Organizations: Shenzhen Key Lab for Advanced Motion Control and Modern Automation Equipments, School of Intelligence Science and Engineering, Harbin Institute of Technology, Shenzhen, Guangdong 518055, China · School of Data Science, Lingnan University, Hong Kong · School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, with M3S, SMART, and with MIT CSAIL · Queen’s University, Kingston, ON K7L 3N6, Canada
Merely pursuing performance may adversely affect safety, while a conservative policy for safe exploration will degrade the performance. How to guarantee both safety and performance in learning-based control problems is an interesting yet challenging issue. This paper aims to enhance system performance with a safety guarantee by solving reinforcement learning (RL)-based optimal control problems for nonlinear systems subject to high-relative-degree state constraints and unknown time-varying disturbance/actuator faults. A new type of control barrier functions (CBFs), termed high-order reciprocal-based control barrier function, is proposed to handle high-relative-degree constraints, which extends the design of CBFs to enforce robust safety without knowing the disturbance bound. The concept of gradient similarity is proposed to quantify the relationship between safety and performance. Finally, gradient manipulation and adaptive mechanisms are introduced in the model-based safe RL framework to enhance the performance with a safety guarantee. Two simulation examples illustrate the efficacy of the proposed algorithms.
Ensuring safe exploration in high-dimensional systems with unknown dynamics remains a significant challenge. Existing safe reinforcement learning methods often provide safety guarantees only in expectation, which can still lead to safety violations. Control-theoretic approaches, in contrast, offer hard constraint-based safety guarantees but typically assume access to known system dynamics or require accurate estimation of control-affine models. In this paper, we propose a safe reinforcement learning framework that learns a probabilistic control-affine dynamics model in an offline setting. The learned model is leveraged to explicitly construct control barrier functions (CBFs) that incorporate model uncertainty to provide conservative safety constraints. These CBF constraints are enforced through an online constraint-based action correction mechanism, enabling safe exploration without overly restricting task performance. Empirical evaluations on nonlinear, complex continuous-control benchmarks demonstrate that our approach achieves returns comparable to those of existing baselines while significantly reducing safety violations.
This paper investigates the optimal safety control problem of nonlinear control systems by proposing novel high-order control barrier functions (HOCBFs). Different from zeroing HOCBFs, two novel HOCBFs are derived and the safety controllers are designed in an explicit way. Next, we implement vector Lyapunov function approach to propose a novel high-order control Lyapunov function (HOCLF) for the stabilization control problem. The relations between the proposed and existing HOCBFs are discussed. Afterwards, the compatibility of the proposed HOCLF and HOCBF is addressed to guarantee the stabilization and safety control objectives simultaneously, and thus the optimal controller is established. Finally, a numerical example from the navigation problem of quadrotors is presented to illustrate the efficacy of the derived results.
Reinforcement learning (RL), while powerful and expressive, can often prioritize performance at the expense of safety. Yet safety violations can lead to catastrophic outcomes in real-world deployments. Control Barrier Functions (CBFs) offer a principled method to enforce dynamic safety -- traditionally deployed online via safety filters. While the result is safe behavior, the fact that the RL policy does not have knowledge of the CBF can lead to conservative behaviors. This paper proposes CBF-RL, a framework for generating safe behaviors with RL by enforcing CBFs in training. CBF-RL has two key attributes: (1) minimally modifying a nominal RL policy to encode safety constraints via a CBF term, (2) and safety filtering of the policy rollouts in training. Theoretically, we prove that continuous-time safety filters can be deployed via closed-form expressions on discrete-time roll-outs. Practically, we demonstrate that CBF-RL internalizes the safety constraints in the learned policy -- both enforcing safer actions and biasing towards safer rewards -- enabling safe deployment without the need for an online safety filter. We validate our framework through ablation studies on navigation tasks and on the Unitree G1 humanoid robot, where CBF-RL enables safer exploration, faster convergence, and robust performance under uncertainty, enabling the humanoid robot to avoid obstacles and climb stairs safely in real-world settings without a runtime safety filter.