Transformers for Trajectory Optimization with Application to Spacecraft Rendezvous

TL;DR

The paper tackles autonomous spacecraft rendezvous trajectory optimization under hard constraints by introducing the Autonomous Rendezvous Transformer (ART), a Transformer-based framework that both forecasts near-optimal trajectories and serves as a warm-start for sequential convex programs solving constrained non-convex optimal control problems. By casting trajectory generation as a sequence-prediction task with performance-to-go and constraint-to-go signals, ART leverages offline data to predict state/control sequences and optionally propagate dynamics in-loop to enforce feasibility. The work demonstrates that ART can outperform recurrent baselines in forecasting fuel-optimal trajectories and substantially accelerate SCP convergence, yielding near-optimal, feasible solutions with runtimes competitive with convex optimization. This approach meaningfully narrows the gap between data-driven and optimization-based methods, enabling onboard capable autonomy for RPOD tasks while preserving hard constraint satisfaction. The study also lays out design choices, including trajectory representation, MDP formulation, and inference strategies, and points to robustness and broader trajectory-optimization applications as future directions.

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.

Figures (8)

• Figure 1: This paper proposes the Autonomous Rendezvous Transformer (ART) for trajectory optimization. Through the combination of efficient dynamics models and the generative capability of modern Transformer networks, the proposed framework is used to enhance traditional sequential convex programs through learning-based warm-starting, thus exploiting the advantages of data-driven approaches while ensuring hard constraint satisfaction.
• Figure 2: The Autonomous Rendezvous Transformer (ART) architecture. Each reward-to-go, constraint-to-go, state, and control vector is fed into modality-specific linear encoders, after which a positional encoding is added. The embeddings are processed by a GPT architecture which predicts future states and controls autoregressively.
• Figure 3: Constraint violations (top) and costs (bottom) realized by ART-predicted trajectories when conditioned on desired (user-specified) performance parameters.
• Figure 4: Control cost comparison. (Left) Absolute sub-optimality gap of different SCP solutions with respect to the convex lower bound. (Right) Percentage improvement brought by ART with respect to the two convex relaxations considered in this work.
• Figure 5: SCP iterations comparison. (Left) The number of iterations required to obtain SCP convergence. (Right) Cost convergence across SCP iterations.