Verifying the safety of controllers is critical for many applications, but is especially challenging for systems with bounded inputs. Backup control barrier functions (bCBFs) offer a structured approach to synthesizing safe controllers that are guaranteed to satisfy input bounds by leveraging the knowledge of a backup controller. While powerful, bCBFs require solving a high-dimensional quadratic program at run-time, which may be too costly for computationally-constrained systems such as aerospace vehicles. We propose an approach that optimally interpolates between a nominal controller and the backup controller, and we derive the solution to this optimization problem in closed form. We prove that this closed-form controller is guaranteed to be safe while obeying input bounds. We demonstrate the effectiveness of the approach on a double integrator and a nonlinear fixed-wing aircraft example.

NCREASING use of robotic systems in real-world applications necessitates advanced controllers that ensure safety, robustness, and effectiveness in human-machine teaming [1]. This letter formalizes and builds upon our recent work on online safety verification and control [2], which introduces gatekeeper as a novel algorithmic component between the planner and the controller of the autonomous system. To briefly illustrate the principle behind gatekeeper, consider a Unmanned Aerial V ehicle (UA V) navigating an unknown environment. The UA V follows a nominal trajectory, generated by its planner and tracked by its controller. At each iteration, gatekeeper performs two key steps: (i) it evaluates the currently known safe set (derived from onboard sensing), and a backup set, which represents a region the UA V can retreat to if the nominal trajectory is predicted to exit the safe set in the future; (ii) it constructs a candidate trajectory by stitching together the nominal trajectory (up to a future time horizon) and a backup trajectory that leads safely into the backup set. The authors would like to acknowledge the support of the National Science Foundation (NSF) under grant no.

Reinforcement learning (RL) excels in applications such as video games and robotics, but ensuring safety and stability remains challenging when using RL to control real-world systems where using model-free algorithms suffering from low sample efficiency might be prohibitive. This paper first provides safety and stability definitions for the RL system, and then introduces a Neural ordinary differential equations-based Lyapunov-Barrier Actor-Critic (NLBAC) framework that leverages Neural Ordinary Differential Equations (NODEs) to approximate system dynamics and integrates the Control Barrier Function (CBF) and Control Lyapunov Function (CLF) frameworks with the actor-critic method to assist in maintaining the safety and stability for the system. Within this framework, we employ the augmented Lagrangian method to update the RL-based controller parameters. Additionally, we introduce an extra backup controller in situations where CBF constraints for safety and the CLF constraint for stability cannot be satisfied simultaneously. Simulation results demonstrate that the framework leads the system to approach the desired state and allows fewer violations of safety constraints with better sample efficiency compared to other methods.

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.

Reinforcement learning (RL) has demonstrated impressive performance in various areas such as video games and robotics. However, ensuring safety and stability, which are two critical properties from a control perspective, remains a significant challenge when using RL to control real-world systems. In this paper, we first provide definitions of safety and stability for the RL system, and then combine the control barrier function (CBF) and control Lyapunov function (CLF) methods with the actor-critic method in RL to propose a Barrier-Lyapunov Actor-Critic (BLAC) framework which helps maintain the aforementioned safety and stability for the system. In this framework, CBF constraints for safety and CLF constraint for stability are constructed based on the data sampled from the replay buffer, and the augmented Lagrangian method is used to update the parameters of the RL-based controller. Furthermore, an additional backup controller is introduced in case the RL-based controller cannot provide valid control signals when safety and stability constraints cannot be satisfied simultaneously. Simulation results show that this framework yields a controller that can help the system approach the desired state and cause fewer violations of safety constraints compared to baseline algorithms.

This paper presents the gatekeeper algorithm, a real-time and computationally-lightweight method to ensure that nonlinear systems can operate safely within unknown and dynamic environments despite limited perception. gatekeeper integrates with existing path planners and feedback controllers by introducing an additional verification step that ensures that proposed trajectories can be executed safely, despite nonlinear dynamics subject to bounded disturbances, input constraints and partial knowledge of the environment. Our key contribution is that (A) we propose an algorithm to recursively construct committed trajectories, and (B) we prove that tracking the committed trajectory ensures the system is safe for all time into the future. The method is demonstrated on a complicated firefighting mission in a dynamic environment, and compares against the state-of-the-art techniques for similar problems.