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.Comment: Submitted to the IEEE Control System Letters (L-CSS) and the 2024 American Control Conference (ACC). 6 pages, 3 figure

Safety-Critical Traffic Control by Connected Automated Vehicles

Connected automated vehicles (CAVs) have shown great potential in improving traffic throughput and stability. Although various longitudinal control strategies have been developed for CAVs to achieve string stability in mixed-autonomy traffic systems, the potential impact of these controllers on safety has not yet been fully addressed. This paper proposes safety-critical traffic control (STC) by CAVs -- a strategy that allows a CAV to stabilize the traffic behind it, while maintaining safety relative to both the preceding vehicle and the following connected human-driven vehicles (HDVs). Specifically, we utilize control barrier functions (CBFs) to impart collision-free behavior with formal safety guarantees to the closed-loop system. The safety of both the CAV and HDVs is incorporated into the framework through a quadratic program-based controller, that minimizes deviation from a nominal stabilizing traffic controller subject to CBF-based safety constraints. Considering that some state information of the following HDVs may be unavailable to the CAV, we employ state observer-based CBFs for STC. Finally, we conduct extensive numerical simulations -- that include vehicle trajectories from real data -- to demonstrate the efficacy of the proposed approach in achieving string stable and, at the same time, provably safe traffic

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.Comment: Accepted to the IEEE Transactions on Intelligent Transportation Systems. 11 pages, 10 figure

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.Comment: Accepted to the 62nd IEEE Conference on Decision and Control. 6 pages, 5 figure

Verifying Safe Transitions between Dynamic Motion Primitives on Legged Robots

Functional autonomous systems often realize complex tasks by utilizing state machines comprised of discrete primitive behaviors and transitions between these behaviors. This architecture has been widely studied in the context of quasi-static and dynamics-independent systems. However, applications of this concept to dynamical systems are relatively sparse, despite extensive research on individual dynamic primitive behaviors, which we refer to as "motion primitives." This paper formalizes a process to determine dynamic-state aware conditions for transitions between motion primitives in the context of safety. The result is framed as a "motion primitive graph" that can be traversed by standard graph search and planning algorithms to realize functional autonomy. To demonstrate this framework, dynamic motion primitives -- including standing up, walking, and jumping -- and the transitions between these behaviors are experimentally realized on a quadrupedal robot

The effects of delay on the HKB model of human motor coordination

Understanding human motor coordination holds the promise of developing diagnostic methods for mental illnesses such as schizophrenia. In this paper, we analyse the celebrated Haken-Kelso-Bunz (HKB) model, describing the dynamics of bimanual coordination, in the presence of delay. We study the linear dynamics, stability, nonlinear behaviour and bifurcations of this model by both theoretical and numerical analysis. We calculate in-phase and anti-phase limit cycles as well as quasi-periodic solutions via double Hopf bifurcation analysis and centre manifold reduction. Moreover, we uncover further details on the global dynamic behaviour by numerical continuation, including the occurrence of limit cycles in phase quadrature and 1-1 locking of quasi-periodic solutions.Comment: Submitted to the SIAM Journal on Applied Dynamical Systems. 27 pages, 8 figure

Safety-Critical Control of Compartmental Epidemiological Models with Measurement Delays

We introduce a methodology to guarantee safety against the spread of infectious diseases by viewing epidemiological models as control systems and by considering human interventions (such as quarantining or social distancing) as control input. We consider a generalized compartmental model that represents the form of the most popular epidemiological models and we design safety-critical controllers that formally guarantee safe evolution with respect to keeping certain populations of interest under prescribed safe limits. Furthermore, we discuss how measurement delays originated from incubation period and testing delays affect safety and how delays can be compensated via predictor feedback. We demonstrate our results by synthesizing active intervention policies that bound the number of infections, hospitalizations and deaths for epidemiological models capturing the spread of COVID-19 in the USA.Comment: Submitted to the IEEE Control System Letters (L-CSS) and the 2021 American Control Conference (ACC). 6 pages, 3 figure

Disturbance Observers for Robust Safety-critical Control with Control Barrier Functions

This work provides formal safety guarantees for control systems with disturbance. A disturbance observer-based robust safety-critical controller is proposed, that estimates the effect of the disturbance on safety and utilizes this estimate with control barrier functions to attain provably safe dynamic behavior. The observer error bound - which consists of transient and steady-state parts - is quantified, and the system is endowed with robustness against this error via the proposed controller. An adaptive cruise control problem is used as illustrative example through simulations including real disturbance data.Comment: 6 pages, 5 figure

Energy-efficient Reactive and Predictive Connected Cruise Control

In this paper, we propose a framework for the longitudinal control of connected and automated vehicles traveling in mixed traffic consisting of connected and non-connected human-driven vehicles. Reactive and predictive controllers are proposed. Reactive controllers are given by explicit feedback control laws. In predictive controllers, the control input is optimized in a receding-horizon fashion, which depends on the predictions of motions of preceding vehicles. Beyond-line-of-sight information is obtained via vehicle-to-vehicle (V2V) communication, and is utilized in the proposed reactive and predictive controllers. Simulations utilizing real traffic data are used to show that connectivity can bring significant energy savings.Comment: 18 pages, 12 figures, submitted to Transportation Research Part C: Emerging Technologie