Dubins Path Research Articles

Multi-AUV Kinematic Task Assignment Based on Self-Organizing Map Neural Network and Dubins Path Generator.

To deal with the task assignment problem of multi-AUV systems under kinematic constraints, which means steering capability constraints for underactuated AUVs or other vehicles likely, an improved task assignment algorithm is proposed combining the Dubins Path algorithm with improved SOM neural network algorithm. At first, the aimed tasks are assigned to the AUVs by the improved SOM neural network method based on workload balance and neighborhood function. When there exists kinematic constraints or obstacles which may cause failure of trajectory planning, task re-assignment will be implemented by changing the weights of SOM neurals, until the AUVs can have paths to reach all the targets. Then, the Dubins paths are generated in several limited cases. The AUV's yaw angle is limited, which results in new assignments to the targets. Computation flow is designed so that the algorithm in MATLAB and Python can realize the path planning to multiple targets. Finally, simulation results prove that the proposed algorithm can effectively accomplish the task assignment task for a multi-AUV system.

Automated packing and piping in an Airbus A320 main landing gear bay: an industrial development case study

AbstractThe packing of given hydraulic equipment together with the hydraulic piping is a challenging design task. Both the hydraulic domain and the geometry domain are highly intercoupled as the packing determines the exact location of the connection points and tangents for the pipes but also defines the installation spaces for the equipment to be positioned which needs to be taken into account as an obstacle during the piping process. For the industrial case study, a mounting rack in an Airbus A320 main landing gear bay is used, where seven pieces of equipment should be packed and 22 pipes should be routed. In the first part of the study, the packing was done manually, assisted by automated routing, while the hydraulic piping was generated automatically. In the second part of the study the packing was automatized as well. For the automated packing process, a particle multi swarm optimisation was used. As objective function a pipe length minimization was implemented, which uses the Dubins Path as a pipe approximation. Constraints taken into account are the collision-free nature of the equipment and its placement on a plate inside the plates borders. The automated packing workflow was used to generate different variants of which for two a pipe work was generated exemplarily. Due to the model-based systems engineering approach, no further interaction in terms of the definition of the connection points, tangents and the installation space is necessary. This demonstrates that an automated packing and piping process in an industrial context using industrial geometries is now feasible.

Global path planning for inland vessels based on fast marching algorithm

Ship path planning is essential for enhancing navigation safety, shipping efficiency, cost savings and autonomy. This paper presents a path planning algorithm specifically designed for inland vessels, exemplified on the Western Scheldt waterway area from Hansweert to Bath in the Netherlands (known as the area of Schaar van Valkenisse). The algorithm utilizes the fast marching (FM) method to generate safe and cost-efficient paths for both autonomous and conventional navigation, considering factors such as water depth, distance to waterway borders, preferential navigation zones (e.g. starboard side and parallel routes), ship dimensions, and manoeuvring characteristics.The fast marching algorithm uses starting points and a velocity grid, generated based on the aforementioned factors, to produce an arrival time map. The velocity here represents preferences for deeper water, and wider and starboard navigation zones. Subsequently, a gradient descent algorithm is applied to determine the fastest route from the destination to the starting point on the arrival time map. To ensure the route is navigable, the optimal path is updated to a Dubins path that satisfies the ships’ dynamic constraints by using a so-called Dubins model filter.Case studies with various navigation scenarios demonstrate that the path planning tool can provide expected results with tunable parameters allowing for customized preferences. This work can further assist in predicting paths for a traffic study, designing fairways, aids to navigation and can possibly serve as an operational tool to assess the accessibility of a (alternative) fairway.

Mathematical Model for Optimal Dubins Path to Intercept a Stationary Target

This paper presents a comprehensive mathematical model designed to determine the most efficient trajectory for intercepting a stationary target, with a primary focus on minimizing interception time and resource utilization. The proposed model incorporates key parameters such as target location, interception speed, and environmental constraints to formulate a set of differential equations that describe the motion dynamics of both the pursuer and the target. The objective function is defined to optimize the interception path. The study employs advanced mathematical techniques, including optimal control theory and numerical optimization algorithms, to solve the formulated equations and derive the optimal path. The model is adaptable to various scenarios, accounting for different pursuit vehicle dynamics and target characteristics. Simulation results are presented to validate the effectiveness of the proposed mathematical model in practical applications.
 GANIT J. Bangladesh Math. Soc. 43.1 (2023) 049- 064

Fixed-Wing UAV Formation Path Planning Based on Formation Control: Theory and Application

Formation path planning is a significant cornerstone for unmanned aerial vehicle (UAV) swarm intelligence. Previous methods were not suitable for large-scale UAV formation, which suffered from poor formation maintenance and low planning efficiency. To this end, this paper proposes a novel millisecond-level path planning method appropriate for large-scale fixed-wing UAV formation, which consists of two parts. Instead of directly planning paths independently for each UAV in the formation, the proposed method first introduces a formation control strategy. It controls the chaotic UAV swarm to move as a single rigid body, so that only one planning can obtain the feasible path of the entire formation. Then, a computationally lightweight Dubins path generation method with a closed-form expression is employed to plan feasible paths for the formation. During flight, the aforementioned formation control strategy maintains the geometric features of the formation and avoids internal collisions within the formation. Finally, the effectiveness of the proposed framework is exemplified through several simulations. The results show that the proposed method can not only achieve millisecond-level path planning for the entire formation but also excellently maintain formation during the flight. Furthermore, simple formation obstacle avoidance in a special case also highlights the application potential of the proposed method.

A novel approach for 3PDP and real-time via point path planning of Dubins’ vehicles in marine applications

This paper addresses the problem of finding the shortest Dubins path between three consecutive via-points with prescribed initial and final orientations and without a prescribed orientation at the intermediate via-point. The problem plays a crucial role for online path planning in many marine applications, as for example, it is instrumental to solve the Dubins Traveling Salesman Problem. A novel solution is proposed using simple tools borrowed from analytic geometry, and an efficient algorithm is presented as a basic routine for real-time path planning algorithms. Extensive simulations confirmed the efficiency of the proposed strategy in terms of both computational complexity and accuracy of the solution. Moreover, a comparative analysis with recent existing approaches is performed showing the effectiveness of the proposed solution.

Local Path Planning for Nonholonomic Mobile Robots Based on Planar G2 Pythagorean Hodograph Degree 7 Bezier Transition Curves

The paper proposes a method that joins two line segments using planar Pythagorean hodograph (PH) degree 7 Bezier transition curves. The objective is to make use of such curvature-continuous curves for the path planning of nonholonomic constrained vehicles moving in 2D space, which requires designing a smooth path while satisfying the constraint of minimum turning radius. We initially present a novel idea that employs PH degree 7 Bezier transition curves for dealing with curvature constraints, the result of which proves to be better than the traditional method based on the “forward simulation”. The properties of PH degree 7 Bezier transition curves are then fully analyzed showing that the curves can be determined by a minimum of three parameters, each of which has an intuitive geometric meaning. The paper also proposes a path planner with direct curvature constraints during the process of path generation in 2D space. The objective function of the optimal path generation can be adjusted to minimize the length of the whole path or to closely follow the original global nonsmooth sequences of line segments. Here, the optimization problem is tactfully converted to a linear programming problem that can be solved efficiently. Finally, we use a kinematic bicycle model for simulation and compare the results with those from Dubins path showing that a [Formula: see text] curve is easier to follow than a [Formula: see text] one.

Adaptive path following control for miniature unmanned aerial vehicle confined to three-dimensional Dubins path: From take-off to landing

This study proposes a method for resolving the challenge of controlling miniature fixed-wing unmanned aerial vehicles (MAVs) along a predetermined three-dimensional (3D) Dubins path while using models with uncertainty and when experiencing external wind disturbances. We provide a multilayered structure that incorporates both guiding and control at the same time. In the guidance layer, a modified vector-field-based approach is presented to enable the MAV to follow a 3D Dubins path, including the takeoff, cruise, and landing processes with three different types of route segments. Then, an adaptive sliding model controller is used for the analysis and management of both wind disturbances and system uncertainties. Finally, both simulated scenarios and in-flight trials demonstrate the applicability of the methodology and the efficiency of the proposed approach.

Fisher-Information-Matrix-Based USBL Cooperative Location in USV-AUV Networks.

With the development of underwater technology and the increasing demand for ocean development, more and more intelligent equipment is being applied to underwater scientific missions. Specifically, autonomous underwater vehicle (AUV) clusters are being used for their flexibility and the advantages of carrying communication and detection units, often performing underwater tasks in formation. In order to locate AUVs with high precision, we introduce an unmanned surface vehicle (USV) with global positioning system (GPS) and propose a USV-AUV network. Furthermore, we propose an ultra-short baseline (USBL) acoustic cooperative location scheme with an orthogonal array, which is based on underwater communication with sonar. Based on the derivation of the Fisher information matrix formula under Cartesian parameters, we analyze the positioning accuracy of AUVs in different positions under the USBL positioning mode to derive the optimal array of the AUV formation. In addition, we propose a USV path planning scheme based on Dubins path planning functions to assist in locating the AUV formation. The simulation results verify that the proposed scheme can ensure the positioning accuracy of the AUV formation and help underwater research missions.

Integrate Assignment of Multiple Heterogeneous Unmanned Aerial Vehicles Performing Dynamic Disaster Inspection and Validation Task With Dubins Path

The actual performance of a task assignment method of unmanned aerial vehicles (UAVs) shows a considerable dependence on the path planning process coupled with it; however, this topic has been rarely studied in the existing literature. This paper considers the problem of maximizing the task-assignment reward of a fleet of heterogeneous UAVs for a dynamic reconnaissance and confirmation task under constraints of critical time and multi-UAV tasks where the coupled path optimization objectives also need to be considered. The existing consensus-based bundle algorithm is extended with an effective method for managing the multi-task and multi-agent constraints. The proposed method can optimize the inherent coupling path using the Dubins path to reduce the differences between the estimated path and the actual path, shortening the operation time by adopting the distributed genetic algorithm. The proposed method is verified by the sample run tests of a disaster area reconnaissance and confirmation task and Monte Carlo comparison simulations with the two existing algorithms. The results verify both the practicality and advantages of the proposed method.

Modelling of aircraft trajectories for emergency landing using kinematoid chains

Most methods that compute trajectories for un- or low-powered flight operate under simplifying assumptions such as constant curve radii and wind conditions. Likewise, changes of air density with altitude that lead to significant differences between equivalent airspeed (EAS) und true airspeed (TAS) are often not considered. Some approaches are based on Dubins paths, which are introduced in Dubins LE (Am J Math 79: 497, 1957). They combine three sections to form a trajectory, which is the shortest from a given start to an end position (In the original work, the position extended by the heading, is referred to as configuration. Since configuration has a different connotation in our context, we use the term state, which can contain other parameters in addition to the position and the heading, e.g. orientation, configuration of landing flaps, landing gear, etc.). A maximum distant landing spot can be reached this way. Often, the targeted landing spot is closer to the aircraft. If it is approached using a Dubins Path, the excess height must be dealt with. Here, we present a method addressing the problem directly, namely finding a trajectory which reduces the excess height over its entire length. Furthermore, it takes spatial and temporal changes of wind and air density into account. Several conditions influence the final shape of the trajectory. For example, avoidance of obstacles and predefined areas is easily achieved. Our method is motivated by kinematic chains, which are used in robotics and computer animation. We extend and modify this principle by incrementally transferring start and end states of the trajectory, modelled as state vectors, into each other. The resulting intermediate states form ends of chain links. To connect initial and final states through the resulting chain, we solve the inverse kinematic problem known from robotics. We extend it by several conditions, which are derived from the flight mechanical characteristics of the modeled aircraft on the one hand and from the desired properties of the trajectory on the other. Using practical examples, we will show the performance of this method, which we have efficiently implemented on off-the-shelf hardware. The method is suitable for systems that assist in the event of engine failures as well as for modeling planned un- or low-powered flights like continuous descent approaches or return flights of space gliders.

Kinegami: Algorithmic Design of Compliant Kinematic Chains From Tubular Origami

Origami processes can generate both rigid and compliant structures from the same homogeneous sheet material. In this article, we advance the origami robotics literature by showing that it is possible to construct an arbitrary rigid kinematic chain with prescribed joint compliance from a single tubular sheet. Our “Kinegami” algorithm converts a Denavit–Hartenberg specification into a single-sheet crease pattern for an equivalent serial robot mechanism by composing origami modules from a catalogue. The algorithm arises from the key observation that tubular origami linkage design reduces to a Dubins path planning problem. The automatically generated structural connections and movable joints that realize the specified design can also be endowed with independent user-specified compliance. We apply the Kinegami algorithm to a number of common robot mechanisms and hand-fold their algorithmically generated single-sheet crease patterns into functioning kinematic chains. We believe this is the first completely automated end-to-end system for converting an abstract manipulator specification into a physically realizable origami design that requires no additional human input.

A new Markov–Dubins hybrid solver with learned decision trees

In this paper, the applicability of machine learning models and techniques to the Markov–Dubins path planning problem have been explored. Machine learning techniques are already applied to several fields, which range from computer vision, to physics simulation, to item recommendation, to user profiling. This pervasiveness has led to marked improvements in the implementation and support for applying machine learning models, in particular for specialised use cases such as low-power devices, embedded hardware, and real-time applications. On the other hand, the Markov–Dubins path planning problem, which is central in robotic nonholonomic trajectory design, is already covered by established numerical and optimisation techniques. However, the benefits of applying machine learning approaches to this problem remain to be investigated. In particular, there is the need to research potential speed-ups or application domains that would be better solved by a machine learning approach compared to the traditional algorithmic approaches. In this study, we train a state-of-the-art machine learning model in a supervised setting on Markov–Dubins and use it in two different ways: to directly predict the solution, and to filter candidate solutions. Also, a comparison of the quality of these predictions with a state-of-the-art Markov–Dubins solver is made. The results obtained indicate that machine learning approaches are comparable to state-of-the-art solutions: our bare model, directly predicting the solution, appears to be 8.3 times faster than the current standard, sacrificing the accuracy, which amounts to a value close to 92%; the hybrid model that filters the solutions prior to finding the best candidate runs in times that are comparable to the classical solver (58 ms) and has over 98% accuracy. A further comparison with alternative solvers and techniques, such as Optimal Control, NonLinear Programming and Mixed Integer NonLinear Programming has been made, confirming the benefits of the machine learning approach over these, for which the computational times are in the range of seconds. This opens new avenues for interdisciplinary applications of machine learning to more general planning problems (e.g., the same problem in 3D), where the number of possible manoeuvres is large and the computation of each of them requires a considerable computational effort, which makes the brute force trial-and-error infeasible.

Online Weapon-target Assignment based on Distributed Auction Mechanism

To solve the problem of online weapon-target assignment (OWTA) in the integration of large-scale search and attack in unknown environment, an OWTA algorithm based on distributed auction mechanism is presented. Aiming at the problem that the traditional combinatorial optimization algorithm needs to set up the global battlefield situation in advance, considering the consumability of resources in the attack process, the integrated search and attack task flow is established. Considering the communication restricted environment, the unmanned aerial vehicles (uavs) are grouped, with centralized architecture within the group and distributed structure between the groups, and the corresponding distributed auction mechanism is constructed to achieve OWTA within the communication range limited. In order to solve the problem that it is difficult to ensure the time consistency of the coordinated attack target, a dubins cooperative path planning based on cooperative particle swarm optimization (CPSO) algorithm is proposed. Particle swarm optimization algorithm is used to adjust the radius of the dubins path of each bomb, so that the uav in the same group can hit the target simultaneously without collision and have the shortest flight range. The simulation results show that the designed distributed auction algorithm takes into account the consumption of attack resources, and quickly redistributes the firepower to the new targets in the dynamic uncertain environment, which ensures the maximization of the execution efficiency of the multi-machine cluster fire allocation task.

Three-Dimensional Dubins-Path-Guided Continuous Curvature Path Smoothing

This paper presents an efficient three-dimensional (3D) Dubins path design and a new continuous curvature path-smoothing algorithm. The proposed 3D Dubins path is a simple extension of the 2D path and serves as a reference path generator to guide the proposed smoothing algorithm. In the smoothing algorithm, the reference path is approximated by several cubic Bezier curves to generate a parametric path that simultaneously satisfies curvature continuity and maximum curvature requirements. The algorithm also provides a criterion to select a required number of Bezier curves to strictly meet the maximum curvature constraint. Therefore, our algorithm can be used for 3D path-following applications in many areas such as aerospace and robotics. The numerical simulation results show that the proposed algorithm produces a continuous curvature path that passes through all waypoints with a slight increase in path length compared with the original 3D Dubins reference path.

Population-Aware Sequential Flight Path Optimization for Low-Noise and Low-Fuel Consumption Departure Trajectory

With the increase in air traffic over the past decades, the reduction of aircraft noise is one of the major challenges facing stakeholders. Flight operating conditions that decrease noise may possibly increase the fuel consumption of aircraft, which is an important factor in airline cost management. In this paper, we propose a methodology to support flight path planning with the aim of optimizing both perceived noise and fuel consumption. We decompose an aircraft flight trajectory into surface and altitude paths to model relevant air transportation constraints. The shortest path for the surface projection is found using Dubins path method and an improved algorithm, which considers guide points according to the flight destination, runway angles, spatial separation of aircraft near the airport, population distribution, and steering motion. The altitude path is optimized for low-perceived noise and low-fuel consumption, which is determined by solving the longitudinal governing equations of motion of flight using the distance computed from this surface path. A modified nondominated sorting genetic algorithm II for discrete optimization is developed to obtain Pareto fronts of the optimum altitude paths with reduced computational effort. The methodology is demonstrated by simulating flights departing from Hong Kong International Airport to two compulsory air-traffic-service reporting points. The results are then compared with Quick Access Recorder data and Standard Instrument Departure (SID) tracks. Although certain factors in air transportation that affect departure path planning, such as weather patterns and air traffic mix, are not considered in this method, the resulting surface path exhibits a close similarity with SID tracks. The resulting Pareto fronts of the altitude path exhibit reductions in fuel consumption and perceived noise levels. The tradeoffs between fuel consumption and perceived noise levels are also discussed based on the relevant flight physics for the different routes.

Dubins Path-Oriented Rapidly Exploring Random Tree* for Three-Dimensional Path Planning of Unmanned Aerial Vehicles

Unmanned aerial vehicles (UAVs) do not collide with obstacles, generate a path in real-time, and must fly to the target point. The sampling-based rapidly exploring random tree (RRT) algorithm has the advantages of fast computation and low computational complexity. It is suitable for real-time path generation, but the optimal path cannot be guaranteed. Further, the direction of the flight and the minimum radius of rotation have not been taken into account for the characteristics of the UAVs. This work proposes a Dubins path-oriented RRT* algorithm, which applies the Dubins path to the RRT algorithm to consider the direction of flight and the minimum radius of rotation and improves optimality and convergence. The proposed algorithm sets the sample node as the target point, orients toward the Dubins path, and then generates a tree. To verify the performance of the proposed algorithm, it is compared with existing RRT algorithms. As a result of performance analysis, the proposed algorithm improved the path length by 14.87% and the calculation time by 82.36%. Finally, the algorithm’s performance is verified by applying the proposed algorithm to a fixed-wing UAV and performing a numerical analysis of the generated path.

Shortest Dubins Paths to Intercept a Target Moving on a Circle

We present a path planning problem for a pursuing unmanned aerial vehicle (UAV) to intercept a target traveling on a circle. The target is cooperative, and its position, heading, and speed are precisely known. The pursuing UAV has nonholonomic motion constraints, and therefore the path traveled must satisfy the minimum turn radius constraints. We consider the class of Dubins paths as candidate solutions, and analyze the characteristics of the six modes of Dubins paths where the final position is restricted to lie on the target circle with heading in the tangential direction of the circle. For each Dubins mode, we derive the feasibility limits, discontinuities, and local extrema. Using this analysis the intercepting paths are found by a systematic bisection search in the feasible regions of each of the Dubins modes. We prove that the algorithm finds the optimal (shortest length) intercepting path if it is a Dubins path. If the shortest intercepting path is not a Dubins path for any given instance, the algorithm finds a tight lower bound and an upper bound to the optimal solution.

Motion Planning of Unmanned Aerial Vehicle Based on Rapid-exploration Random Tree Algorithm

In the study of route planning problems in complex environments, in order to reduce the flight cost of unmanned aerial vehicles (UAVs), it is necessary to achieve a better balance between planning time and path quality. This paper utilizes the Rapid-exploration Random Tree (RRT) algorithm for motion planning of a fixed-wing UAV and a multi-rotor UAV (i.e., a quad-rotor UAV), and gives the origin and destination locations on a 3-D map. By following aerodynamic constraints such as maximum roll angle, flight path angle, and airspeed, a collision-free and flight-friendly path is found through simulation. In addition, this paper employs a path smoothing algorithm to simplify the 3-D Dubins path and generates the shortest trajectory. The simulation results show that the RRT and the optimization method have faster convergence speed and shorter search time, reduce redundant planning points, shorten the planning track, and improve the track planning efficiency.

Development of Fixed-Wing UAV 3D Coverage Paths for Urban Air Quality Profiling.

Due to the ever-increasing industrial activity, humans and the environment suffer from deteriorating air quality, making the long-term monitoring of air particle indicators essential. The advances in unmanned aerial vehicles (UAVs) offer the potential to utilize UAVs for various forms of monitoring, of which air quality data acquisition is one. Nevertheless, most current UAV-based air monitoring suffers from a low payload, short endurance, and limited range, as they are primarily dependent on rotary aerial vehicles. In contrast, a fixed-wing UAV may be a better alternative. Additionally, one of the most critical modules for 3D profiling of a UAV system is path planning, as it directly impacts the final results of the spatial coverage and temporal efficiency. Therefore, this work focused on developing 3D coverage path planning based upon current commercial ground control software, where the method mainly depends on the Boustrophedon and Dubins paths. Furthermore, a user interface was also designed for easy accessibility, which provides a generalized tool module that links up the proposed algorithm, the ground control software, and the flight controller. Simulations were conducted to assess the proposed methods. The result showed that the proposed methods outperformed the existing coverage paths generated by ground control software, as it showed a better coverage rate with a sampling density of 50 m.