Online Safety Verification and Control for Nonlinear Systems in Dynamic Environments

Core Concepts

A computationally-lightweight algorithm called gatekeeper that ensures trajectories of a nonlinear system satisfy safety constraints despite sensing limitations and dynamic environments.

Abstract

The paper presents the gatekeeper algorithm, a real-time and computationally-efficient method to ensure the safety of nonlinear systems operating in dynamic environments with partial knowledge. The key contributions are: An algorithm to recursively construct safe trajectories by numerically forward propagating the system over a finite horizon. A proof that tracking such a committed trajectory ensures the system remains safe for all future time, beyond the finite horizon. The method integrates with existing path planners and feedback controllers by introducing an additional verification step to ensure that proposed trajectories can be executed safely, despite nonlinear dynamics subject to bounded disturbances, input constraints and partial knowledge of the environment. The paper makes the following assumptions: A perception system that can estimate a subset of the safe set online. A nominal planner that generates desired trajectories. An input-to-state stable tracking controller. A backup controller that can stabilize the system to a controlled-invariant set. The gatekeeper algorithm constructs a "committed trajectory" by simulating the tracking controller for a finite horizon, and then executing the backup controller. This committed trajectory is guaranteed to be safe for all future time. The controller always tracks the last committed trajectory, ensuring safety. The paper demonstrates the method in simulation of a dynamic firefighting mission, and in physical experiments of a quadrotor navigating in an obstacle environment sensed online. Comparisons are provided against state-of-the-art techniques.

Stats

The paper does not provide specific numerical data or metrics, but rather focuses on the theoretical framework and algorithmic contributions.

Quotes

"A key contribution of this paper is to show how we can perform this check by verifying only a finite horizon." "The controller always tracks the last committed trajectory, thereby ensuring safety." "The overall algorithm is computationally efficient compared to similar methods, e.g. Model Predictive Control (MPC). In our simulations VI, gatekeeper was approximately 3-10 times faster than MPC."

Key Insights Distilled From

gatekeeper

by Devansh R Ag... at arxiv.org 03-29-2024

https://arxiv.org/pdf/2211.14361.pdf

Deeper Inquiries

How can the backup controller and set be automatically designed for a given robotic system and environment

Designing the backup controller and set for a robotic system and environment can be achieved through various methods. One approach is to utilize reachability analysis to determine the region of attraction around a stabilizable equilibrium point. By linearizing the system dynamics around this point, an LQR controller can be designed to render a small set of states around the equilibrium point forward invariant. This method ensures that the system remains within a safe region. Additionally, reachability analysis can be used to compute reachable sets and design controllers that guarantee safety in the presence of disturbances. Another approach involves learning-based methods, where reinforcement learning or neural network-based approaches can be employed to learn the control policies that keep the system within a safe set. These methods can adapt to the system's dynamics and environment, providing robust control in uncertain conditions.

What are the limitations of the gatekeeper approach, and how can it be extended to handle more complex scenarios, such as systems with unstable zero dynamics or environments with adversarial obstacles

The gatekeeper approach, while effective in ensuring safety in dynamic environments with limited sensing capabilities, has certain limitations. One limitation is the assumption that a suitable backup controller and set exist, which may not always be the case for all robotic systems and environments. To address this limitation, the gatekeeper framework can be extended to handle more complex scenarios. For systems with unstable zero dynamics, advanced control techniques such as sliding mode control or adaptive control can be integrated into the gatekeeper algorithm to stabilize the system around critical points. In environments with adversarial obstacles, game-theoretic approaches can be employed to anticipate and counteract the actions of the obstacles, ensuring safe navigation. By incorporating these advanced control strategies, the gatekeeper framework can be enhanced to handle a wider range of challenging scenarios.

Can the gatekeeper framework be integrated with learning-based perception and planning modules to handle highly uncertain and unstructured environments

The gatekeeper framework can be integrated with learning-based perception and planning modules to enhance its capabilities in handling highly uncertain and unstructured environments. By incorporating machine learning algorithms, the system can adapt and learn from its interactions with the environment, improving its decision-making processes over time. Reinforcement learning can be used to train the system to navigate complex and dynamic environments by rewarding safe behaviors and penalizing risky actions. Additionally, deep learning models can be employed for perception tasks, enabling the system to better understand and interpret sensor data in real-time. By combining the gatekeeper framework with learning-based approaches, the system can become more adaptive, robust, and capable of handling the challenges posed by uncertain and unstructured environments.