Dubins Curve Research Articles

Research on Path Planning Method for Autonomous Patrol Robots

For autonomous patrol robots, how to complete multi-point path planning efficiently is a crucial challenge. To address this issue, this work proposes a practical and efficient path planning method for patrol robots. Firstly, the evaluation function of the traditional A* method is improved to ensure that the planned path maintains a safe distance from the obstacles. Secondly, a Dubins curve is used to optimize the planned path to minimize the number of turning points while adhering to kinematic constraints. Thirdly, a trajectory-preserving strategy is proposed to preserve the continuous trajectory, linking multi-points for future inspection tasks. Finally, the proposed method is validated through both simulation and real-world experiments. Experimental results demonstrate that our proposed method performs exceptionally well in terms of safety, actual trajectory distance, and total execution efficiency.

Collaborative planning and control of heterogeneous multi-ground unmanned platforms

With the rapid development of intelligent vehicles, mobile robots, warehousing and logistics, exploration and testing and other industries, multi-platform collaborative work research has become the future research focus of ground platforms. This paper mainly studies the multi-ground platform collaborative system as follows: Combined with the multi-vehicle collaborative scenario, a three-layer system Artificial Intelligence control framework is proposed, which is composed of a task assignment layer, trajectory planning layer and multi-vehicle control layer. Firstly, the multi-car task assignment algorithm based on the Dubins curve is studied. Secondly, the vehicle motion planning algorithm based on the D*Lite algorithm is designed, and the driving direction and the optional grid range are improved. Then, the obstacle scene of multi-vehicle formation is analyzed, two obstacle avoidance schemes of formation are proposed and the process analysis is carried out. Finally, the application in engineering is conducted to verify the effectiveness of obstacle avoidance strategy, trajectory planning strategy and the overall system framework.

A method for obtaining the starting set of formation based on IPSO

The formation of intelligent platforms is a multi-objective constraint problem. It is necessary for the multi-agent to automatically generate the path from the initial position to the specified end point, and at the same time meet the constraints of space collision avoidance on the multi-target intersection path and the constraint of the agent’s motion ability, and pursue the shortest formation time of the whole formation as much as possible. In this paper, we propose an improved method for obtaining the starting set of multi-agent formation based on particle swarm optimization. First, the starting point set of the formation is defined, and then the particle swarm optimization algorithm is selected as the optimization algorithm to find the best starting point of the formation. Then the turning performance of the intelligent platform is studied, and the assembly route of each agent is designed by combining the Dubins curve. The simulation results show that the proposed method avoids collision between agents, shortens the time of agent formation assembly, and effectively ensures the reliability of the assembly route.

Segmented guidance method for multi-UAVs cooperative attack with spatio-temporal constraints

This paper presents a segmented guidance method for multi-UAVs (unmanned aerial vehicles) cooperative attack with spatio-temporal constraints, and successfully implemented in the flight tests. First, the uniform distribution of UAVs around the target is completed through cooperative path planning and tracking in the mid-course phase. The path planning method for cooperative arrival is proposed based on Dubins curve, and the guidance strategy for circular formation flight enables the UAVs to accurately track the reference points which are evenly distributed on the circle. Second, the terminal guidance law in 3D space with impact time cooperation is proposed during the cooperative attack stage, which would further eliminate the accumulated deviation. Finally, simulations and field flight tests for coordinated attack are carried out, which show the effectiveness of the proposed method.

Framework for formation control of jet-propelled unmanned surface vehicles

This study focuses on the research of spray-pump type unmanned surface vehicles (USVs). Based on the analysis of the dynamics and motion characteristics of USVs, a method combining Dubins curves and the particle swarm optimization algorithm is proposed to find the optimal or suboptimal solution for the formation path. The research goal is to switch multiple USVs from an unordered state to a formation state, taking the speed of USVs and the formation endpoint as dynamic variables and integrating Dubins curve theory into the particle swarm optimization algorithm. A theoretical framework for the formation of spray-pump type USVs is proposed. Finally, the formation of three USVs is realized in a simulation platform.

An Optimal Smooth-Path Motion Planning Method for a Car-like Mobile Robot

This paper proposes an optimal motion planning method consisting of a genetic algorithm (GA), potential field (PF), and Dubins curve for a Car-like mobile robot to solve the problem of finding the shortest and most feasible path in the global environment. Firstly, the GA finds the shortest path by evaluating, selecting, crossing over, and mutating from the initial population and finally provides the strongest individual evolution. Then the result from the GA is further applied with the PF algorithm to improve the ability of obstacle avoidance in the environment. Finally, the Dubins curve method is combined to smooth the path and helps the Car-like mobile robot solve the nonholonomic constraints problem. The major advantages of this method include finding the shortest path, improving avoidance obstacle ability, and smoothing the output path in an environment effectively. The simulation of the proposed method is executed on MATLAB to verify the ability to solve motion planning problems for a Car-like mobile robot.

Automatic Docking Trajectory Design-Based Time-Varying-Radius Dubins for Unmanned Surface Vessel

Facing the demand of efficient automatic docking for USV, this paper proposes a new kind of iterative varying-radius Dubins curve design. Due to the special mobility of dockyards, one novel trajectory optimization problem considering time optimum is modeled first. Then, we use the ant colony optimization (ACO) algorithm to solve such a complex problem. In addition to the global exhaustive search algorithm and ACO-based solution, a novel distributed local path planning algorithm named ADTA-TRD is proposed to obtain the solution of the above optimization problem restricted by the local perception of the USV. In essence, this paper draws lessons from the idea of the circular arc segment and straight line segment in the traditional Dubins curve, and consequently, the smoothness of the derived automatic docking trajectory can be guaranteed. Finally, the performance of proposed automatic docking path planning method is verified through simulation results and an actual sea trial.

Path Planning Based on the Improved RRT* Algorithm for the Mining Truck

Planning a reasonable driving path for trucks in mining areas is a key point to improve mining efficiency. In this paper, a path planning method based on Rapidly-exploring Random Tree Star (RRT*) is proposed, and several optimizations are carried out in the algorithm. Firstly, the selection process of growth target points is optimized. Secondly, the process of selecting the parent node is optimized and a Dubins curve is used to constraint it. Then, the expansion process from tree node to random point is optimized by the gravitational repulsion field method and dynamic step method. In the obstacle detection process, Dubins curve constraint is used, and the bidirectional RRT* algorithm is adopted to speed up the iteration of the algorithm. After that, the obtained paths are smoothed by using the greedy algorithm and cubic B-spline interpolation. In addition, to verify the superiority and correctness of the algorithm, an unmanned mining vehicle kinematic model in the form of front-wheel steering is developed based on the Ackermann steering principle and simulated for CoppeliaSim. In the simulation, the Stanley algorithm is used for path tracking and Reeds-Shepp curve to adjust the final parking attitude of the truck. Finally, the experimental comparison shows that the improved bidirectional RRT* algorithm performs well in the simulation experiment, and outperforms the common RRT* algorithm in various aspects.

Subsea field layout optimization (part III) --- the location-allocation problem of drilling sites

This study proposes an efficient method to optimize the subsea field layout with the aim of minimizing the subsea field development cost, based on the two methods introduced in Part I and Part II for solving the well trajectory planning problem and the location-allocation problem, i.e., 3D Dubins Curve method and Binary Linear Programming (BLP) method, respectively. The most complex part in subsea field layout optimization is essentially a location-allocation problem of drilling sites embedded with the well trajectory optimization. The full process of our method is clearly summarized in a flowchart. Abundant case studies with comparison to the existing results demonstrate the optimality and the flexibility of our method to solve practical subsea field layout optimization problems. In the cases studies, we also reveal how different user-defined cost items affect the optimal field layout. Details of implementing our method for a better performance is also discussed. This work is the third of a series of papers which systematically introduce an efficient method for subsea field layout optimization to minimize the development cost.

Subsea field layout optimization (Part I) – directional well trajectory planning based on 3D Dubins Curve

Directional well trajectory planning, which includes the optimization of the drilling site location and the trajectory between the drilling site to the completion interval, plays an important role in reducing subsea field development cost. The traditional well trajectory planning methods are based on the projected 2D profile of the wellbore trajectory with empirical knowledge or trial-and-error method to select a proper drilling site. In this study, we propose a new efficient optimization method based on the 3D Dubins curve, which has been widely used in autopilot for path planning but has never been mentioned in drilling industry. In short, we use gradient descent method to find the best drilling site location while adopting the 3D Dubins curve as the optimal wellbore trajectory to reach each completion interval so that the “1-site-n-wells” problem can be easily solved. Abundant case studies including both mathematically representative cases and the real practical field cases are conducted to demonstrate the feasibility and efficiency of our method. Wider application of our method for more complex situations are also discussed. This work is the first of a series of papers which systematically introduce an efficient method for subsea field layout optimization to minimize the development cost.

Evasion guidance of re-entry vehicle satisfying no-fly zone constraints based on virtual goals

An evasion guidance method based on virtual goals is proposed for re-entry vehicles to avoid a no-fly zone. The guidance method combined with the Dubins curve path planning method and proportion guidance can effectively avoid the no-fly zone based on the maneuverability analysis of the re-entry vehicle. This method designed an energy-based motion model combined with the Quasi equilibrium glide conditions, enabling the prediction-correction guidance to correct the errors caused by evasion and meet the altitude as well as voyage constraints. The simulation shows that the evasion guidance method can effectively avoid the no-fly zone, meet the re-entry terminal constraints, and the algorithm is robust and adaptable.

Trajectory planning for unmanned aerial vehicles in complicated urban environments: A control network approach

Trajectory planning is crucial for Unmanned Aerial Vehicles (UAVs) applications. It is still a challenge to plan UAV trajectories in large-scale complicated three-dimensional urban environments, mainly due to the complexities associated with handling a tremendous number of obstacles. To relieve this difficulty, this study proposes a two-stage control network approach. The first stage is an offline planning stage, aiming at constructing a discrete control network in the working environment achieving collision avoidance and meanwhile considering UAV kinetic properties. The second stage is an online planning stage, where a feasible corridor is generated based on the shortest path in the control network, and the obtained route is smoothed by a three-dimensional Dubins curve algorithm; then, a time-optimal trajectory generation algorithm is applied to trace the designed spatial path. Numerical studies based on a virtual city as well as a large-scale real-world urban area are conducted. The results show that the proposed approach is able to identify reasonable UAV trajectories within negligible computational time.

Novel obstacle-avoiding path planning for crop protection UAV using optimized Dubins curve

In recent years, the crop protection unmanned aerial vehicle (UAV) has been raised great attention around the world due to the advantages of more efficient operation and lower requirement of special landing airport. However, there are few researches on obstacle-avoiding path planning for crop protection UAV. In this study, an improved Dubins curve algorithm was proposed for path planning with multiple obstacle constraints. First, according to the flight parameters of UAV and the types of obstacles in the field, the obstacle circle model and the small obstacle model were established. Second, after selecting the appropriate Dubins curve to generate the obstacle-avoiding path for multiple obstacles, the genetic algorithm (GA) was used to search the optimal obstacle-avoiding path. Third, for turning in the path planning, a strategy considering the size of the spray width and the UAV’s minimum turning radius was presented, which could decrease the speed change times. The results showed that the proposed algorithm can decrease the area of overlap and skip to 205.1%, while the path length increased by only 1.6% in comparison with the traditional Dubins obstacle-avoiding algorithm under the same conditions. With the increase of obstacle radius, the area of overlap and skip reduced effectively with no significant increase in path length. Therefore, the algorithm can efficiently improve the validity of path planning with multiple obstacle constraints and ensure the safety of flight. Keywords: Dubins curve, path planning, genetic algorithm, overlap and skip spray, crop protection UAV DOI: 10.25165/j.ijabe.20201304.3205 Citation: Zhang X H, Fan C G, Cao Z Y, Fang J L, Jia Y J. Novel obstacle-avoiding path planning for crop protection UAV using optimized Dubins curve. Int J Agric & Biol Eng, 2020; 13(4): 172–177.

Online planning for relative optimal and safe paths for USVs using a dual sampling domain reduction-based RRT* method

A heuristic Dual sampling domain Reduction-based Optimal Rapidly-exploring Random Tree scheme is proposed by guiding the planning procedure of the optimal rapidly-exploring random tree (RRT*) method through learning environmental knowledge. The scheme aims to plan low fuel expenditure, easy-execution, and low collision probability paths online for an unmanned surface vehicle (USV) under constraints. First, an elliptic sampling domain, which is subject to an elliptic equation and the shortest obstacle avoidance path estimation, is created to plan short paths. Second, by the consideration of the USV motion states, obstacles and external interferences of the current, the near sampling domains of tree nodes are reduced to exclude high-cost sampling domains. Path feasibility is ensured by explicitly handling motion constraints. Third, a safe distance-based collision detection (CD) scheme and a velocity-based bounding box of USV are proposed to decrease the path collision probability. Additionally, a layered USV online path planning framework is built in accordance with the model predictive control method, and the path smoothing scheme is applied via the Dubins curve under the curvature constraint. Results demonstrate that the proposed dual sampling domain reduction method outperforms traditional reduction schemes in terms of improving the execution efficiency of RRT*. Meanwhile, the proposed CD method is more reliable than the conventional one.

Optimization Dubins Path of Multiple UAVs for Post-Earthquake Rapid-Assessment

In the last decade, with the wide application of UAVs in post-earthquake relief operations, the images and videos of affected areas obtained by UAVs immediately after a seismic event have become an important source of information for post-earthquake rapid assessment, which is crucial for initiating effective emergency response operations. In this study, we first consider the kinematic constraints of UAV and the Dubins curve is introduced to fit the shortest flyable path for each UAV that meets the maximum curvature constraint. Second, based on the actual requirements of post-earthquake rapid assessment, heterogeneous UAVs, multi-depot launching, and targets allowed access to multiple times, the paper proposes a multi-UAV rapid-assessment routing problem (MURARP). The MURARP is modeled as the multi-depot revisit-allowed Dubins TOP with variable profit (MD-RDTOP-VP) which is a variant of the team orienteering problem (TOP). Third, a hybrid genetic simulated annealing (HGSA) algorithm is developed to solve the problem. The result of numerical experiments shows that the HGSA algorithm can quickly plan flyable paths for heterogeneous UAVs to maximize the expected profit. Finally, a case study based on real data of the 2017 Jiuzhaigou earthquake in China shows how the method can be applied in a post-earthquake scenario.

Novel obstacle-avoiding path planning for crop protection UAV using optimized Dubins curve

Novel obstacle-avoiding path planning for crop protection UAV using optimized Dubins curve

Pushing revisited: Differential flatness, trajectory planning, and stabilization

We prove that quasi-static pushing with a sticking contact and ellipsoid approximation of the limit surface is differential flat. Both graphical and algebraic derivations are given. A major conclusion is that the pusher–slider system is reducible to the Dubins car problem where the sticking contact constraints translate to bounded curvature. Planning is as easy as computing a Dubins curve with the additional benefit of time-optimality. For trajectory stabilization, we design closed-loop control using dynamic feedback linearization or open-loop control using two contact points as a form of mechanical feedback. We conduct robotic experiments using objects with different pressure distributions, shape, and contact materials placed at different initial poses that require difficult switching action maneuvers to the goal pose. The average error is within 1.67 mm in translation and 0.5° in orientation over 60 experimental trials. We also show an example of pushing among obstacles using a RRT planner with exact steering.

Distributed intelligent self-organized mission planning of multi-UAV for dynamic targets cooperative search-attack

This article studies the cooperative search-attack mission problem with dynamic targets and threats, and presents a Distributed Intelligent Self-Organized Mission Planning (DISOMP) algorithm for multiple Unmanned Aerial Vehicles (multi-UAV). The DISOMP algorithm can be divided into four modules: a search module designed based on the distributed Ant Colony Optimization (ACO) algorithm, an attack module designed based on the Parallel Approach (PA) scheme, a threat avoidance module designed based on the Dubins Curve (DC) and a communication module designed for information exchange among the multi-UAV system and the dynamic environment. A series of simulations of multi-UAV searching and attacking the moving targets are carried out, in which the search-attack mission completeness, execution efficiency and system suitability of the DISOMP algorithm are analyzed. The simulation results exhibit that the DISOMP algorithm based on online distributed down-top strategy is characterized by good flexibility, scalability and adaptability, in the dynamic targets searching and attacking problem.

A Hierarchical Cooperative Mission Planning Mechanism for Multiple Unmanned Aerial Vehicles

In this paper, the cooperative multi-task online mission planning for multiple Unmanned Aerial Vehicles (UAVs) is studied. Firstly, the dynamics of unmanned aerial vehicles and the mission planning problem are studied. Secondly, a hierarchical mechanism is proposed to deal with the complex multi-UAV multi-task mission planning problem. In the first stage, the flight paths of UAVs are generated by the Dubins curve and B-spline mixed method, which are defined as “CBC)” curves, where “C” stands for circular arc and “B” stands for B-spline segment. In the second stage, the task assignment problem is solved as multi-base multi-traveling salesman problem, in which the “CBC” flight paths are used to estimate the trajectory costs. In the third stage, the flight trajectories of UAVs are generated by using Gaussian pseudospectral method (GPM). Thirdly, to improve the computational efficiency, the continuous and differential initial trajectories are generated based on the “CBC” flight paths. Finally, numerical simulations are presented to demonstrate the proposed approach, the designed initial solution search algorithm is compared with existing methods. These results indicate that the proposed hierarchical mission planning method can produce satisfactory mission planning results efficiently.

Internet-Of-Things in Motion: A UAV Coalition Model for Remote Sensing in Smart Cities.

Unmanned aerial vehicles (UAVs) or drones are increasingly used in cities to provide service tasks that are too dangerous, expensive or difficult for human beings. Drones are also used in cases where a task can be performed more economically and or more efficiently than if done by humans. These include remote sensing tasks where drones can be required to form coalitions by pooling their resources to meet the service requirements at different locations of interest in a city. During such coalition formation, finding the shortest path from a source to a location of interest is key to efficient service delivery. For fixed-wing UAVs, Dubins curves can be applied to find the shortest flight path. When a UAV flies to a location of interest, the angle or orientation of the UAV upon its arrival is often not important. In such a case, a simplified version of the Dubins curve consisting of two instead of three parts can be used. This paper proposes a novel model for UAV coalition and an algorithm derived from basic geometry that generates a path derived from the original Dubins curve for application in remote sensing missions of fixed-wing UAVs. The algorithm is tested by incorporating it into three cooperative coalition formation algorithms. The performance of the model is evaluated by varying the number of types of resources and the sensor ranges of the UAVs to reveal the relevance and practicality of the proposed model.