Safe Controller Optimization for Quadrotors with Gaussian Processes (1509.01066v4)

Abstract: One of the most fundamental problems when designing controllers for dynamic systems is the tuning of the controller parameters. Typically, a model of the system is used to obtain an initial controller, but ultimately the controller parameters must be tuned manually on the real system to achieve the best performance. To avoid this manual tuning step, methods from machine learning, such as Bayesian optimization, have been used. However, as these methods evaluate different controller parameters on the real system, safety-critical system failures may happen. In this paper, we overcome this problem by applying, for the first time, a recently developed safe optimization algorithm, SafeOpt, to the problem of automatic controller parameter tuning. Given an initial, low-performance controller, SafeOpt automatically optimizes the parameters of a control law while guaranteeing safety. It models the underlying performance measure as a Gaussian process and only explores new controller parameters whose performance lies above a safe performance threshold with high probability. Experimental results on a quadrotor vehicle indicate that the proposed method enables fast, automatic, and safe optimization of controller parameters without human intervention.

• The paper introduces a safe tuning method for quadrotors by integrating Gaussian Processes with Bayesian Optimization to prevent system failures.
• It employs the SafeOpt algorithm to methodically explore controller parameters while only testing those exceeding a preset safety threshold.
• Real flight tests validate significant improvements in quadrotor performance, enhancing speed, stability, and overall control safety.

Safe Controller Optimization for Quadrotors with Gaussian Processes

The paper by Berkenkamp, Schoellig, and Krause presents a novel approach to controller parameter tuning for quadrotors that incorporates a safe optimization framework, specifically utilizing Gaussian Processes (GPs) and Bayesian Optimization. This seminal work introduces the adaptation of a safe optimization algorithm, SafeOpt, to automatically tune controller parameters while maintaining safety constraints during the testing process. This research addresses the major challenge in controller design of balancing the tuning for performance improvement and maintaining safety to avoid system failures.

Overview

Traditionally, controller tuning in dynamic systems like quadrotors involves a cycle of manual adjustments and evaluations. This often leads to time-consuming processes and potential for safety-critical failures if incorrect parameters are tested. Previous approaches such as model-based tuning, gradient approximation methods, or machine learning techniques like genetic algorithms either rely heavily on accurate models or require an impractical number of evaluations to ensure global optimization.

The authors propose a method leveraging SafeOpt that iteratively refines controller parameters using a probabilistic model of performance based on GPs. Unlike conventional Bayesian optimization, SafeOpt is designed to evaluate only those parameters that are predicted to remain above a predefined safety threshold, thereby practically eliminating the risk of critical failures during optimization.

Methodology and Results

The core of the method is to model the control performance as a GP, which offers a way to manage uncertainty in predictions and update beliefs about the system's behavior as new data is observed. The SafeOpt algorithm utilizes these GP predictions to determine a set of potentially optimal or safely expandable controller parameters at each iteration.

Significantly, the algorithm was experimentally validated using real quadrotor flight tests. The paper provides strong numerical evidence of the effectiveness of the method. Controller performance was optimized through a defined cost function improvement, leading to significant enhancements in quadrotor control dynamics (e.g., improved speed and stability during flight tests) without incurring system failures.

Implications and Future Work

Practically, the application of Safe Bayesian Optimization advances the field by allowing more efficient tuning of robotic controllers without the extensive human intervention typically required. This method could be extensively useful in situations where models are difficult to obtain or unreliable due to system complexities like unmodeled dynamics or unknown delays.

Theoretically, the research extends the applicability of safe optimization techniques in machine learning to real-world robotics. This provides a pathway for future work to explore the adaptability of safe optimization in other safety-critical domains or with more complex systems who can benefit from autonomous, safe parameter tuning.

The success of SafeOpt with GPs on robotic systems such as quadrotors opens multiple avenues for further studies. Future developments may focus on extending these techniques to encompass a wider range of robotic systems, increasing the adaptability of the algorithm to dynamic environments, or refining the computational efficiency of managing large parameter spaces in real-time applications.

In conclusion, this work contributes a significant advancement in controller design methodology, marking a step forward in the integration of machine learning techniques in practical robotic applications, and highlights the potential for safety-centered approaches to optimize dynamic systems autonomously.