Learning Safe Control Laws from Expert Driving Demonstrations with Uncertain Dynamics and State Estimation

Core Concepts

The core message of this paper is to learn safe output feedback control laws for unknown systems with uncertain dynamics and state estimation errors by constructing robust output control barrier functions (ROCBFs) from expert driving demonstrations.

Abstract

The paper addresses the problem of learning safe output feedback control laws for unknown systems with uncertain dynamics and state estimation errors. The authors propose robust output control barrier functions (ROCBFs) as a means to guarantee safety, defined through controlled forward invariance of a safe set. They formulate an optimization problem to learn ROCBFs from expert demonstrations that exhibit safe system behavior, such as data collected from a human operator or an expert controller. The key highlights and insights are: The authors present ROCBFs that account for both system model and state estimation uncertainties to establish safety under output feedback control. They provide verifiable conditions in terms of the density of the data, smoothness of the system model and state estimator, and the size of the error bounds that guarantee validity of the obtained ROCBF. For the general case, the authors propose an approximate unconstrained optimization problem that can be solved efficiently. They discuss the algorithmic implementation of their framework to learn ROCBFs in practice, including techniques to construct the required datasets and estimate Lipschitz constants. The authors validate their approach in the autonomous driving simulator CARLA and demonstrate how to learn safe control laws from simulated RGB camera images.

Stats

"The authors assume known nominal models ˆF and ˆG together with functions ΔF and ΔG that bound their respective errors." "The authors assume to have a known model ˆX together with a function ΔX that bounds the error in the state estimator."

Quotes

"We assume that a model of the system dynamics and a state estimator are available along with corresponding error bounds, e.g., estimated from data in practice." "We first propose robust output control barrier functions (ROCBFs) as a means to guarantee safety, as defined through controlled forward invariance of a safe set." "We then formulate an optimization problem to learn ROCBFs from expert demonstrations that exhibit safe system behavior, e.g., data collected from a human operator or an expert controller."

Key Insights Distilled From

Learning Robust Output Control Barrier Functions from Safe Expert Demonstrations

by Lars Lindema... at arxiv.org 04-04-2024

https://arxiv.org/pdf/2111.09971.pdf

Deeper Inquiries

How can the proposed framework be extended to handle partially unknown system dynamics and state estimation models, beyond the assumed error bounds

To extend the proposed framework to handle partially unknown system dynamics and state estimation models beyond the assumed error bounds, one could incorporate adaptive learning techniques. This would involve continuously updating the model parameters based on real-time data feedback. By integrating online learning algorithms such as reinforcement learning or adaptive control, the system could adjust to variations in the dynamics and estimation models. Additionally, incorporating Bayesian inference methods could help in updating the uncertainty bounds based on new observations, allowing for a more flexible and robust control framework.

What are the implications of the exponential growth in the amount of data needed to satisfy the conditions as the state dimension increases

The exponential growth in the amount of data needed to satisfy the conditions as the state dimension increases poses a significant challenge. To mitigate this, more efficient sampling strategies can be employed. Techniques such as active learning, where the algorithm selects the most informative data points to label, can reduce the amount of data required. Additionally, dimensionality reduction methods like principal component analysis (PCA) can help in capturing the essential features of high-dimensional data, reducing the data complexity. Another approach could be to leverage transfer learning, where knowledge from a related domain or task is used to accelerate learning in the new, high-dimensional setting.

Can this be mitigated through more efficient sampling strategies or alternative approaches

The learned ROCBFs can be further refined or adapted online as the system operates by implementing adaptive control strategies. One approach is to incorporate model predictive control (MPC), where the control policy is updated at each time step based on the current state and predictions of future behavior. This allows for real-time adjustments to changing environmental conditions or system dynamics. Additionally, reinforcement learning techniques can be used to continuously improve the control policy through trial and error learning, adapting to new scenarios as they arise. By combining these adaptive control methods with the learned ROCBFs, the system can dynamically respond to evolving conditions.