Transformer-based Model Predictive Control: Trajectory Optimization via Sequence Modeling (2410.23916v1)

Abstract: Model predictive control (MPC) has established itself as the primary methodology for constrained control, enabling general-purpose robot autonomy in diverse real-world scenarios. However, for most problems of interest, MPC relies on the recursive solution of highly non-convex trajectory optimization problems, leading to high computational complexity and strong dependency on initialization. In this work, we present a unified framework to combine the main strengths of optimization-based and learning-based methods for MPC. Our approach entails embedding high-capacity, transformer-based neural network models within the optimization process for trajectory generation, whereby the transformer provides a near-optimal initial guess, or target plan, to a non-convex optimization problem. Our experiments, performed in simulation and the real world onboard a free flyer platform, demonstrate the capabilities of our framework to improve MPC convergence and runtime. Compared to purely optimization-based approaches, results show that our approach can improve trajectory generation performance by up to 75%, reduce the number of solver iterations by up to 45%, and improve overall MPC runtime by 7x without loss in performance.

• The paper introduces a novel hybrid approach that integrates transformer models into MPC to warm-start optimization and improve convergence rates by up to 7x.
• It employs a pre-training with fine-tuning strategy to adapt transformers for closed-loop control, effectively managing distribution shifts over long horizons.
• Experimental tests on spacecraft, quadrotors, and free-flying platforms show reductions in trajectory generation costs by up to 75% and solver iterations by up to 45%.

On Transformer-Based Model Predictive Control for Trajectory Optimization

The recent exploration of embedding transformer-based neural network models within Model Predictive Control (MPC) frameworks presents a promising methodological advancement for optimizing trajectory generation in robotics. The paper "Transformer-based Model Predictive Control: Trajectory Optimization via Sequence Modeling" by Celestini et al., proposes an innovative framework combining the strengths of both optimization and learning-based methods, aimed at enhancing MPC efficiency and effectiveness.

Core Contributions

1. Unified Optimization and Learning: The paper introduces a novel technique for embedding high-capacity transformer models within the MPC process. The transformer model is employed to generate a near-optimal trajectory that serves as an initial guess for solving a non-convex optimization problem. This integration serves two primary purposes: it ameliorates the convergence rates of the optimization algorithm and improves the overall computational runtime by up to 7x.
2. Fine-tuning and Long-horizon Guidance: The authors propose a pre-training with subsequent fine-tuning regime to adapt the transformer model for closed-loop MPC applications. The fine-tuning is specifically geared towards managing the distribution shifts encountered during closed-loop execution, thereby enhancing robustness and maintaining performance over long horizons.
3. Application and Performance: The framework was tested across diverse scenarios including spacecraft rendezvous, quadrotor flight, and onboard control of free-flying platforms. The approach demonstrated substantial improvements: reducing trajectory generation costs by up to 75% and the number of solver iterations by up to 45%.

Methodological Insights

The methodological essence lies in the transformer model's ability to efficiently predict and suggest trajectory paths that can be closer to the optimal solution from the start, thereby reducing computational effort. Transformers provide a streamlined sequence modeling process that leverages high-dimensional representations and autoregressive capabilities, crucial for handling complex trajectory optimization tasks typically grappling with real-time constraints.

In the implementation, Celestini et al. grounded their framework in real-world testing scenarios, ensuring applicability and robustness in practical, non-simulated environments. This strengthens the validity of their approach beyond theoretical confines.

Theoretical and Practical Implications

The paper's approach combines the deterministic assurance of optimization-based methods with the flexible capability of learning-based methods, particularly transformers, suggesting a potential paradigm shift in how robotic control systems address trajectory prediction and compliance. The implications are twofold:

1. Theoretical Lens: This framework sets a foundation for further exploration into hybrid methodologies that bind learning models with traditional algorithms. The blend of pre-training and fine-tuning strategies showcases a path towards reducing the sensitivity of learning models to initial conditions and distribution variations.
2. Practical Deployment: From a practical standpoint, this methodology promises significant improvements in the deployment of autonomous systems requiring rapid real-time decision-making. The ability to warm-start optimization processes with learned knowledge markedly cuts down on computational hindrance, making systems more responsive and agile.

Future Prospects

Looking forward, the trajectory optimization landscape could see further disruptions and improvements with continued research into:

• Extending model capabilities to handle multi-tasking and stochastic uncertainties through broader generalization techniques.
• Employing alternative fine-tuning methods such as reinforcement learning to refine the sequence modeling and trajectory generation without sacrificing robustness.
• Expanding the model’s adaptability across varying robotics applications and operational environments, thereby broadening its usability and resilience.

In conclusion, Celestini et al.'s innovative application of transformers within the MPC framework presents a significant stride towards realizing more efficient and effective control models for robotic autonomy. As highlighted, future work promises to further enhance the adaptability and robustness of these systems, vital for exploring complex real-world applications and theoretical boundaries.