Safe Learning of Quadrotor Dynamics Using Barrier Certificates (1710.05472v1)

Abstract: To effectively control complex dynamical systems, accurate nonlinear models are typically needed. However, these models are not always known. In this paper, we present a data-driven approach based on Gaussian processes that learns models of quadrotors operating in partially unknown environments. What makes this challenging is that if the learning process is not carefully controlled, the system will go unstable, i.e., the quadcopter will crash. To this end, barrier certificates are employed for safe learning. The barrier certificates establish a non-conservative forward invariant safe region, in which high probability safety guarantees are provided based on the statistics of the Gaussian Process. A learning controller is designed to efficiently explore those uncertain states and expand the barrier certified safe region based on an adaptive sampling scheme. In addition, a recursive Gaussian Process prediction method is developed to learn the complex quadrotor dynamics in real-time. Simulation results are provided to demonstrate the effectiveness of the proposed approach.

• The paper proposes a data-driven approach using Gaussian Processes to learn quadrotor dynamics safely in unknown environments, ensuring stability with barrier certificates.
• The methodology incorporates adaptive sampling for efficient exploration of uncertain states and recursive GP prediction for real-time online learning.
• Simulation results demonstrate successful safe learning, crash avoidance, and improved trajectory tracking, highlighting the practical implications for autonomous systems in complex, dynamic settings.

Safe Learning of Quadrotor Dynamics Using Barrier Certificates

The paper "Safe Learning of Quadrotor Dynamics Using Barrier Certificates" addresses a critical problem in control systems, particularly those involving quadrotors, emphasizing both safety and performance in unknown and dynamic environments. The paper proposes a data-driven approach using Gaussian Processes (GPs) to build accurate nonlinear models for quadrotor control in environments where the dynamics are not fully known. A core challenge addressed is ensuring stability and preventing crashes during the learning process, which is achieved through the use of barrier certificates.

Key Contributions and Methodology

The authors introduce several key contributions in this work:

1. Barrier Certificates: The use of barrier certificates in this context provides a non-conservative forward invariant safe region. These certificates offer high probability safety guarantees based on the statistical properties of GPs. The approach leverages barrier certificates to delineate and expand a safe operational region within the state space of the quadrotor.
2. Adaptive Sampling: The exploration of uncertain states in the system dynamics is controlled using an adaptive sampling scheme. This efficiently extends the certified safe region, striking a balance between exploration and exploitation, and reducing computational demands by adapting the sampling density according to the certainty in different regions of the state space.
3. Recursive GP Prediction: In addition to employing GPs for learning the quadrotor dynamics, a recursive prediction method is utilized, allowing for real-time learning and adaptation. This facilitates the inclusion of new data into the model without overwhelming computational resources, making online learning feasible.

The methodology detailed includes constructing a safe region using barrier certificates and incrementally expanding this region as the model becomes more certain about dynamic properties. The quadrotor's dynamics are learned iteratively, and safety is ensured by retaining operations within the dynamically growing barrier-certified safe regions.

Numerical Results and Implications

The paper provides simulation results demonstrating the effectiveness of the proposed strategy. Key numerical results include the successful learning of quadrotor dynamics while maintaining safety and avoiding crashes, despite the initial inaccuracies in the quadrotor model and external disturbances such as wind. The adaptive sampling and recursive GP methods enable efficient learning and control, ultimately improving trajectory tracking performance.

Implications and Future Developments

The research has significant practical implications in the field of autonomous vehicles and robotics, particularly for systems where the dynamics are partially unknown or subject to external disturbances. By ensuring safety through learning-based control, the system's applicability in real-world scenarios increases, promoting robust and efficient operations in complex, dynamic environments.

Theoretically, this work emphasizes the potential of combining machine learning techniques, such as GPs—capable of capturing intricate dynamical behaviors—with classical control concepts like barrier certificates to enhance control system safety without sacrificing performance. It points toward an exciting future where learning and safety can coexist robustly, facilitating the deployment of autonomous systems in previously inaccessible settings.

The paper invites future exploration into further reducing computational demands, extending the dimensionality and complexity of systems considered, and refining the balance between safe exploration and efficient performance optimization in real-time applications. Additionally, there is potential for further integration with other machine learning methodologies to augment model accuracy and control sophistication.