Safety-Critical Control for Autonomous Systems: Control Barrier Functions via Reduced-Order Models

Modern autonomous systems, such as flying, legged, and wheeled robots, are generally characterized by high-dimensional nonlinear dynamics, which presents challenges for model-based safety-critical control design. Motivated by the success of reduced-order models in robotics, this paper presents a tutorial on constructive safety-critical control via reduced-order models and control barrier functions (CBFs). To this end, we provide a unified formulation of techniques in the literature that share a common foundation of constructing CBFs for complex systems from CBFs for much simpler systems. Such ideas are illustrated through formal results, simple numerical examples, and case studies of real-world systems to which these techniques have been experimentally applied.

Collision Avoidance and Geofencing for Fixed-wing Aircraft with Control Barrier Functions

Safety-critical failures often have fatal consequences in aerospace control. Control systems on aircraft, therefore, must ensure the strict satisfaction of safety constraints, preferably with formal guarantees of safe behavior. This paper establishes the safety-critical control of fixed-wing aircraft in collision avoidance and geofencing tasks. A control framework is developed wherein a run-time assurance (RTA) system modulates the nominal flight controller of the aircraft whenever necessary to prevent it from colliding with other aircraft or crossing a boundary (geofence) in space. The RTA is formulated as a safety filter using control barrier functions (CBFs) with formal guarantees of safe behavior. CBFs are constructed and compared for a nonlinear kinematic fixed-wing aircraft model. The proposed CBF-based controllers showcase the capability of safely executing simultaneous collision avoidance and geofencing, as demonstrated by simulations on the kinematic model and a high-fidelity dynamical model.

Safety-critical Control of Quadrupedal Robots with Rolling Arms for Autonomous Inspection of Complex Environments

This paper presents a safety-critical control framework tailored for quadruped robots equipped with a roller arm, particularly when performing locomotive tasks such as autonomous robotic inspection in complex, multi-tiered environments. In this study, we consider the problem of operating a quadrupedal robot in distillation columns, locomoting on column trays and transitioning between these trays with a roller arm. To address this problem, our framework encompasses the following key elements: 1) Trajectory generation for seamless transitions between columns, 2) Foothold re-planning in regions deemed unsafe, 3) Safety-critical control incorporating control barrier functions, 4) Gait transitions based on safety levels, and 5) A low-level controller. Our comprehensive framework, comprising these components, enables autonomous and safe locomotion across multiple layers. We incorporate reduced-order and full-body models to ensure safety, integrating safety-critical control and footstep re-planning approaches. We validate the effectiveness of our proposed framework through practical experiments involving a quadruped robot equipped with a roller arm, successfully navigating and transitioning between different levels within the column tray structure.

A Learning-Based Framework for Safe Human-Robot Collaboration with Multiple Backup Control Barrier Functions

Ensuring robot safety in complex environments is a difficult task due to actuation limits, such as torque bounds. This paper presents a safety-critical control framework that leverages learning-based switching between multiple backup controllers to formally guarantee safety under bounded control inputs while satisfying driver intention. By leveraging backup controllers designed to uphold safety and input constraints, backup control barrier functions (BCBFs) construct implicitly defined control invariance sets via a feasible quadratic program (QP). However, BCBF performance largely depends on the design and conservativeness of the chosen backup controller, especially in our setting of human-driven vehicles in complex, e.g, off-road, conditions. While conservativeness can be reduced by using multiple backup controllers, determining when to switch is an open problem. Consequently, we develop a broadcast scheme that estimates driver intention and integrates BCBFs with multiple backup strategies for human-robot interaction. An LSTM classifier uses data inputs from the robot, human, and safety algorithms to continually choose a backup controller in real-time. We demonstrate our method's efficacy on a dual-track robot in obstacle avoidance scenarios. Our framework guarantees robot safety while adhering to driver intention.

Composing Control Barrier Functions for Complex Safety Specifications

The increasing complexity of control systems necessitates control laws that guarantee safety w.r.t. complex combinations of constraints. In this letter, we propose a framework to describe compositional safety specifications with control barrier functions (CBFs). The specifications are formulated as Boolean compositions of state constraints, and we propose an algorithmic way to create a single continuously differentiable CBF that captures these constraints and enables safety-critical control. We describe the properties of the proposed CBF, and we demonstrate its efficacy by numerical simulations.

On the Safety of Connected Cruise Control: Analysis and Synthesis with Control Barrier Functions

Connected automated vehicles have shown great potential to improve the efficiency of transportation systems in terms of passenger comfort, fuel economy, stability of driving behavior and mitigation of traffic congestions. Yet, to deploy these vehicles and leverage their benefits, the underlying algorithms must ensure their safe operation. In this paper, we address the safety of connected cruise control strategies for longitudinal car following using control barrier function (CBF) theory. In particular, we consider various safety measures such as minimum distance, time headway and time to conflict, and provide a formal analysis of these measures through the lens of CBFs. Additionally, motivated by how stability charts facilitate stable controller design, we derive safety charts for existing connected cruise controllers to identify safe choices of controller parameters. Finally, we combine the analysis of safety measures and the corresponding stability charts to synthesize safety-critical connected cruise controllers using CBFs. We verify our theoretical results by numerical simulations.

Safety-Critical Control with Bounded Inputs via Reduced Order Models

Guaranteeing safe behavior on complex autonomous systems -- from cars to walking robots -- is challenging due to the inherently high dimensional nature of these systems and the corresponding complex models that may be difficult to determine in practice. With this as motivation, this paper presents a safety-critical control framework that leverages reduced order models to ensure safety on the full order dynamics -- even when these models are subject to disturbances and bounded inputs (e.g., actuation limits). To handle input constraints, the backup set method is reformulated in the context of reduced order models, and conditions for the provably safe behavior of the full order system are derived. Then, the input-to-state safe backup set method is introduced to provide robustness against discrepancies between the reduced order model and the actual system. Finally, the proposed framework is demonstrated in high-fidelity simulation, where a quadrupedal robot is safely navigated around an obstacle with legged locomotion by the help of the unicycle model.

Experimental Validation of a Safe Controller Integration Scheme for Connected Automated Trucks

Accomplishing safe and efficient driving is one of the predominant challenges in the controller design of connected automated vehicles (CAVs). It is often more convenient to address these goals separately and integrate the resulting controllers. In this study, we propose a controller integration scheme to fuse performance-based controllers and safety-oriented controllers safely for the longitudinal motion of a CAV. The resulting structure is compatible with a large class of controllers, and offers flexibility to design each controller individually without affecting the performance of the others. We implement the proposed safe integration scheme on a connected automated truck using an optimal-in-energy controller and a safety-oriented connected cruise controller. We validate the premise of the safe integration through experiments with a full-scale truck in two scenarios: a controlled experiment on a test track and a real-world experiment on a public highway. In both scenarios, we achieve energy efficient driving without violating safety.

Connected Cruise and Traffic Control for Pairs of Connected Automated Vehicles

This paper considers mixed traffic consisting of connected automated vehicles equipped with vehicle-to-everything (V2X) connectivity and human-driven vehicles. A control strategy is proposed for communicating pairs of connected automated vehicles, where the two vehicles regulate their longitudinal motion by responding to each other, and, at the same time, stabilize the human-driven traffic between them. Stability analysis is conducted to find stabilizing controllers, and simulations are used to show the efficacy of the proposed approach. The impact of the penetration of connectivity and automation on the string stability of traffic is quantified. It is shown that, even with moderate penetration, connected automated vehicle pairs executing the proposed controllers achieve significant benefits compared to when these vehicles are disconnected and controlled independently.

Control Barrier Functionals: Safety-critical Control for Time Delay Systems

This work presents a theoretical framework for the safety-critical control of time delay systems. The theory of control barrier functions, that provides formal safety guarantees for delay-free systems, is extended to systems with state delay. The notion of control barrier functionals is introduced to attain formal safety guarantees, by enforcing the forward invariance of safe sets defined in the infinite dimensional state space. The proposed framework is able to handle multiple delays and distributed delays both in the dynamics and in the safety condition, and provides an affine constraint on the control input that yields provable safety. This constraint can be incorporated into optimization problems to synthesize pointwise optimal and provable safe controllers. The applicability of the proposed method is demonstrated by numerical simulation examples.