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Learning to Control an Unstable System with One Minute of Data: Leveraging Gaussian Process Differentiation in Predictive Control (2103.04548v2)

Published 8 Mar 2021 in cs.RO, cs.LG, cs.SY, and eess.SY

Abstract: We present a straightforward and efficient way to control unstable robotic systems using an estimated dynamics model. Specifically, we show how to exploit the differentiability of Gaussian Processes to create a state-dependent linearized approximation of the true continuous dynamics that can be integrated with model predictive control. Our approach is compatible with most Gaussian process approaches for system identification, and can learn an accurate model using modest amounts of training data. We validate our approach by learning the dynamics of an unstable system such as a segway with a 7-D state space and 2-D input space (using only one minute of data), and we show that the resulting controller is robust to unmodelled dynamics and disturbances, while state-of-the-art control methods based on nominal models can fail under small perturbations. Code is open sourced at https://github.com/learning-and-control/core .

Citations (2)

Summary

  • The paper demonstrates a novel GP-based method that learns unstable system dynamics from just one minute of data.
  • The paper integrates GP differentiation with MPC to generate real-time control policies that robustly handle constraints and perturbations.
  • The paper validates its approach on a robotic segway, achieving stability and performance comparable to models using true dynamics.

Overview of "Learning to Control an Unstable System with One Minute of Data: Leveraging Gaussian Process Differentiation in Predictive Control"

The paper "Learning to Control an Unstable System with One Minute of Data: Leveraging Gaussian Process Differentiation in Predictive Control" details a novel methodology for identifying and controlling unstable robotic systems by leveraging Gaussian Processes (GPs). The work primarily focuses on offering a data-efficient approach for system identification using the inherent differentiability properties of GPs, which is then integrated with Model Predictive Control (MPC) to manage real-world constraints and perturbations.

Key Contributions

The paper addresses the challenge of controlling systems with unstable dynamics, where even slight modeling inaccuracies can lead to instability. Traditional approaches often rely on nominal model dynamics or require extensive data collection, neither of which are ideal for fast or resource-limited scenarios. The authors propose a method that can reliably learn an accurate model of the dynamics with only a minute's worth of data, significantly reducing the requisite data collection costs.

  • Gaussian Process Exploitation: The authors apply GPs to estimate the full dynamics of the system by differentiating the GP to obtain a state-dependent linearization of the true system dynamics. This stands in contrast to previous methods where GPs were used primarily for learning residual dynamics or required more computationally expensive procedures. The approach enables quick adaptation to new systems or changes in dynamics with minimal data.
  • Integration with MPC: By deriving a local state-dependent linear approximation of dynamics using GPs, the authors effectively integrate this model with MPC. This integration allows for real-time control policies that are both efficient and capable of handling constraints and perturbations robustly.
  • Validation and Real-World Impact: The methodology is validated both in simulation and experimentally on a physical robotic segway. The performance of the GP-based approach was demonstrated to perform comparably to scenarios using the true dynamics in simulations. Importantly, on hardware, the approach proved resilient to significant perturbations, effectively stabilizing a system under substantial unmodeled disturbances where traditional MPC with nominal models failed.

Strong Numerical Results and Implications

The work highlights the GP-based framework's ability to stabilize a segway using only one minute of collected data, contrasting the significant data demands of existing approaches. This methodological advance implies that robotics applications, particularly those involving unstable systems, can now employ rapid deployment and adaptation without extensive pre-collection of data or reliance on heavily parameterized models prone to error in dynamic scenarios.

The implications stretch beyond immediate practical application to potentially altering the traditional balance between model accuracy and computational efficiency in control systems. By enabling effective learning with minimal data, this approach broadens the range of feasible real-world applications for predictive control, allowing systems to be more agile, adaptive, and robust.

Future Developments

The paper suggests directions for future exploration in dealing with noise and delays in state estimation, which remain challenges in volatile systems. Additionally, expanding the methodology to higher-dimensional systems or more complex dynamics while maintaining or enhancing data efficiency would represent a significant advancement. Moreover, integrating more advanced uncertainty quantification methods within the GP framework could enhance safety assurances in learning-based control.

Scalability of the GP model with respect to the size of training data remains an open area for further development, with existing literature on GP approximations and scalability potentially offering pathways to address this aspect.

Overall, the paper's contributions to learning-based control represent a meaningful evolution in data-driven approaches to managing unstable systems, offering a balance of efficiency, robustness, and practicality in deployment.

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