Episodic Learning with Control Lyapunov Functions for Uncertain Robotic Systems (1903.01577v1)

Abstract: Many modern nonlinear control methods aim to endow systems with guaranteed properties, such as stability or safety, and have been successfully applied to the domain of robotics. However, model uncertainty remains a persistent challenge, weakening theoretical guarantees and causing implementation failures on physical systems. This paper develops a machine learning framework centered around Control Lyapunov Functions (CLFs) to adapt to parametric uncertainty and unmodeled dynamics in general robotic systems. Our proposed method proceeds by iteratively updating estimates of Lyapunov function derivatives and improving controllers, ultimately yielding a stabilizing quadratic program model-based controller. We validate our approach on a planar Segway simulation, demonstrating substantial performance improvements by iteratively refining on a base model-free controller.

• The paper introduces an episodic framework that integrates machine learning with CLFs to iteratively adapt controllers for uncertain robotic systems.
• It details a novel methodology where CLF-guided quadratic programming refines control stability and improves trajectory tracking in simulations.
• The approach demonstrates significant improvements over model-free controllers, ensuring reliable performance despite parametric uncertainties.

Episodic Learning with Control Lyapunov Functions for Uncertain Robotic Systems

The paper introduces an innovative approach that combines machine learning techniques with Control Lyapunov Functions (CLFs) to address the persistent issue of model uncertainty in nonlinear control of robotic systems. The authors focus on robotic platforms where robust control is necessary but challenged by parametric uncertainty and unmodeled dynamics, which can compromise stability and effectiveness.

Methodology

The authors propose a novel episodic learning framework that iteratively refines the controller design. The core idea is to use CLFs to guide the learning process, ensuring stability while adapting to model uncertainties. By iteratively updating estimates of Lyapunov function derivatives, the approach yields a stabilizing quadratic program controller that is fundamentally model-based but iteratively refined through learning.

The research leverages the structure of CLFs to propose controllers that adapt to model uncertainties. Stability is achieved by ensuring that the chosen Lyapunov function satisfies certain conditions, leveraging the computationally efficient format of a quadratic program for the control inputs.

Key Results

Validation of the approach is conducted through simulations on a planar Segway model, demonstrating significant improvements over a base model-free controller. Numerical results show that the proposed method leads to enhanced trajectory tracking while maintaining control stability.

Implications

The presented framework has both theoretical and practical implications. Theoretically, it offers a new perspective on integrating machine learning approaches with classical control theories, particularly CLFs, in a mathematically coherent manner. Practically, the proposed method paves the way for more robust and reliable robotic systems capable of operating under significant model uncertainties.

Future Directions

The paper highlights potential future developments in leveraging more sophisticated episodic learning algorithms such as SEARN, AggreVaTeD, or MoBIL. These could yield improved performance and learning-theoretic convergence guarantees. Furthermore, exploration of different model classes for the Lyapunov function derivative may enhance control performance across various robotic platforms.

Overall, this work provides a meaningful advancement in the field of robotic control, suggesting a promising direction for research addressing the adaptation of control systems to dynamic and uncertain environments. This integration of learning with control theory stands to make robotic systems more versatile and resilient to unforeseen disturbances.