Control barrier functions (CBFs) have recently emerged as a means to ensure safety of controlled dynamical systems. CBFs are suitable for obstacle avoidance, where the CBF is often constructed from the distance and relative velocity between the vehicle and the obstacle. For vehicles required to maintain non-zero forward speed, ordinary (non-hybrid) CBFs cannot ensure safety due to vanishing control authority when the vehicle is oriented directly towards the obstacle. In this paper, synergistic CBFs are proposed, which is an intuitive extension of CBFs using ideas from synergistic Lyapunov functions. A synergistic CBF for obstacle avoidance for nonholonomic vehicles is constructed by shifting the orientations with vanishing control authority. This induces a penalty for traversing the obstacle in the counterclockwise or clockwise direction, where a logic variable is used to determine the preferred direction. The performance of the CBF is illustrated by a case study.

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Resilience is an important feature of autonomous systems. To be resilient, a control system must be stable, robust, and safe. This paper explores the use of hybrid feedback controllers to ensure robustness towards uncertainties and disturbances in motion control systems for autonomous ships. Motivated by recent developments in control barrier functions (CBFs) for safe maneuvering of autonomous ships, a CBF-based hybrid kinematic controller for obstacle avoidance is proposed. The controller uses course angle as control input, making it suitable for ships with a limited speed envelope. The performance of the controller is illustrated by simulations, using an underactuated ship as a case study.

This paper presents a hybrid feedback controller suitable for orientation control of ships. A hybrid kinematic controller on the unit circle is constructed from the gradient of a synergistic potential function, which globally asymptotically stabilizes a desired orientation, with yaw rate viewed as control input. While this idea is not new, the potential function is novel and possesses some desired properties. The kinematic controller generates smooth reference signals for the desired velocity and acceleration, except at instances when the controller switches. Continuity of velocity and acceleration is achieved by controlling the yaw rate through a double integrator. Moreover, the velocity and acceleration converge to their desired values exponentially. The resulting closed-loop system is stable, provided the controller gains satisfy mild constraints. This is shown using a hybrid Lyapunov function.

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