Dubins Path Research Articles

Minimal curvature-constrained networks

This paper introduces an exact algorithm for the construction of a shortest curvature-constrained network interconnecting a given set of directed points in the plane and a gradient descent method for doing so in 3D space. Such a network will be referred to as a minimum Dubins tree, since its edges are Dubins paths (or slight variants thereof). The problem of constructing a minimum Dubins tree appears in the context of underground mining optimisation, where the objective is to construct a least-cost network of tunnels navigable by trucks with a minimum turning radius. The Dubins tree problem is similar to the Steiner tree problem, except the terminals are directed and there is a curvature constraint. We propose the minimum curvature-constrained Steiner point algorithm for determining the optimal location of the Steiner point in a 3-terminal network. We show that when two terminals are fixed and the third varied in the planar version of the problem, the Steiner point traces out a limacon.

T⋆: Time-Optimal Risk-Aware Motion Planning for Curvature-Constrained Vehicles

This letter addresses the time-optimal risk-aware motion planning problem for curvature-constrained variable-speed vehicles in the presence of obstacles. To the best of our knowledge, this problem has not been solved. To obtain a feasible solution, we present a grid-based method, called T $^\star$ , which computes the time-optimal risk-aware path by finding the optimal sequence of vehicle states from the start to the goal with the minimum total cost of time and risk. We propose a novel risk function based on the concept of collision time, which utilizes the complete information of the vehicle state, including its location with respect to obstacles, heading angle, and speed. We also propose a state pruning technique that can significantly reduce the computational complexity. The algorithm was validated in simulations of complex obstacle-rich scenarios, and the resulting paths are shown to be superior than the Dubins paths.

A Fixed Wing UAV Path Planning Algorithm Based On Genetic Algorithm and Dubins Curve Theory

Path planning is an essential problem in the autonomy research of UAVs. This paper proposes a new path planning algorithm for fixed wing UAVs based on genetic algorithm (GA) and Dubins curve theory. Path planning is treated as a global optimization problem under certain constraints, including the velocity vectors of initial and goal points and the minimum turning radius of UAVs. Dubins curve theory is utilized to satisfy the velocity vector constraints. GA is utilized to generate the shortest threats avoidance path in a 2D environment. A new encoding scheme is proposed, taking into account initial circles, goal circles, threats circles and the positional relationship between the path and these circles. The 2D Dubins path is converted to Dubins airplane path by adding a flight-path angle to it. The algorithm was tested in a complex flight environment and the planned path was tracked by a 6DOF Simulink model of a fixed wing UAV. Results show that the algorithm can generate shortest threats avoidance path in a complicated 3D environment and meanwhile satisfy constraints mentioned above.

Adaptation of Dubins Paths for UAV Ground Obstacle Avoidance When Using a Low Cost On-Board GNSS Sensor.

Current research on Unmanned Aerial Vehicles (UAVs) shows a lot of interest in autonomous UAV navigation. This interest is mainly driven by the necessity to meet the rules and restrictions for small UAV flights that are issued by various international and national legal organizations. In order to lower these restrictions, new levels of automation and flight safety must be reached. In this paper, a new method for ground obstacle avoidance derived by using UAV navigation based on the Dubins paths algorithm is presented. The accuracy of the proposed method has been tested, and research results have been obtained by using Software-in-the-Loop (SITL) simulation and real UAV flights, with the measurements done with a low cost Global Navigation Satellite System (GNSS) sensor. All tests were carried out in a three-dimensional space, but the height accuracy was not assessed. The GNSS navigation data for the ground obstacle avoidance algorithm is evaluated statistically.

Task Assignment and Path Planning for Multiple Autonomous Underwater Vehicles Using 3D Dubins Curves †.

This paper investigates the task assignment and path planning problem for multiple AUVs in three dimensional (3D) underwater wireless sensor networks where nonholonomic motion constraints of underwater AUVs in 3D space are considered. The multi-target task assignment and path planning problem is modeled by the Multiple Traveling Sales Person (MTSP) problem and the Genetic Algorithm (GA) is used to solve the MTSP problem with Euclidean distance as the cost function and the Tour Hop Balance (THB) or Tour Length Balance (TLB) constraints as the stop criterion. The resulting tour sequences are mapped to 2D Dubins curves in the plane, and then interpolated linearly to obtain the Z coordinates. We demonstrate that the linear interpolation fails to achieve continuity in the 3D Dubins path for multiple targets. Therefore, the interpolated 3D Dubins curves are checked against the AUV dynamics constraint and the ones satisfying the constraint are accepted to finalize the 3D Dubins curve selection. Simulation results demonstrate that the integration of the 3D Dubins curve with the MTSP model is successful and effective for solving the 3D target assignment and path planning problem.

Automated trajectory generation and airport selection for an emergency landing procedure of a CS23 aircraft

Aircraft in general aviation usually are operated in single pilot mode. Especially, in case of an incapability of the pilot to control the aircraft, an automated emergency procedure is desirable in order to reduce the risk of fatalities. The finding of a solution for an emergency landing maneuver includes preselecting possible landing sites with regard to the available aircraft capabilities and creation of feasible trajectories to these sites. A search tree in four-dimensional search space with an efficient implementation of a rapidly exploring random tree algorithm (RRT*) is created. The algorithm performance is increased by use of basic geometrical sets to construct the final route as a combination of Dubins path segments. To further reduce the route length, a gradient based local optimization routine is added after completion of the RRT* algorithm. At the moment of creation, terrain avoidance is verified and accordance with legal airspace structure is considered. An emergency procedure is created by combining a selected landing site and a flyable trajectory to this site. Each of these combinations is scored, and the most promising emergency landing procedure is chosen and delivered to flight management system of the aircraft. The flight management system controls a full-authority auto-flight system that is capable of performing en-route flight and auto-land procedures as well.

Tightly Bounding the Shortest Dubins Paths Through a Sequence of Points

This article addresses an important path planning problem for robots and Unmanned Aerial Vehicles (UAVs), which is to find the shortest path of bounded curvature passing through a given sequence of target points on a ground plane. Currently, no algorithm exists that can compute an optimal solution to this problem. Therefore, tight lower bounds are vital in determining the quality of any feasible solution to this problem. Novel tight lower bounding algorithms are presented in this article by relaxing some of the heading angle constraints at the target points. The proposed approach requires us to solve variants of an optimization problem called the Dubins interval problem between two points where the heading angles at the points are constrained to be within a specified interval. These variants are solved using tools from optimal control theory. Using these approaches, two lower bounding algorithms are presented and these bounds are then compared with existing results in the literature. Computational results are presented to corroborate the performance of the proposed algorithms; the average reduction in the difference between upper bounds and lower bounds is 80 % to 85 % with respect to the trivial Euclidean lower bounds.

Three-Dimensional Underwater Path Planning Based on Modified Wolf Pack Algorithm

Path planning is an important problem in autonomous control technology. This paper aims to overcome the shortcomings of the wolf pack algorithm (WPA), such as slow rate of convergence and low convergence precision, by improving the three intelligent behaviors of the WPA, namely, scouting, summoning, and beleaguering. To improve the scouting behavior, interactive scouting is proposed to increase the interactivity among wolf pack. Furthermore, to improve the summoning behavior, a prey-based adaptive step model is established to improve the searching ability. Finally, calculation rules of new beleaguering behavior are designed, which enhance the local fine search ability considerably. A fast path planning method based on dubins path was proposed, which applied the dubins path planning to meet angle control constraint and tunes the turning radius to meet control constraint. The dubins path planning method based on the modified WPA is proposed by establishing the underwater environment threat model under the condition of autonomous underwater vehicle constraint. The path between the path points is the shortest, the threat is minimal, and the energy consumption is the least without the consideration of ocean current. Simulation results show that the modified WPA has a high rate of convergence and good local search capability in the high-precision, high-dimensional, and multi-peak function; moreover, it does not converge prematurely.

Optimization of Pesticide Spraying Tasks via Multi-UAVs Using Genetic Algorithm

Task allocation is the key factor in the spraying pesticides process using unmanned aerial vehicles (UAVs), and maximizing the effects of pesticide spraying is the goal of optimizing UAV pesticide spraying. In this study, we first introduce each UAV’s kinematic constraint and extend the Euclidean distance between fields to the Dubins path distance. We then analyze the two factors affecting the pesticide spraying effects, which are the type of pesticides and the temperature during the pesticide spraying. The time window of the pesticide spraying is dynamically generated according to the temperature and is introduced to the pesticide spraying efficacy function. Finally, according to the extensions, we propose a team orienteering problem with variable time windows and variable profits model. We propose the genetic algorithm to solve the above model and give the methods of encoding, crossover, and mutation in the algorithm. The experimental results show that this model and its solution method have clear advantages over the common manual allocation strategy and can provide the same results as those of the enumeration method in small-scale scenarios. In addition, the results also show that the algorithm parameter can affect the solution, and we provide the optimal parameters configuration for the algorithm.

Simplex Solutions for Optimal Control Flight Paths in Urban Environments

This paper identifies feasible fight paths for Small Unmanned Aircraft Systems in a highly constrained environment. Optimal control software has long been used for vehicle path planning and has proven most successful when an adequate initial guess is presented to an optimal control solver. Leveraging computer animation techniques, a large search space is discretized into a set of simplexes where a Dubins path solution is generated and contained in a polygonal search corridor free of path constraints. Direct optimal control methods are then used to determine the optimal flight path through the newly defined search corridor. Two scenarios are evaluated. The first is limited to heading rate control only, requiring the air vehicle to maintain constant speed. The second allows for velocity control which permits slower speeds, reducing the vehicles minimum turn radius and increasing the search domain. Results illustrate the benefits gained when including speed control to path planning algorithms by comparing trajectory and convergence times, resulting in a reliable, hybrid solution method to the SUAS constrained optimal control problem.

Optimizing Steady Turns for Gliding Trajectories

Dubins planners provide minimum-length planar paths between waypoints for turning constrained vehicles. For a no-thrust or glider aircraft, Dubins paths have been extrapolated to three dimensions by augmenting the planar path with a constant flight-path angle in each path segment. Best-glide flight maximizes the horizontal distance traveled per unit altitude loss, but steeper flight-path angles result in a maximum heading change per unit altitude loss. This paper investigates combinations of bank and flight-path angles yielding maximum ranges for gliding Dubins trajectories. Starting from the extrema flight-path angles usually applied in the literature, it is shown that the maximum range along each flight radial from an initial point (that is, the footprint) is obtained at a maximum glidepath angle for a given turn radius. This result is applied in a novel three-dimensional maximum-range Dubins path. Three-dimensional Dubins examples with different heading constraints are presented. The impact of constraining solutions to a single pair of turning bank and flight-path angles is analyzed.

Development of Return to Base Flight Trajectory Generator Based on Dubins Path - Vector Field Method

In a Return to Base (RTB) situation, aircraft needs to immediately fly back to its origin airport. Since there is no published flight procedure for an RTB, an Air Traffic Controller (ATC) will assist the pilot for the flight procedure to fly. The objective of this work is to generate a flight trajectory in RTB situation based on the available airport flight procedures (departure and arrival) in Kertajati airport. The Dubins Path was used as a method to generate the flight trajectory and supported by the Vector-Field Methodology. The Python programming simulation was used to simulate the flight trajectory generation in the normal condition, second closest waypoint condition, and different parameters value condition. The trajectory was simulated based on flight characteristic of a single engine aircraft (Cesna 172) and multi-engine aircrafts (Boeing 737-800NG). The simulation results show that the Dubins Path and Vector-Field methodology success to generate the flight trajectory in different types of condition and parameters. The increase in aircraft velocity and the decrease in aircraft bank angle caused an increase in the aircraft turning radius. While, the decrease in aircraft flight path angle caused increase in the length of Dubins Path line.

Toward Optimal Rendezvous of Multiple Underwater Gliders: 3D Path Planning with Combined Sawtooth and Spiral Motion

In this paper, a path planning system is proposed for optimal rendezvous of multiple underwater gliders in three-dimensional (3D) space. Inspired by the Dubins Paths consisting of straight lines and circular arcs, this paper presents the first attempt to extend the 3D Dubins curve to accommodate the characteristic glider motions include upwards and downwards straight glides in a sawtooth pattern and gliding in a vertical spiral. This modified 3D Dubins scheme is combined with genetic algorithm (GA), together with a rendezvous position selection scheme to find rendezvous trajectories for multiple gliders with minimal energy consumption over all participating vehicles. The properties and capabilities of the proposed path planning methodology are illustrated for several rendezvous mission scenarios. First, a simple application was performed for a single glider to rendezvous with a fix dock. Simulation results show the proposed planner is able to obtain more optimized trajectories when compared with the typical Dubins trajectory with nominal velocity. Additional representative simulations were run to analyse the performance of this path planner for multiple gliders rendezvous. The results demonstrate that the proposed path planner identifies the optimal rendezvous location and generates the corresponding rendezvous trajectories for multiple gliders that ensures they reach their destination with optimized energy consumption.

Dubins path‐based dynamic soaring trajectory planning and tracking control in a gradient wind field

SummaryThis paper studies small unmanned aerial vehicle dynamic soaring for conserving onboard energy to extend flight endurance performance. A novel dynamic soaring path planning approach is proposed using the Dubins path. It enjoys a significant improvement in computational efficiency. In addition, a custom‐built trajectory tracking controller is developed for a nonlinear unmanned aerial vehicle dynamics model to verify the implementation of the proposed path planning approach. Extensive numerical simulations are conducted to demonstrate the effectiveness of the proposed design and development. Copyright © 2016 John Wiley & Sons, Ltd.

Online Path Planning for Surface Vehicles Exposed to Unknown Ocean Currents Using Pseudospectral Optimal Control

Abstract: This paper investigates the feasibility of using pseudospectral (PS) optimal control in real-time path planning for marine surface vehicles in environments where both obstacles and unknown disturbances are present. In particular, the simplified kinematic equations of an underactuated marine surface vehicle exposed to unknown ocean currents are considered, and the software package DIDO is used to compute the optimal path via PS optimization, initially assuming the ocean current is zero. In that case, the resulting path is minimum-length (similar to Dubins path) but not minimum-time. The main contribution concerns the addition of a nonlinear observer, which estimates online the effects of the ocean current on the vehicle, and that of a guidance system which generates appropriate reference trajectories in order to minimize the position error and track the optimal trajectory successfully. It is shown that through occasional replanning, according to the information about the ocean current parameters coming from the observer, the updated path converges to the minimum-time path. Two different implementations of the approach are presented and illustrated through numerical simulations.

Time-Optimal Guidance for Lateral Interception of Moving Targets

A Dubins paths–based guidance methodology for minimum-time lateral interception of a moving and nonmaneuvering target is considered and existence of Dubins paths is established for the scenario. The path lengths and the interception points are obtained for all possible Dubins paths. The shortest path among the Dubins set is proven to be the minimum-time path for lateral interception of moving targets. A classification for the initial geometries is analyzed for deducing the time-optimal path from the Dubins set. Corresponding capture regions are obtained for individual Dubins paths. Simulations are carried out complying with the analytic findings.

Line-of-Sight Path Following for Dubins Paths With Adaptive Sideslip Compensation of Drift Forces

We present a nonlinear adaptive path following controller that compensates for drift forces through vehicle sideslip. Vehicle sideslip arises during path following when the vehicle is subject to drift forces caused by ocean currents, wind, and waves. The proposed algorithm is motivated by a line-of-sight (LOS) guidance principle used by ancient navigators, which is here extended to path following of Dubins paths. The unknown sideslip angle is treated as a constant parameter, which is estimated using an adaptation law. The equilibrium points of the cross-track and parameter estimation errors are proven to be uniformly semiglobally exponentially stable. This guarantees that the estimated sideslip angle converges to its true value exponentially. The adaptive control law is in fact an integral LOS controller for path following since the parameter adaptation law provides integral action. The proposed guidance law is intended for maneuvering in the horizontal-plane at given speeds and typical applications are marine craft, autonomous underwater vehicles, unmanned aerial vehicles as well as other vehicles and crafts, where the goal is to follow a predefined parametrized curve without time constraints. Two vehicle cases studies are included to verify the theoretical results.

Real-Time Dynamic Dubins-Helix Method for 3-D Trajectory Smoothing

This brief presents the real-time dynamic Dubins-Helix (RDDH) method for trajectory smoothing, which consists of Dubins-Helix trajectory generation and pitch angle smoothing. The generated 3-D trajectory is called the RDDH trajectory. On one hand, the projection of 3-D trajectory on the horizontal plane is partially generated by Dubins path planner such that the curvature radius constraint is satisfied. On the other hand, the Helix curve is constructed to satisfy the pitch angle constraint, even in the case that the initial and final poses are close. Furthermore, by analyzing the relationship between the parameters and the effectiveness of the RDDH trajectory, the smoothing algorithm is designed to obtain appropriate parameters for a shorter and smoother trajectory. In the end, the numerical results show the proposed method can generate an effective trajectory under diverse initial conditions and achieve real-time computation.

On Dubins paths to intercept a moving target

We examine the problem of interception by a Dubins vehicle of a target that moves at constant speed along an a priori known planar trajectory. We establish sufficient conditions under which the shortest interception paths coincide with the shortest Dubins paths from the initial configuration of the pursuer to the point of interception, and show by means of examples that this is not always the case if the conditions are violated. Motivated by the problem of simultaneous interception of a target by a team of pursuers, we also analyze the problem of interception at a predefined time by a single pursuer. We present three path elongation algorithms, along with conditions that guarantee continuous elongation, and provide a sufficient condition for simultaneous interception. The analysis culminates in a centralized coordination scheme for simultaneous interception.

On the Length of Dubins Path with Any Initial and Terminal Configurations

Dubins has proved in 1957 that the minimum length path between an initial and a terminal configuration can be found among the six paths {LSL, RSR, LSR, RSL, RLR, LRL}. Skel and Lumelsky have studied the length of Dubins path with the initial configuration (0, 0; α) and the terminal configuration (d, 0; β) and the minimal turning radius ρ=1 in 2001. We extended the Skel and Lumelsky’s results to the case that the initial and terminal configuration is(x0, y0, α), (x1, y1, β), respectively (where x0, y0, x1, y1ϵℝ), and the minimal turning radius is ρ>0.