Z. Lin, A. Desmaison, L. Antiga, and A. Lerer, “Automatic differentiation in pytorch,” 2017.
- “Huggingface’s Tranformers Library,” https://huggingface.co/docs/transformers/index.