Smooth Path Research Articles

A real‐time decoupling trajectory planning method for on‐road autonomous driving

AbstractTrajectory planning is a core technology for autonomous vehicle directlyreflecting the driving safety and efficiency. In this paper, a spatial‐speed decoupled planning method is studied for real‐time trajectory generation in the on‐road environment. The proposed approach mainly includes two parts: optimization‐based lateral planning and selection‐based longitudinal speed planning. The optimization‐based lateral planning is employed to generate an optimal collision‐free and smooth path by solving a quadratic programming problem. Specifically, the lateral planning first constructs a safe corridor by integrating obstacles and initial risky corridor together in the Frénet frame. The safe corridor is useful for quadratic programming problem formulation. The selecting‐based longitudinal speed planning is proposed to generate a suitable and continuous velocity trajectory. The novel speed selector considering four cases is designed to select a more suitable reference velocity in different lane situations. The continuous velocity trajectory is obtained by solving piecewise continuous quartic polynomial. As a result, the combination of the spatial path and the velocity trajectory is the final planning result. The proposed algorithm is tested extensively in a simulation environment. Experimental results demonstrate that the proposed algorithm has good real‐time property and practical validity.

Obstacle avoidance path planning of mobile robot based on improved DWA

A new dynamic window algorithm is proposed to solve the problem that the optimal trajectory is difficult to plan and the trajectory is not smooth due to the dense obstacles in the complex workshop path planning task. The algorithm sets the initial direction angle, and then improves the evaluation function through the direction angle change factor to improve the efficiency and flexibility of the algorithm; The fuzzy controller is used to adjust the coefficient of the evaluation function, which improves the adaptability of the mobile robot to the complex workshop environment. The MATLAB simulation results show that the improved DWA can plan a more reasonable and smooth running path in the area with dense obstacles, and has better obstacle avoidance effect while ensuring the safety of the robot.

Skeleton Extraction and Greedy-Algorithm-Based Path Planning and its Application in UAV Trajectory Tracking

Space research is of great significance to increasingly decentralized and distributed space systems, and path planning in space systems has become a research hotspot for maintaining their safety, security, and reliability. To explore the passable path connecting the starting point and the target point, and optimize a smooth trajectory that can be tracked by unmanned aerial vehicles (UAVs) in 3-D space, a skeleton-extraction- and greedy-algorithm-based path planning has been proposed to guide the flight of UAVs. First, the rapidly exploring random tree (RRT) has been introduced for path search. To speed up the path search process, the spatial skeleton extraction method has been introduced to calculate the skeleton of free space The greedy algorithm has been utilized to increase the RRT expansion and reduce unnecessary bends in the path. The skeleton extraction and greedy-algorithm-based Lazy RRT and RRT-Connect have been proposed to build compared experiments. Second, the minimum snap has been applied to generate a smooth flight trajectory, and the flight time is allocated according to the distance between the waypoints. Third, the UAV Simulink model has been established, and the spatial position of the optimized trajectory is tracked. The experimental results prove that the skeleton extraction can significantly speed up the search process, and greedy algorithm can shorten the path length effectively. The minimum snap combined with the time allocation strategy can produce a smooth and feasible path. The UAV Simulink model also proves that the classic proportion-differentiation controller can accurately track the generated trajectory. The greedy algorithm and skeleton extraction reduce the average path length of RRT by 9.780 and 8.251%, respectively. The greedy algorithm and skeleton extraction reduce the average path length of RRT, Lazy RRT, and RRT-Connect by about 10–13%. The greedy algorithm and skeleton extraction reduce the time consumption of RRT by 62.781 and 36.276%, respectively.

Trajectory Tracking and Obstacle Avoidance for Wheeled Mobile Robots Based on EMPC With an Adaptive Prediction Horizon.

This article develops an event-triggered model-predictive control (EMPC) strategy to realize trajectory tracking and obstacle avoidance for a wheeled mobile robot (WMR) subject to input constraints and external disturbances. In the EMPC strategy, a potential field is introduced in the cost function to guarantee a smooth path for the WMR. An event-triggered mechanism is designed to reduce the computational load of solving an optimal control problem (OCP). Moreover, an adaptive prediction horizon is utilized to further achieve computation reduction. Both recursive feasibility of the OCP and practical stability of the resulting closed-loop system are analyzed for the WMR with the input constraints and the external disturbances. Simulation results are provided to demonstrate the effectiveness and superiority of the proposed EMPC strategy.

Oxygen vacancy-mediated WO3 phase junction to steering photogenerated charge separation for enhanced water splitting

Effective charge separation and transfer is deemed to be the contributing factor to achieve high photoelectrochemical (PEC) water splitting performance on photoelectrodes. Building a phase junction structure with controllable phase transition of WO3 can further improve the photocatalytic performance. In this work, we realized the transition from orthorhombic to monoclinic by regulating the annealing temperatures, and constructed an orthorhombic-monoclinic WO3 (o-WO3/m-WO3) phase junction. The formation of oxygen vacancies causes an imbalance of the charge distribution in the crystal structure, which changes the W-O bond length and bond angle, accelerating the phase transition. As expected, an optimum PEC activity was achieved over the o-WO3/m-WO3 phase junction in WO3-450 photoelectrode, yielding the maximum O2 evolution rate roughly 32 times higher than that of pure WO3-250 without any sacrificial agents under visible light irradiation. The enhancement of catalytic activity is attributed to the atomically smooth interface with a highly matched lattice and robust built-in electric field around the phase junction, which leads to a less-defective and abrupt interface and provides a smooth interfacial charge separation and transfer path, leading to improved charge separation and transfer efficiency and a great enhancement in photocatalytic activity. This work strikes out on new paths in the formation of an oxygen vacancy-induced phase transition and provides new ideas for the design of catalysts.

Smooth Complete Coverage Trajectory Planning Algorithm for a Nonholonomic Robot.

The complete coverage path planning is a process of finding a path which ensures that a mobile robot completely covers the entire environment while following the planned path. In this paper, we propose a complete coverage path planning algorithm that generates smooth complete coverage paths based on clothoids that allow a nonholonomic mobile robot to move in optimal time while following the path. This algorithm greatly reduces coverage time, the path length, and overlap area, and increases the coverage rate compared to the state-of-the-art complete coverage algorithms, which is verified by simulation. Furthermore, the proposed algorithm is suitable for real-time operation due to its computational simplicity and allows path replanning in case the robot encounters unknown obstacles. The efficiency of the proposed algorithm is validated by experimental results on the Pioneer 3DX mobile robot.

Ameliorated equilibrium optimizer with application in smooth path planning oriented unmanned ground vehicle

To enhance the performance of equilibrium optimizer (EO) and expand its application for smooth path planning of the unmanned ground vehicle (UGV), an ameliorated equilibrium optimizer (AEO) is developed and applied to the UGV smooth path planning problem. The main characteristics of AEO are the population initialization by an opposition-based learning (OBL) strategy, the concentration updating by a centroid opposition-based learning (COBL) strategy, and the concentration updating by a proposed self-learning strategy. The three improvement strategies in the AEO enhance the optimization performance of EO through utilizing the information of the opposite space, the neighborhood space, and the whole population. The performance of AEO is examined by comparing it with several well-known algorithms on 29 commonly used benchmark functions. The comparison results show that the AEO is superior to the compared algorithms and ranks first in performance evaluation. Furthermore, a smooth path planning method AEO-HB is proposed by optimizing the control points from high-order Bezier curve based on the AEO. Simulation experiment results manifest that the AEO-HB solves the smooth path planning problem and ranks first among the compared algorithms for the performance evaluation in three different cases. The above results of numerical experiments and smooth path planning experiments indicate that the proposed improvement strategies in the AEO enhance the performance of solving global optimization problems, which makes the AEO have the potential to deal with global optimization problems in more types of application scenarios.

Path Planning of Mobile Robot Based on Improved PRM Based on Cubic Spline

In view of the shortcomings of low search efficiency and many path turning points of Probabilistic Roadmaps (PRM), a bidirectional search PRM global path planning algorithm is proposed. The algorithm improves the search connection rules by using the positive and negative directions to search the path alternately, so that the connection of unnecessary nodes reduces, thereby speeding up the efficiency of path planning. Besides, the algorithm incorporates cubic spline interpolation. That will increase the smoothness of path planning and ensure that the mobile robot can realize the path planning task more smoothly and safely. The simulation results show that the improved algorithm can effectively improve the convergence speed and path smoothness of the algorithm. Finally, the improved algorithm is applied to the actual mobile robot navigation experiment. The experimental results have proven that the path planning strategy was able to a superior advantage over traditional PRM in path quality and computational time.

A novel hybrid Chaotic Aquila Optimization algorithm with Simulated Annealing for Unmanned Aerial Vehicles path planning

Unmanned Aerial Vehicles path planning is one of the critical issues in terms of guaranteeing good performance in real-world applications. Basically, it is responsible for determining and ensuring a short, smooth, and collision-free path between two positions from a source to a destination point. This paper presents a hybrid optimization scheme based on the hybridization of Chaotic Aquila Optimization with Simulated Annealing for solving the Unmanned Aerial Vehicles path planning problem. The main purpose of using Simulated Annealing is to provide a more suitable balance between exploitation/exploration. The performance of the proposed algorithm is assessed using three benchmark maps with various numbers of threats. Compared to nine well-known meta-heuristics, the results of simulated experiments demonstrate that the proposed algorithm performs better in the majority of the scenarios by obtaining a significant enhancement in minimizing the fitness value and the path cost up to 36% and 19%, respectively.

Path Planning For Unmanned Surface Vehicles Based On Modified Artificial Fish Swarm Algorithm With Local Optimizer

The appeal for safe navigation of autonomous surface vessels (ASVs) has deemed the path planning problem as an attractive research interest. However, most of the previous works to solve the path planning problem focus on finding the shortest and collision-free path, but the solutions are scarcely satisfied by the safety requirements and constraints related to the USVs’ mechanical systems. To address this challenge, we present a novel path planning method based on a modified artificial fish swarm algorithm in combination with a path optimizer. The modifications are made from two perspectives: (1) Four customized operators and an adaptive factor are applied to improve the convergence performance of the algorithm. (2) A local path optimizer is proposed to enhance its feasibility of cooperating with the USV control system. Path safety, path smoothness, and nonholonomic constraints are considered. The path planning benchmark experiments have demonstrated its superior performance in terms of efficiency and path quality compared to other state-of-the-art algorithms. Moreover, the proposed method is also integrated into the USV’s control system in a practical environment with satisfactory feasibility. The simulation results provide strong evidence that the proposed method can be regarded as a practical approach for USV path planning problems.

An Optimization-Based Motion Planner for Car-like Logistics Robots on Narrow Roads.

Thanks to their strong maneuverability and high load capacity, car-like robots with non-holonomic constraints are often used in logistics to improve efficiency. However, it is difficult to plan a safe and smooth optimal path in real time on the restricted narrow roads of the logistics park. To solve this problem, an optimization-based motion planning method inspired by the Timed-Elastic-Band algorithm is proposed, called Narrow-Roads-Timed-Elastic-Band (NRTEB). Three optimization modules are added to the inner and outer workflow of the Timed-Elastic-Band framework. The simulation results show that the proposed method achieves safe reversing planning on narrow roads while the jerk of the trajectory is reduced by 72.11% compared to the original method. Real-world experiments reveal that the proposed method safely and smoothly avoids dynamic obstacles in real time when navigating forward and backward. The motion planner provides a safer and smoother trajectory for car-like robots on narrow roads in real time, which greatly enhances the safety, robustness and reliability of the Timed-Elastic-Band planner in logistics parks.

Sensor Fusion for Social Navigation on a Mobile Robot Based on Fast Marching Square and Gaussian Mixture Model.

Mobile robot navigation has been studied for a long time, and it is nowadays widely used in multiple applications. However, it is traditionally focused on two-dimensional geometric characteristics of the environments. There are situations in which robots need to share space with people, so additional aspects, such as social distancing, need to be considered. In this work, an approach for social navigation is presented. A multi-layer model of the environment containing geometric and topological characteristics is built based on the fusion of multiple sensor information. This is later used for navigating the environment considering social distancing from individuals and groups of people. The main novelty is combining fast marching square for path planning and navigation with Gaussian models to represent people. This combination allows to create a continuous representation of the environment from which smooth paths can be extracted and modified according to dynamically captured data. Results prove the practical application of the method on an assistive robot for navigating indoor scenarios, including a behavior for crossing narrow passages. People are efficiently detected and modeled to assure their comfort when robots are around.

Research on Path-Planning Algorithm Integrating Optimization A-Star Algorithm and Artificial Potential Field Method

A fusion pathfinding algorithm based on the optimized A-star algorithm, the artificial potential field method and the least squares method is proposed to meet the performance requirements of path smoothing, response speed and computation time for the path planning of home cleaning robots. The fusion algorithm improves the operation rules of the traditional A-star algorithm, enabling global path planning to be completed quickly. At the same time, the operating rules of the artificial potential field method are changed according to the path points found by the optimal A-star algorithm, thus greatly avoiding the dilemma of being trapped in local optima. Finally, the least squares method is applied to fit the complete path to obtain a smooth path trajectory. Experiments show that the fusion algorithm significantly improves pathfinding efficiency and produces smoother and more continuous paths. Through simulation comparison experiments, the optimized A-star algorithm reduced path-planning time by 60% compared to the traditional A-star algorithm and 65.2% compared to the bidirectional A-star algorithm path-planning time. The fusion algorithm reduced the path-planning time by 65.2% compared to the ant colony algorithm and 83.64% compared to the RRT algorithm path-planning time.

Control optimisation of automated guided vehicles in container terminal based on Petri network and dynamic path planning

• The task optimization and path planning of vehicles considering dynamic obstacle avoidance remain to be the urgent problems to be solved, so as to realize intelligence of container handling in container terminals. • The scheduling framework model of automated guided vehicle is established based on heuristic rules and OOTCSPN with vehicle behavior pattern as the top-level object, which can direct the traffic order and position sequence of the automated guided vehicle fleet. • Based on A* fusion DWA, path planning algorithm of automated guided vehicles is designed. Experiments show that the improved algorithm can improve vehicle operation efficiency, plan the route more smoothly and achieve random obstacle avoidance. To solve the problem of path optimisation and obstacle avoidance of automated guided vehicles (AGV) in the horizontal transportation of container terminals, this study proposed three operation modes of terminal vehicles and summarised four vehicle behaviour modes. Considering the vehicle behaviour pattern as the top-level object, based on heuristic rules and an object-oriented timed coloured stochastic Petri network (OOTCSPN) algorithm, a scheduling framework model of the AGV was established to optimise vehicle scheduling. A path planning model for three vehicle operation modes was designed for AGV path planning and real-time random obstacle avoidance based on the A-star(A*) algorithm fusion dynamic window approach (DWA). The simulation results indicate that the container handling efficiency increased by 13.2% using the improved algorithm. The scaled-down experiment confirms that the proposed method makes the planned path smoother and can also achieve real-time obstacle avoidance.

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.

Path planning of unmanned surface vessel in an unknown environment based on improved D*Lite algorithm

To solve the problem of path planning for an unmanned surface vessel in an unknown environment, this paper proposes a path planning algorithm based on the improved D*Lite algorithm. First, to improve the computational efficiency of the traditional D*Lite algorithm, the path cost function is improved to reduce the expansion range of nodes, and the node expansion direction is limited to avoid double node computation. Second, the path planned by the traditional D*Lite algorithm on the grid map is suboptimal; so, the inverse distance weighted (IDW) interpolation method is applied to shorten the path length. To improve the smoothness of the planned path by the traditional D*Lite algorithm, the Dubins algorithm is introduced for local path smoothing, and a smooth collision-free path that conforms to the motion dynamics of the unmanned surface vessel is obtained. The proposed algorithm was verified by experiments in known and unknown environments. The performance of the proposed algorithm was compared with the traditional D*Lite algorithm in terms of planning time, path length, and path smoothness. The results revealed that the proposed algorithm has the shortest path length, a shorter planning time, and the best smooth path.

An Intelligent Inspection Robot for Underground Cable Trenches Based on Adaptive 2D-SLAM

With the rapid growth of underground cable trenches, the corresponding inspections become a heavy burden, and an intelligent inspection robot for automatic examinations in underground cable trenches would be a suitable solution. To achieve this, this paper establishes one new navigation methodology for intelligent inspection robots, especially when applied in complex scenarios and the corresponding hardware. Firstly, to map the underground trenches with higher precision, an improved graph optimization cartographer-SLAM algorithm is proposed, which is based on the combination of depth camera and LIDAR. The depth image is converted into pseudo laser data, and fused with LIDAR data for calibration. Secondly, to overcome the low precision of the Laser odometer due to the uneven ground, an adaptive keyframe selection method is designed. Thirdly, the forward A* model is presented, which has been adjusted in three aspects, including the convergence of node searching, the cost function, and the path smoothness, to adapt to the narrow underground environment for global path planning. Fourthly, to realize dynamic obstacle avoidance, an improved fusion scheme is built to integrate the proposed global path planning algorithm and the dynamic window approach (DWA). In the case study, the simulation experiments showed the advantage of the forward A* algorithm over the state-of-the-art algorithm in both time consumption and the number of inflection points generated, the field tests illustrated the effect of the fusion of depth camera images and LIDAR. Hence, the feasibility of this navigation methodology can be verified, and the average length of path and time consumption decreased by 6.5% and 17.8%, respectively, compared with the traditional methods.

Path Planning of Mobile Robot Based on Improved Genetic Algorithm

With the continuous development of science and technology, mobile robots are gradually applied to people’s routine life. As one of the key technologies of mobile robots, the performance of path planning algorithms is a significant factor affecting its efficiency. On the basis of using a traditional Genetic Algorithm for path planning, combined with specific application scenarios, this paper proposes a new path planning algorithm for mobile robots. The path smoothness and the number of path corners are added to the fitness function to evaluate the path, so as to select a more superior path. Simulation experiments in MATLAB show the validity and feasibility of the modified method. By comparison to the traditional GA and other classical path planning algorithms, the optimal path selected has fewer turning angles under the same path length, which has a better application effect and greatly improves the working efficiency and stability.

Tri-Sectional Approximation of the Shortest Path to Long-Term Voltage Stability Boundary With Distributed Energy Resources

Ensuring long-term voltage stability is critical for reliable operations of power grids. High share of distributed energy resources (DERs) can create complicated system operation modes that may invalidate the traditional long-term voltage stability analysis based on typical operation modes. To address this challenge, this paper investigates how to compute the shortest path to the voltage stability boundary in the DER aggregated load space with large dispersion. Instead of working in the Euclidean space, we establish the analysis and computations on the algebraic power flow manifold to better capture the curvature change of the shortest path along the direction of losing stability. A modified optimal control framework is presented for obtaining the ground-truth of the smooth shortest path on the manifold. To efficiently and accurately solve for the shortest path, we further leverage the geometric features of the power flow manifold and propose a tri-sectional approximation model that is scalable for large-scale systems. Several numerical examples, up to the 1354-bus system, with different DER penetration levels and high dimensional renewable power injection variations are evaluated. The simulation results demonstrate that the tri-sectional approximation achieves high accuracy and efficiency to approximate the shortest path to the voltage stability boundary.

A Guidance and Maneuvering Control System Design With Anti-Collision Using Stream Functions With Vortex Flows for Autonomous Marine Vessels

Autonomous marine vessels are expected to avoid intervessel collisions and comply with the international regulations for safe voyages. This article presents a stepwise path planning method using stream functions. The dynamic flow of fluids is used as a guidance model, where the collision avoidance in static environments is achieved by applying the circular theorem in the sink flow. We extend this method to dynamic environments by adding vortex flows in the flow field. The stream function is recursively updated to enable “on the fly” waypoint decisions. The vessel avoids collisions and also complies with several rules of the convention on the International Regulations for Preventing Collisions at Sea. The method is conceptually and computationally simple and convenient to tune and yet versatile to handle complex and dense marine traffic with multiple dynamic obstacles. The ship dynamics are taken into account, by using Bézier curves to generate a sufficiently smooth path with feasible curvature. Numerical simulations are conducted to verify the proposed method.