Rapidly Exploring Random Tree (RRT) algorithms, notably used for nonholonomic vehicle navigation in complex environments, are often not thoroughly evaluated for their specific challenges. This paper presents a first such comparison study of the variants Potential-Quick RRT* (PQ-RRT*), Informed RRT* (IRRT*), RRT*, and RRT, in maritime single-query nonholonomic motion planning. Additionally, the practicalities of using these algorithms in maritime environments are discussed and outlined. We also contend that these algorithms are beneficial not only for trajectory planning in Collision Avoidance Systems (CAS) but also for CAS verification when used as vessel behavior generators. Optimal RRT variants tend to produce more distance-optimal paths but require more computational time due to complex tree wiring and nearest neighbor searches. Our findings, supported by Welch`s t-test at a significance level of Alpha = 0.05, indicate that PQ-RRT* slightly outperform IRRT* and RRT* in achieving shorter trajectory length but at the expense of higher tuning complexity and longer run-times. Based on the results, we argue that these RRT algorithms are better suited for smaller-scale problems or environments with low obstacle congestion ratio. This is attributed to the curse of dimensionality, and trade-off with available memory and computational resources.

In this article, full-scale experiments with a dynamic obstacle intention-aware Collision Avoidance System (CAS) are presented. The CAS consists of the Probabilistic Scenario-Based Model Predictive Control (PSB-MPC) for trajectory planning, dynamic obstacle avoidance, and antigrounding, with a Dynamic Bayesian Network (DBN) used for inferring obstacle intentions online. The novelty of this article lies in the utilization of intention information in deliberate collision-free planning. By inferring multiple different intention states on how and if nearby obstacles adhere to the COLREGS, the PSB-MPC can plan COLREGS-compliant avoidance maneuvers when possible, taking into account its awareness of the situation. The experiments put emphasis on hazardous situations where this intention information is both useful and necessary in order to avoid high collision risk. To the authors’ knowledge, the work is the first field experimental validation of such a probabilistic intention-aware CAS with consideration of multiple intention states. The experimental results demonstrate the validity of the proposed CAS scheme, with adherence to the traffic rules (COLREGS) 7, 8 and 13–17 in a diverse set of situations. The strengths and weaknesses of the proposed CAS are also discussed, giving insights that can be useful for researchers and practitioners in the field. Here, challenges related to detecting obstacle maneuvers and making the intention inference more robust to noise should be addressed as future work to make the scheme better suited for general usage on ships engaged in real traffic.

Navigating the highly unstructured maritime environment poses significant challenges for autonomous ships, particularly in the vicinity of static obstacles and inland waterways. Real-time algorithms capable of comprehending the complexity of nearby grounding hazards are crucial for safe and efficient operations. Electronic Navigational Charts (ENCs) serve as the standard for representing the static environment, providing detailed polygon-based information about obstacles and grounding hazards. However, the non-convex nature of these polygons presents difficulties for optimal control and Model Predictive Control (MPC) schemes. This article introduces an accurate and computationally feasible method for extracting and representing non-convex static obstacle polygons, specifically tailored for use in numerical optimization-based planning, path-following, and trajectory tracking close to static hazards. By employing geometric surface interpolation techniques, Thin Plate Spline (TPS) type of Radial Basis Function (RBF) interpolants are derived from each grounding hazard polygon's point set. These surface approximation functions are then utilized as inequality constraints within a Nonlinear MPC (NMPC) planning scheme to facilitate trajectory tracking with anti-grounding functionality. The integration of surface functions enables the NMPC to consider higher-detail maps, enabling the proposed control system to closely follow trajectories within the unstructured environment's hazardous areas, demonstrated through proof-of-concept simulations.

This article proposes an approach for collision avoidance, path following, and anti-grounding of autonomous surface vessels under consideration of environmental forces based on Nonlinear Model Predictive Control (NMPC). Artificial Potential Fields (APFs) set the foundation for the cost function of the optimal control problem in terms of collision avoidance and anti-grounding. Depending on the risk of a collision given by the resulting force of the APFs, the controller optimizes regarding an adapted heading and travel speed by additionally following a desired path. For this purpose, nonlinear vessel dynamics are used for the NMPC. To extend the situational awareness concerning environmental disturbances impacted by wind, waves, and sea currents, a nonlinear disturbance observer is coupled to the entire NMPC scheme, allowing for the correction of an incorrect vessel motion due to external forces. In addition, the most essential rules according to the Convention on the International Regulations for Preventing Collisions at Sea (COLREGs) are considered. The results of the simulations show that the proposed framework can control an autonomous surface vessel under various challenging scenarios, including environmental disturbances, to avoid collisions and follow desired paths.

The number of maritime projects is increasing yearly, including offshore applications, underwater robotics for ocean condition monitoring, and autonomous ship transport. Many of these activities are safety-critical, making it essential to have a robust closed-loop control system that satisfies constraints arising from underlying physical limitations and safety aspects. However, this is often challenging to achieve for real-world systems. For example, autonomous ships at sea have non-linear and uncertain dynamics and are subject to numerous time-varying environmental disturbances such as waves, currents, and wind. There is growing interest in using machine learning-based approaches to adapt these systems to more complex scenarios. However, there is currently no standard framework to guarantee the safety and stability of such systems. Predictive safety filters have emerged recently as a valuable method for ensuring constraint satisfaction, even when unsafe control inputs are used. The safety filter approach leads to a modular separation of the problem, allowing the usage of arbitrary control policies in a task-agnostic way. In this work, a predictive safety filter is developed to ensure anti-grounding and ship collision avoidance for a small prototype ferry. The filter takes in a nominal input sequence from a potentially unsafe controller and solves an optimization problem to compute a minimal perturbation of the nominal control inputs, which adheres to physical and safety-related constraints. The system is validated by simulations for several realistic scenarios with map data from Trondheim, Norway. It is demonstrated that the predictive safety filter can avoid collisions with static and dynamic obstacles. The predictive safety filter approach is flexible and can be used to improve the robustness of various offshore applications, e.g. wind turbine stabilization, autonomous vessels, and marine robotics.

Research on maritime automatic collision avoidance algorithms is nowadays abundant, and becoming more mature. Moreover, methods for the evaluation of such algorithms are emerging. Therefore, we propose a software environment for simulation and an evaluation framework for maritime collision avoidance, used for testing and evaluating control algorithms. The system comes with a set of standard scenarios that can be augmented with random variations and a database of scenarios based on historical Automatic Identification System (AIS) data that can be used in the simulation. In this framework, the user can set up scenarios with pre-programmed target ship routes, or with target ships that exhibit proactive and reactive collision avoidance maneuvers. Moreover, the user can specify uncertainty in the tracking of target ships and situational awareness, and include the presence of grounding hazards from Electronic Navigational Charts (ENCs). The evaluation tool computes penalties and scores on algorithm performance according to the maritime traffic rules (COLREGS), safety, and other performance-related metrics. The framework can be used for verification and assurance, and further enables automatic adjustment of collision avoidance planners online or offline.

The ability to effectively process large amounts of information in reasonable time will be important for robust deliberative collision avoidance (COLAV) planning algorithms. Failure to do so can lead to collision, and can be compared to lack of proper supervision from officers on watch (OOW). The main contribution in this article is a parallelized implementation of the Probabilistic Scenario-Based Model Predictive Control (PSB-MPC) on a Graphical Processing Unit (GPU) platform which incorporates both dynamic obstacle avoidance and anti-grounding. Simulation results demonstrate that the COLAV planner can produce collision-free trajectories with respect to grounding hazards and nearby vessels at relatively low computational cost, and which also comply to the COLREGS when deemed possible. Corresponding run-time results show that the algorithm utilizing parallel processing performs better than the alternative for increasing numbers of own-ship control behaviours, nearby static and dynamic obstacles, and dynamic obstacle prediction scenarios considered.

In this article, a new approach for ship-ship collision probability estimation based on the Cross-Entropy (CE) method is introduced, which can be treated as an adaptive importance sampler. It has the advantage of attaining low variance estimates of small collision probabilities, which will most often be the case in realistic scenarios. Furthermore, a risk-based Collision Avoidance (COLAV) system being able to take obstacle kinematic uncertainty and intention uncertainty into account is presented, namely the Probabilistic Scenario-Based Model Predictive Control (PSB-MPC). The collision probability estimator (CPE) is used in the risk assessment of the PSB-MPC, and tested in a simulation study, where the total system is validated. Simulation results show that the MPC is able to utilize the CPE for better risk assessment than the original version, in order to make safer decisions in close quarter situations and cases where nearby obstacles make unexpected maneuvers. It is also shown that when all vessels involved use the PSB-MPC, situations are resolved according to the traffic rules in a safe manner.

Maritime traffic increases every year, and therefore also the amount of traffic data from the Automatic Identification System (AIS). Utilizing these data on traffic patterns and possible destinations for long-term vessel prediction is here an important way of gaining maritime situational awareness (MSA) for use in the decision making in autonomous ships, such as collision avoidance algorithms, which can reduce collision risk during voyage. In this article, we present a destination inference method based on piece-wise Ornstein-Uhlenbeck (OU) processes for predicting vessel motions along common traffic lanes toward a set of destinations. The mean velocities of the processes are inferred through the creation of a maritime graph that represents the major traffic patterns in the area of consideration. After using an OU process for prediction along major sea lanes, the Equilibrium Reverting Velocity (ERV) bridging model is used to enable convergence of the prediction towards considered destinations. Then, based on the OU process and ERV bridging model for prediction, Bayesian inference is used to estimate the posterior destination distribution. Tested on a real-time AIS dataset, the method is shown to perform better than current state-of-the art methods in destination inference as it indirectly takes land and passed destinations into account.

The open wording of the traffic rules of the sea, COLREGS, and the existence of unwritten rules, make it essential for an autonomous ship to understand the intentions of meeting traffic. This article uses a dynamic Bayesian network (DBN) to model and infer the intentions of other ships based on their observed real-time behavior. Multiple intention nodes are included to describe the different ways a ship can interpret and conflict with the behavioral rules outlined in CORLEGS. The prior distributions of the intention nodes are adapted to the current situation based on observable characteristics such as location and relative ship size. When a new observation is made, the probability distributions of the intention variables are updated by excluding all combinations of intention states that conflict with the observed behavior. This way of modeling makes the intention probabilities independent of how often observations are made. The resulting model is able to identify situations that are prone to cause misunderstandings and infer the state of multiple intention variables that describe the behavior. Different collision avoidance algorithms can use the resulting intention information to better know if, when, and how to act.

A robust and efficient Collision Avoidance (COLAV) system for autonomous ships is dependent on a high degree of situational awareness. This includes inference of the intent of nearby obstacles, including compliance with traffic rules such as COLREGS, in order to enable more intelligent decision making for the autonomous agent. Here, a generalized framework for obstacle intent inference is introduced. Different obstacle intentions are then considered in the Probabilistic Scenario-Based Model Predictive Control (PSB-MPC) COLAV algorithm using an examplatory intent model, when statistics about traffic rules compliance and the next waypoint for an obstacle are assumed known. Simulation results show that the resulting COLAV system is able to make safer decisions when utilizing the extra intent information.

Collision Avoidance (COLAV) for autonomous ships is challenging since it relies on track estimates of nearby obstacles which are inherently uncertain in both state and intent. This uncertainty must be accounted for in the COLAV system in order to ensure both safe and efficient operation of the vessel in accordance with the traffic rules. Here, a COLAV system built on the Scenario-based Model Predictive Control (SB-MPC) with dynamic probabilistic risk treatment is presented. The system estimates the probability of collision with all nearby obstacles using a combination of Monte Carlo simulation (MCS) and a Kalman Filter (KF), taking the uncertainty in both position and velocity into account. A probabilistic collision cost is then used in the MPC to penalize risk-taking maneuvers. Simulation results show that the proposed method may provide increased robustness due to increased situational awareness, while also being able to efficiently follow the nominal path and adhere to the traffic rules.