Control Lyapunov functions (CLFs) and Control Barrier Functions (CBFs) have been used to develop provably safe controllers by means of quadratic programs (QPs). This framework guarantees safety in the form of trajectory invariance with respect to a given set, but it can introduce undesirable equilibrium points to the closed loop system, which can be asymptotically stable. In this work, we present a detailed study of the formation and stability of equilibrium points with the CLF-CBF-QP framework with multiple CBFs. In particular, we prove that undesirable equilibrium points occur for most systems, and their stability is dependent on the CLF and CBF geometrical properties. We introduce the concept of CLF-CBF compatibility for a system, regarding a CLF-CBF pair inducing no stable equilibrium points other than the CLF global minimum on the corresponding closed-loop dynamics. Sufficient conditions for CLF-CBF compatibility for LTI and drift-less full-rank systems with quadratic CLF and CBFs are derived, and we propose a novel control strategy to induce smooth changes in the CLF geometry at certain regions of the state space in order to satisfy the CLF-CBF compatibility conditions, aiming to achieve safety with respect to multiple safety objectives and quasi-global convergence of the trajectories towards the CLF minimum. Numerical simulations illustrate the applicability of the proposed method.
In this paper, we analyze the system behavior for general nonlinear control-affine systems when a control barrier function-induced quadratic program-based controller is employed for feedback. In particular, we characterize the existence and locations of possible equilibrium points of the closed-loop system and also provide analytical results on how design parameters affect them. Based on this analysis, a simple modification on the existing quadratic program-based controller is provided, which, without any assumptions other than those taken in the original program, inherits the safety set forwa…
A fundamental concern in progressing Airborne Wind Energy (AWE) operations towards commercial success, is guaranteeing that safety requirements placed on the systems are met. Due to the high dimensional complexity of AWE systems, however, formal mathematical robustness guarantees become difficult to compute. We draw on research from Hamilton-Jacobi (HJ) reachability analysis to compute the optimal control policy for tracking a flight path, while enforcing safety constraints on the system. In addition, the zero-sublevel set of the computed value function inherent in HJ reachability analysis ind…
CNRS（法国国家科学研究中心）；University of Rennes（雷恩大学）；Inria（法国国家信息与自动化研究所）；IRISA（法国信息与随机系统研究所）；University of Innsbruck（因斯布鲁克大学）
This paper presents an approach to deal with safety of dynamical systems in presence of multiple non-convex unsafe sets. While optimal control and model predictive control strategies can be employed in these scenarios, they suffer from high computational complexity in case of general nonlinear systems. Leveraging control barrier functions, on the other hand, results in computationally efficient control algorithms. Nevertheless, when safety guarantees have to be enforced alongside stability objectives, undesired asymptotically stable equilibrium points have been shown to arise. We propose a com…
Safe Feedback Optimization through Control Barrier Functions
AI4I institute（AI4I研究所）；Eindhoven University of Technology（埃因霍温理工大学）；California Institute of Technology（加州理工学院）；University of California San Diego（加利福尼亚大学圣地亚哥分校）
Assuring system stability is typically a major control design objective. In this paper, we present a system where instability provides a crucial benefit. We consider multi-agent collision avoidance using Control Barrier Functions (CBF) and study trade-offs between safety and liveness -- the ability to reach a destination without large detours or gridlock. We compare two standard decentralized policies, with only the local (host) control available, to co-optimization policies (PCCA and CCS) where everyone's (virtual) control action is available. The co-optimization policies compute control for …
ETH Zürich（苏黎世联邦理工学院）；University of Stuttgart（斯图加特大学）；Gymnasium Burgdorf（堡多夫中学）；Swiss Institute for Empirical Economic Research (SEW), University of St.Gallen（圣加仑大学瑞士实证经济研究所）
