Learning-Based Safety-Critical Control Under Uncertainty with Applications to Mobile Robots

Abstract

Control theory is one of the key ingredients of the remarkable rise in robotics. Due to technological advancements, the use of automated robots, which was once primarily limited to industrial and manufacturing settings, has now expanded to impact many different parts of everyday life. Various control strategies have been developed to satisfy a wide range of performance criteria arising from recent applications. These strategies have different characteristics depending on the problem they solve. But, they all have to guarantee stability before satisfying any performance-driven criteria. However, as robotic technologies become increasingly integrated into everyday life, they introduce safety concerns. For autonomous systems to be trusted by the public, they must guarantee safety. In recent years, the concept of set invariance has been incorporated into modern control strategies to enable systematic safety guarantees. In this thesis, we aim to develop safety-critical control methods that can guarantee safety while satisfying performance-driven requirements. In the proposed strategies, we considered formal safety guarantees, robustness to uncertainty, and computational efficiency to be the highest design priorities. Each of them introduces new challenges which are addressed with theoretical contributions. We selected motion control in mobile robots as a use case for proposed controllers which is an active area of research integrating safety, stability, and performance in various scenarios. In particular, we focused on multi-body mobile robots, an area with limited research on safe operation. We provide a comprehensive survey of the recent methods that formalize safety for the dynamical systems via set invariance. A discussion on the strengths and limitations of each method demonstrates the capabilities of control barrier functions (CBFs) as a systematic tool for safety assurance in motion control. A safety filter module is also introduced as a tool to enforce safety. CBF constraints can be enforced as hard constraints in quadratic programming (QP) optimization, which rectifies the nominal control law based on the set of safe inputs.

We propose a multiple CBF scheme that enforces several safety constraints with high relative degrees. Using the multi-input multi-output (MIMO) feedback linearization technique, we derive conditions that ensure all control inputs contribute effectively to safety. This control structure is essential for challenging robotic applications requiring multiple safety criteria to be met simultaneously. To demonstrate the capabilities of our approach, we address reactive obstacle avoidance for a class of multi-body mobile robots, specifically tractor-trailer systems. The lack of fast response due to poor maneuverability makes reactive obstacle avoidance difficult for these systems. We develop a control structure based on a multiple CBFs scheme for a multi-steering tractor-trailer system to ensure a collision-free maneuver for both the tractor and trailer in the presence of several obstacles. Model predictive control serves as the nominal tracking controller, and we validate the proposed strategy in several challenging scenarios.

Although the CBF method has demonstrated a great potential for ensuring safety, it is a model-based method and its effectiveness is closely tied to an accurate system model. In practice, model uncertainty compromises safety guarantees and may lead to conservative safety constraints, or conversely, allow the system to operate in unsafe regions. To address this, we explore developing safety-critical controllers that account for model uncertainty. Achieving this requires combining the theoretical guarantees of model-based methods with the adaptability of data-driven techniques. For this study, we selected Gaussian processes (GPs) which bring together required capabilities. It provides bounds on the posterior distribution, enabling theoretical analysis, and producing reliable approximations even with a low amount of training data, which is common in data-driven control. The proposed strategy mitigates the adverse effects of uncertainty on high-order CBFs (HOCBFs). A particular structure of the covariance function is designed that enables us to convert the chance constraints of HOCBFs into a second-order cone constraint, which results in a convex constrained optimization as a safety filter. A discussion on the feasibility of the resulting optimization is presented which provides the necessary and sufficient conditions for feasibility. In addition, we consider an alternative approach that uses matrix variate GP (MVGP) to approximate unknown system dynamics. A comparative analysis is presented which highlights the differences and similarities of both methods. The proposed strategy is validated on adaptive cruise control and active suspension systems, common applications in mobile robots.

This study next explores the safety of switching systems, focusing on cases where system stability is assured through control Lyapunov functions (CLFs) and CBFs are applied for safety. We show that the effect of uncertainty on the safety and stability constraint forms piecewise residuals for each switching surface. We introduce a batch multi-output Gaussian process (MOGP) framework to approximate these piecewise residuals, thereby mitigating the adverse effects of uncertainty. We show that by leveraging a specific covariance function, the chance constrained safety filter can be converted to a convex optimization, that is solvable in real-time. We analyze the feasibility of the resulting optimization and provide the necessary and sufficient conditions for feasibility. The effectiveness of the proposed strategy is validated through a simulation of a switching adaptive cruise control system.