Dubins Path Research Articles

Path Following Using Rendezvous Dubins Curves and Integral Line-of-Sight for Unmanned Marine Systems

Accurately following a prescribed path is critical for safe and efficient operation of autonomous systems in the field, especially for marine robots that typically operate away from human support and with sporadic communication abilities. Traditionally, variations of a lookahead control strategy have been employed for unmanned marine systems; however, these strategies can encounter problems when faced with disturbances and discontinuities in localization. In underwater applications, intermittent global localization updates are common due to constraints imposed by the lack of external updates from GPS. This paper examines the application of an online replanning tool based on Dubins curves to a path follower based on integral line-of-sight (ILOS) control. The fundamental idea is to drive the vehicle towards the prescribed path along a Dubins path. The proposed guidance strategy enables the path following controller to be tuned to aggressively track the path, improving disturbance rejection of an ILOS implementation without rendezvous ability by twofold in the simulated scenarios. The proposed method is experimentally validated on both an autonomous underwater vehicle and an autonomous surface vehicle with extended testing in a pond environment. Results indicate that the guidance strategy is able to track paths through disturbances and intermittent localization discontinuities in both surface and underwater use. This work has broad applications to field deployments of marine robots as a means to efficiently link mission level plans to vehicle level control signals considering realistic constraints on localization and control. Specific near-term applications focus on mobile underwater docking for undersea persistence.

Dynamic Modeling and Hybrid Fireworks Algorithm-Based Path Planning of an Amphibious Robot

The task of path planning in amphibious environments requires additional consideration due to the complexity of the amphibious environments. This paper presents a path planning method for an amphibious robot named “AmphiRobot” with its dynamic constraints considered. First, an explicit dynamic model using Kane’s method is presented. The hydrodynamic parameters are obtained through computational fluid dynamics simulations. Furthermore, a path planning method based on a hybrid fireworks algorithm is proposed, combining the fireworks algorithm and bare bones fireworks algorithm, aiming at the amphibious robot’s characteristics of multiple motion modes and working environments. The initially planned path is then smoothed using Dubins path under constraints determined by the dynamic model. Simulation reveals that the performance of the hybrid fireworks algorithm approach is better than the fireworks algorithm and bare bones fireworks algorithm is applied separately in the amphibious environment scenarios.

Construction of movement trajectories for objects based on the Dubins car problem, taking into account constant external influences

The paper considers an approach in terms of optimal speed problem for Dubins cars to the formation of control trajectories of moving objects (airplanes, ships), that have control restrictions, under external influences that are constant in magnitude and direction and constant control values at each part of the trajectory. Instead of solving the Pontryagin maximum principle, it is proposed to use a simple comparison of possible control strategies in order to determine the best among them in terms of speed. For each strategy, the calculation of control switching points on the trajectory is based on minimizing the difference between the specified coordinates of the endpoint and the coordinates of the point at which the trajectory comes, depending on the choice of the parameters of two intermediate control switching points. The problem of finding the best speed trajectory for an object from one point to another is solved using the Dubins approach, and their coordinates and heading angles are given for both points. All calculations were carried out taking into account wind and water disturbances, which are constant in magnitude and direction and distort the trajectory. The problem of finding the Dubins paths is reduced to finding the parameters of two intermediate points at which the control changes. Different possibilities for changing controls are considered, taking into account the existing restrictions. The lengths of the trajectories are calculated and the best travel time is selected. The proposed method considers several trajectories acceptable in terms of constraints, taking into account the external influences, from which the optimal path is selected by comparison. Having multiple feasible strategies is beneficial when choosing a trajectory depending on the environment. Instead of solving the problem of nonlinear optimization of the Pontryagin maximum principle, a simple comparison of possible control strategies is used in order to determine the best among them in terms of speed, each of the possible strategies is sought from the condition of minimizing the residual of the analytical solution and the boundary condition at the end of the trajectory. When searching for possible trajectories, control constraints, the influence of external influences, that are constant in magnitude and direction, and the constancy of the control value at each part of the trajectory are taken into account. And all these factors make it possible to sufficiently and adequately simulate the movement of the ship. Physically, restrictions on control (turning radius) are associated with a limited steering angle. Restrictions can be associated not only with restrictions on the turning radius, but also with geographical features of a specific area: for unmanned aerial vehicles this may be due to the buildings and terrain, and for ships this may be due to the coastline, shoals, islands, etc. In this regard, it may turn out that the solution found optimal in terms of speed cannot be realizable in practice. Then the method proposed in the work has the ability to choose another trajectory among the less optimal in terms of speed.

Performance-based emergency landing trajectory planning applying meta-heuristic and Dubins paths

Emergency Landing is a complex problem of optimal path planning of an impaired airplane in presence of obstacles, while the airplane performance characteristics have degraded. Some in-flight failures can affect the airplane dynamics and therefore the new dynamic constraints must be considered in flight planning to the desired landing site. This paper introduces a novel hybrid form of Dubins-simulated annealing (HDSA) optimization framework for emergency landing. The proposed architecture applies Dubins paths and Apollonius’ tangent line to generate candidate pieces of trajectories respecting the post-failure performance characteristics of the distressed airplane. The optimization pattern is used to select the optimal combination of the candidate trajectories based on the cost functions and the environmental constraints to lead the airplane to the desired landing site. Analytical performance-based equations are developed to achieve an admissible solution in emergency trajectory planning. The goal is to provide a general optimal framework, which can enhance the flight management system by assisting the pilot to plan the most suitable and admissible trajectory to the landing site in emergency flight conditions. The effectiveness of the proposed approach is demonstrated through simulations.

An Approach to Air-to-Surface Mission Planner on 3D Environments for an Unmanned Combat Aerial Vehicle

Recently, interest in mission autonomy related to Unmanned Combat Aerial Vehicles(UCAVs) for performing highly dangerous Air-to-Surface Missions(ASMs) has been increasing. Regarding autonomous mission planners, studies currently being conducted in this field have been mainly focused on creating a path from a macroscopic 2D environment to a dense target area or proposing a route for intercepting a target. For further improvement, this paper treats a mission planning algorithm on an ASM which can plan the path to the target dense area in consideration of threats spread in a 3D terrain environment while planning the shortest path to intercept multiple targets. To do so, ASMs are considered three sequential mission elements: ingress, intercept, and egress. The ingress and egress elements require a terrain flight path to penetrate deep into the enemy territory. Thus, the proposed terrain flight path planner generates a nap-of-the-earth path to avoid detection by enemy radar while avoiding enemy air defense threats. In the intercept element, the shortest intercept path planner based on the Dubins path concept combined with nonlinear programming is developed to minimize exposure time for survivability. Finally, the integrated ASM planner is applied to several mission scenarios and validated by simulations using a rotorcraft model.

A Hybrid Autonomous Recovery Scheme for AUV Based Dubins Path and Non-Singular Terminal Sliding Mode Control Method

In order to improve the persistent operation capacity of autonomous underwater vehicle (AUV), autonomous recovery system draws more and more attention in recent years. A hybrid scheme combined with navigation, guidance and control is proposed to complete the function of autonomous recov-ery of AUV in the paper. Based on the hybrid scheme, the autonomous recovery is firstly transformed into the trajectory tracking problem, and the Dubins path planning method is adopted to build the three-dimensional(3D) motion path of AUV. Secondly, the virtual target guidance strategy is introduced to guide the AUV to track the desired path. Finally, a non-singular terminal sliding mode controller is designed to control the AUV. Due to the existence of model inaccuracy of AUV and external disturbances from the environment, a finite-time disturbance observer is adopted to estimate the disturbance and uncertainty in the system. Numerical simulation is conducted to verify its performance. The simulation results show that a 3D motion path can be planed and the AUV can track the motion path well.

Optimal route design for an airship collecting and delivering logs in difficult environmental conditions

In this paper, we consider the problem of computing the optimal route to be followed by an airship collecting logs in order to bring them to a sawmill. The problem is separated into two phases. In the first one, we aim to determine the touring order and the number of logs to be collected for each round-trip between the logging area and the sawmill. The strategy is designed by taking into account the airship sensitivity to atmospheric conditions, which makes the cost to join a heap of logs highly dependent on the vehicle orientation with respect to the wind direction. The determination is achieved by solving an instance of a combinatorial problem called Asymmetric Capacitated Vehicle Routing Problem (ACVRP). We introduce airship enhanced Dubins paths taking the wind influence into account to compare more realistic transition costs easily. During the second phase, the resulting heap-to-heap trajectories are calculated so as to minimize the travel cost consisting of the time and energy consumption. The equations of generic nonlinear airship dynamics are derived and used for trajectory optimization. The resulting performances are illustrated with a mountainous scenario with varying windspeed. The overall scheme forms an innovative approach to solve issues related to typical airship missions.

Angular Rate Constrained Sliding Mode Control of UAVs for Path Following

In this work, a sliding-mode-based attitude controller constrained with the angular rate for unmanned aerial vehicles (UAVs) is addressed to withstand conditions below the allowable maximum angular velocity of UAVs in order to avoid the possibility of structural failure and to operate UAVs safely. The sliding mode controller suggested in this work defines a new sliding surface, inherently having two equilibrium points. These equilibrium points are carefully inspected, and the stability of the system controlled by means of the proposed approach is also analyzed using Lyapunov stability theory. To highlight the angular-rate constrained attitude control technique, a three-dimensional path is constructed using the Dubins path technique, and three-axis attitude commands for UAV are also generated by augmenting the line-of-sight algorithm. Compared with conventional sliding mode control measures, the excellent performance of the suggested control algorithm has been demonstrated by conducting numerical simulations.

AUV path planning for coverage search of static target in ocean environment

Aiming at the path planning problem for searching static target by autonomous underwater vehicles (AUVs) in ocean environment, this paper proposes a hierarchical method based on the maximum cumulative detection reward or search efficiency. First, the mission sea region is described in the form of target probability map, and the subregions with high search value are extracted by the method of expectation-maximization (EM). For multiple AUVs, we propose the bidirectional negotiation with biased min-consensus (BN-BMC) algorithm to determine the allocation and prioritization of subregions to be searched. On this basis, we utilize an adaptive oval spiral coverage (AOSC) strategy to plan the coverage path within each subregion, and take the Dubins path satisfying the AUV kinematic constraint as the transition path between subregions. Finally, the simulation results validate the advantage of our method.

Geometric approach to the solution of the Dubins car problem in the formation of program trajectories

The paper considers an approach to the formation of control program trajectories of moving objects (UAVs, ships) as a solution to the optimal problem in terms of Dubins path search. Instead of directly solving the Pontryagin’s maximum principle, it is proposed to use a simple analysis of possible control strategies in order to determine among them the optimal one in terms of time spent on a trajectory. The problem of finding the shortest trajectory of movement of an object from one point to another is solved, and for both points their coordinates and heading angles at these points are given, as well as three absolute values of the circulation radii corresponding to the given control signals on each of the three sections of the trajectory. The problem of finding the Dubins curves is reduced to determining the parameters of two intermediate points at which the control changes. All possible directions of control change options are considered, taking into account the existing constraints, also the lengths of the corresponding motion trajectories are calculated, and the optimal one is selected. The problem of constructing a trajectory is solved as well, which ensures a smooth conjugation of two linear fragments of trajectories and passes through the point of their intersection. The solution of the optimal trajectory problem using the Dubins car gives a single trajectory. In contrast to this, the proposed method considers several trajectories admissible by the constraints, from which the optimal one is selected by exhaustive search. The presence of several feasible strategies gives advantages for each specific situation of choosing a trajectory depending on the environment. Instead of directly solving the Pontryagin’s maximum principle and constructing a three-dimensional optimal trajectory, the authors used a simple analysis of possible control strategies in order to determine among them the optimal one in terms of elapsed time. The approach was motivated by the limited number of possible control strategies for Dubins paths, as well as the simplicity of analytical calculations for each of them, which allows performing these calculations in real time. The high speed of calculations for the problem of determining the optimal trajectory is due to the fact that the proposed method does not require complex calculations to solve the problem of nonlinear optimization, which follows from the Pontryagin’s principle.

A Multi-Dimensional Goal Aircraft Guidance Approach Based on Reinforcement Learning with a Reward Shaping Algorithm.

Guiding an aircraft to 4D waypoints at a certain heading is a multi-dimensional goal aircraft guidance problem. In order to improve the performance and solve this problem, this paper proposes a multi-layer RL approach. The approach enables the autopilot in an ATC simulator to guide an aircraft to 4D waypoints at certain latitude, longitude, altitude, heading, and arrival time, respectively. To be specific, a multi-layer RL approach is proposed to simplify the neural network structure and reduce the state dimensions. A shaped reward function that involves the potential function and Dubins path method is applied. Experimental and simulation results show that the proposed approach can significantly improve the convergence efficiency and trajectory performance. Furthermore, the results indicate possible application prospects in team aircraft guidance tasks, since the aircraft can directly approach a goal without waiting in a specific pattern, thereby overcoming the problem of current ATC simulators.

Unmanned Aerial Vehicle Mid-Air Collision Detection and Resolution Using Avoidance Maps

Collision avoidance for fixed-wing unmanned aerial vehicles (UAVs), using a novel methodology of avoidance map, is addressed in this work. Avoidance map is defined as a mapping in the control input space of a pair of UAVs, which partitions the control space into avoidance and collision regions, respectively. The choice of maneuvers to execute successful avoidance can be effectively obtained by using the avoidance map. The duration of control application is determined by a simple method that is time optimal and computationally efficient. Different versions of the map portraying the evolution of the concept are also given. Precision control, defined as a gradual reduction in control, is discussed to reduce the control input demand for the entire duration of avoidance. The concept is extended to multiple UAVs, and the additional requirement of the UAVs to return to nominal trajectory after avoidance, using Dubins paths, is also addressed. Finally, simulation results using realistic UAV models are considered, and some needed modifications to the basic avoidance strategy, made necessary by realistic maneuver models, are discussed. Several illustrative simulation results are given to support the applicability of the proposed method.

Online flight path planning with flight time constraints for fixed-wing UAVs in dynamic environments

PurposeA major challenge for mission planning of aircraft is to generate flight paths in highly dynamic environments. This paper presents a new approach for online flight path planning with flight time constraints for fixed-wing UAVs. The flight paths must take into account the kinematic restrictions of the vehicle and be collision-free with terrain, obstacles and no-fly areas. Moreover, the flight paths are subject to time constraints such as predetermined time of arrival at the target or arrival within a specified time interval.Design/methodology/approachThe proposed flight path planning algorithm is an evolution of the well-known RRT* algorithm. It uses three-dimensional Dubins paths to reflect the flight capabilities of the air vehicle. Requirements for the flight time are realized by skillfully concatenating two rapidly exploring random trees rooted in the start and target point, respectively.FindingsThe approach allows to consider static obstacles, obstacles which might pop up unexpectedly, as well as moving obstacles. Targets might be static or moving with constantly changing course. Even a change of the target during flight, a change of the target approach direction or a change of the requested time of arrival is included.Originality/valueThe capability of the flight path algorithm is demonstrated by simulation results. Response times of fractions of a second qualify the algorithm for real-time applications in highly dynamic scenarios.

Vector field path following of a full-wing solar-powered Unmanned Aerial Vehicle (UAV) landing based on Dubins path: a lesson from multiple landing failures

Abstract The full-wing solar-powered UAV has a large aspect ratio, special configuration, and excellent aerodynamic performance. This UAV converts solar energy into electrical energy for level flight and storage to improve endurance performance. The UAV only uses a differential throttle for lateral control, and the insufficient control capability during crosswind landing results in a large lateral distance bias and leads to multiple landing failures. This paper analyzes 11 landing failures and finds that a large lateral distance bias at the beginning of the approach and the coupling of base and differential throttle control is the main reason for multiple landing failures. To improve the landing performance, a heading angle-based vector field (VF) method is applied to the straight-line and orbit paths following and two novel 3D Dubins landing paths are proposed to reduce the initial lateral control bias. The results show that the straight-line path simulation exhibits similar phenomenon with the practical failure; the single helical path has the highest lateral control accuracy; the left-arc to left-arc (L-L) path avoids the saturation of the differential throttle; and both paths effectively improve the probability of successful landing.

Underwater Docking Approach and Homing to Enable Persistent Operation.

One of the main limiting factors in deployment of marine robots is the issue of energy sustainability. This is particularly challenging for traditional propeller-driven autonomous underwater vehicles which operate using energy intensive thrusters. One emerging technology to enable persistent performance is the use of autonomous recharging and retasking through underwater docking stations. This paper presents an integrated navigational algorithm to facilitate reliable underwater docking of autonomous underwater vehicles. Specifically, the algorithm dynamically re-plans Dubins paths to create an efficient trajectory from the current vehicle position through approach into terminal homing. The path is followed using integral line of sight control until handoff to the terminal homing method. A light tracking algorithm drives the vehicle from the handoff location into the dock. In experimental testing using an Oceanserver Iver3 and Bluefin SandShark, the approach phase reached the target handoff within 2 m in 48 of 48 tests. The terminal homing phase was capable of handling up to 5 m offsets with approximately 70% accuracy (12 of 17 tests). In the event of failed docking, a Dubins path is generated to efficiently drive the vehicle to re-attempt docking. The vehicle should be able to successfully dock in the majority of foreseeable scenarios when re-attempts are considered. This method, when combined with recent work on docking station design, intelligent cooperative path planning, underwater communication, and underwater power transfer, will enable true persistent undersea operation in the extremely dynamic ocean environment.

Time-optimal guidance for intercepting moving targets by Dubins vehicles

This paper is concerned with a Minimum-Time Intercept Problem (MTIP), for which a Dubins vehicle is guided from a position with a prescribed initial heading angle to intercept a moving target in minimum time. Some geometric properties for the solution of the MTIP are presented, showing that the solution paths must lie in a sufficient family of 4 candidates. Necessary and sufficient conditions for optimality of each candidate are established. By employing the geometric properties, it is found that the 4 candidates are determined by the zeros of some real-valued functions when the target’s velocity is constant. In order to compute all the 4 candidates, the derivatives of these real-valued functions are transformed to polynomials so that the extrema of those real-valued functions can be computed by standard polynomial solvers. This allows employing a simple bisection method to find all the 4 candidates. Since the MTIP with a constant target’s velocity is equivalent to the path planning problem of Dubins vehicle in a constant drift field, developing such an algorithm also enables efficiently finding the shortest Dubins path in a constant drift field. Finally, some numerical examples are presented, demonstrating and verifying the developments of the paper.

각속도 제한을 고려한 무인기의 Dubins 경로 생성 및 추적

각속도 제한을 고려한 무인기의 Dubins 경로 생성 및 추적

The Orbiting Dubins Traveling Salesman Problem: planning inspection tours for a minehunting AUV

The Orbiting Dubins Traveling Salesman Problem (ODTSP) is to plan a minimum-time tour for a Dubins vehicle model to inspect a set of targets in the plane by orbiting each target along a circular arc. This problem arises in underwater minehunting, where targets are mine-like objects on the sea bottom that are inspected by a sonar-equipped underwater vehicle. Each orbit subtends a prescribed angle so that the target’s acoustic response is measured from a variety of target-sensor relative geometries to aid in classifying it. ODTSP tours consist of circular-arc orbits joined by Dubins paths, and the optimization problem is to partition the set of targets into orbits and determine the position, radius, direction, and vehicle entry angle of each. Algorithms are presented for the restricted case, where each orbit inspects a single target (only), and the general case, where orbits inspect multiple targets. The approach is facilitated by analytical conditions that identify admissible clusters of targets as cliques of a disk graph. The ODTSP is extended to consider path planning in the presence of a steady uniform current.

A Formation Reconfiguration Method for Multiple Unmanned Surface Vehicles Executing Target Interception Missions

This paper presents a formation reconfiguration method for multiple unmanned surface vehicles (MUSVs) executing target interception missions. In its essence, the objective can be described as follows: given a target at a given position and a set of USVs, maneuver the USVs from their initial positions towards the target so that they end forming a “protective barrier” in the vicinity of the target. In its simplest form, this barrier can be simply obtained through a colinear formation of the USVs, with the center at an appropriate distance from the target. This can be done in two distinct phases: maneuver planning and vehicle task assignment. In terms of maneuver planning, an adaptive null-space-based (ANSB) strategy is adopted. In order to address explicitly the maneuverability constraints of each vehicle (for example, intrinsic limitations on the rate of turn while progressing at a given linear speed), an improved adaptive null space method (IMANSB) is proposed for vehicle speed assignment. In terms of task assignment, by introducing the virtual attractive force and rigid body dynamics, a method of redefined Dubins path was proposed, which can more quickly match the optimal path that conforms to the heading angle of the departure and the heading angle of the destination. And, a method of formation reconfiguration for sea surface target interception of USV was presented, including spatial decoupling search and redefined Dubins path planning, in order to solve the problem of multi-objective optimization of the MUSV formation internal reconfiguration which is helpful to accelerate formation forming by considering the influence of cooperative time consistency and total distance. To verify the feasibility of proposed method, a simulation platform for the formation control of MUSVs was established, and a simulation experiment was conducted.

Rapid path planning for Dubins vehicles under environmental currents

This paper presents a rapid (real time) solution to the minimum-time path planning problem for Dubins vehicles under environmental currents (wind or ocean currents). Real-time solutions are essential in time-critical situations (such as replanning under dynamically changing environments or tracking fast moving targets). Typically, Dubins problem requires to solve for six path types; however, due to the presence of currents, four of these path types require to solve the root-finding problem involving transcendental functions. Thus, the existing methods result in high computation times and their applicability for real-time applications is limited. In this regard, in order to obtain a real-time solution, this paper proposes a novel approach where only a subset of two Dubins path types (LSL and RSR) are used which have direct analytical solutions in the presence of currents. However, these two path types do not provide full reachability. We show that by extending the feasible range of circular arcs in the LSL and RSR path types from 2π to 4π: (1) full reachability of any goal pose is guaranteed, and (2) paths with lower time costs as compared to the corresponding 2π-arc paths can be produced. Theoretical properties are rigorously established, supported by several examples, and evaluated in comparison to the Dubins solutions by extensive Monte-Carlo simulations.