Path Smoothing Method Research Articles

Improved Collision Avoidance Algorithm of Autonomous Rice Transplanter Based on Virtual Goal Point

To ensure the operation safety and efficiency of an autonomous rice transplanter, a path planning method of obstacle avoidance based on the improved artificial potential field is proposed. Firstly, the obstacles are divided into circular or elliptic obstacles according to the difference between the length and width of an obstacle as well as the angle between the vehicle’s forward direction and the length direction of the obstacle. Secondly, improved repulsive fields for circular and elliptic models are developed. To escape the local minimum and goal inaccessibility of the traditional artificial potential field as well as meet the requirements of agronomy and vehicle kinematics constraints, the adaptive setting and adjusting strategy for virtual goal points is proposed according to relative azimuth between obstacle and vehicle. The path smoothing method based on the B-spline interpolation method is presented. Finally, the intelligent obstacle avoidance algorithm is designed, and the path evaluation rule is given to obtain the low-cost, non-collision, smooth and shortest obstacle avoidance path. To verify the effectiveness of the proposed obstacle avoidance algorithm, simulation and field experiments are conducted. Simulation and experimental results demonstrate that the proposed improved collision avoidance algorithm is highly effective and realizable.

Five-axis path smoothing based on sliding convolution windows for CNC machining

Tiny linear toolpaths widely used in five-axis CNC machine tools only meet G0 continuity at the junctions of adjacent paths, the tangential and curvature discontinuities at the corners result in decelerations and fluctuations of machine tools. Although the corner smoothing for the three-axis tool path is relatively mature, the five-axis tool pose path smoothing is still difficult to plan due to the nonlinear motions of the rotational axes and the parameter synchronization between the tool center point (TCP) path and the tool orientation vector (TOV) path. Therefore, this paper aims to extend the smoothing scopes of previously presented mixed tiny path smoothing method based on sliding convolution windows for three-axis CNC machining (Zhang et al. in Journal of Manufacturing Process 102:685–699, [19]). Compared with the previous work, this paper converts the five-axis tool pose path into the tool position signal and tool orientation signal, and the interpolation points of the two path signals in the convolution window are directly processed on the basis of the synchronous motions of all axes. The original parameter synchronization relationship between the TCP path and the TOV path is still maintained. Besides, the smoothing error prediction model is constructed. The proposed five-axis path smoothing method has been integrated into a self-developed open-architecture CNC system and its effectiveness for the five-axis path optimization is validated via the simulation and experiment.

PRM Path Smoothening by Circular Arc Fillet Method for Mobile Robot Navigation

The problem of motion planning and navigation for mobile robots in complex environments has been a central issue in robotics. Navigating these environments requires sophisticated algorithms that handle obstacles and provide smooth, efficient paths. The Probabilistic Roadmap (PRM) method is a widespread technique in robotics for constructing paths for mobile robot navigation. In this study, we propose a novel path-smoothing method using arc fillets for path planning, building on PRM's foundation in the presence of obstacles. Our method operates in two primary stages to improve path efficiency and quality. The first stage generates the shortest path between the initial and goal states in an obstacle-rich environment using PRM, constructing a straight-line, collision-free route. The second stage smooths corners caused by nodes with arc fillets, ensuring smooth turns and minimizing abrupt changes in direction, resulting in more natural and efficient robot motion. We conducted simulations and tests using various PRM features to evaluate the proposed method. The results indicate that the built route offers a smooth turning motion and quicker, more compact movement while evading obstacles. This study contributes to mobile robot navigation by offering a practical approach to improving pathway quality in challenging environments.

Mixed tiny path smoothing method based on sliding convolution windows for CNC machining

The machining toolpaths of complex free-form surface parts are generated using computer-aided manufacturing (CAM) systems and programmed by a series of mixed tiny paths composed of tiny lines, arcs, and non-uniform rational B-spline (NURBS). The mixed tiny paths need to be smoothed to eliminate the tangential discontinuities at corners. This paper proposes a mixed tiny path smoothing method based on sliding convolution windows (MSSCW). In this method, the mixed tiny path is firstly converted into a positional signal along the travel length in the spatial domain, and then sliding convolution windows, which centered on each original interpolation point, are used to generate high-order continuous smoothed toolpath. Finally, the smoothing error is checked and corrected by modifying the length duration of the sliding convolution windows. Compared with conventional path smoothing method, the MSSCW method is suitable for various computer numerical control (CNC) machining toolpaths, and the continuity of the smoothed toolpath can be adjusted according to user requirements. Consequently, the feasibility and effectiveness of the proposed method are validated in simulations and experimental results which realize the improvement of the machining quality of complex free-form surfaces.

A Cooperative Hunting Method for Multi-USV Based on the A* Algorithm in an Environment with Obstacles.

A single unmanned surface combatant (USV) has poor mission execution capability, so the cooperation of multiple unmanned surface ships is widely used. Cooperative hunting is an important aspect of multi USV collaborative research. Therefore, this paper proposed a cooperative hunting method for multi-USV based on the A* algorithm in an environment with obstacles. First, based on the traditional A* algorithm, a path smoothing method based on USV minimum turning radius is proposed. At the same time, the post order traversal recursive algorithm in the binary tree method is used to replace the enumeration algorithm to obtain the optimal path, which improves the efficiency of the A* algorithm. Second, a biomimetic multi USV swarm collaborative hunting method is proposed. Multiple USV clusters simulate the hunting strategy of lions to pre-form on the target's path, so multiple USV clusters do not require manual formation. During the hunting process, the formation of multiple USV groups is adjusted to limit the movement and turning of the target, thereby reducing the range of activity of the target and improving the effectiveness of the algorithm. To verify the effectiveness of the algorithm, two sets of simulation experiments were conducted. The results show that the algorithm has good performance in path planning and target search.

An analytical local tool path smoothing method with curvature control

In traditional multi-axis machining, the linear tool path generated by computer-aided manufacturing systems is still in a broad tool path format, resulting in discontinuities at the corners, which slow down tool motion, and also trigger tool vibration, reducing machining accuracy and surface quality. In order to ensure the C3 continuity of the tool during the multi-axis machining process, this paper proposes an analytical B-spline local smoothing method with curvature control. The tool position trajectory and tool orientation are both smoothed by a 5th spline curve with 9 control points. Optimal control points are determined for position and orientation splines to achieve C3 continuity at the junctions between the spline and linear segment while preserving the predefined geometric tolerance limits and minimizing the maximum curvature of the inserted B-spline curve. The smoothed tool path is expected to have less curvature fluctuation, which can significantly improve both the kinematic performance of the machine tool and the machining efficiency. Both computer simulations and physical printing experiments are carried out to demonstrate the improvements of our proposed method in motion smoothness and tracking accuracy in multi-axis machining tasks.

A Real-time Look-ahead Trajectory Planning Methodology for Multi Small Line Segments Path

When a robot is required to machine a complex curved workpiece with high precision and speed, the tool path is typically dispersed into a series of points and transmitted to the robot. The conventional trajectory planning method requires frequent starts and stops at each dispersed point to complete the task. This method not only reduces precision but also causes damage to the motors and robot. A real-time look-ahead algorithm is proposed in this paper to improve precision and minimize damage. The proposed algorithm includes a path-smoothing algorithm, a trajectory planning method, and a bidirectional scanning module. The path-smoothing method inserts a quintic Bezier curve between small adjacent line segments to achieve G^{2} continuity at the junctions. The trajectory planning method utilizes a quartic polynomial and a double-quartic polynomial that can achieve a constant velocity at the velocity limitation. The bidirectional scanning module calculates the velocity at each trajectory planning segment point, simplifying calculation complexity and can be run in real time. The feasibility of the proposed algorithm is verified through simulations and experiments, which can be run in real time. In addition, high machining precision can be achieved by adjusting the relevant parameters.

Robot Pose Optimization and Joint Path Smoothing Method for Aero-engine Complex Casing Deep Cavity Measurement

Robot Pose Optimization and Joint Path Smoothing Method for Aero-engine Complex Casing Deep Cavity Measurement

Linear Tool Path-Smoothing Method in High-Speed Machining Based on Error Feasible Area and Curvature Optimization

Linear tool path is widely used in high-speed NC machining. However, the geometrical discontinuity of the corner between the linear tool paths will lead to fluctuations in speed, acceleration and jerk, which can excite machinery vibration and reduce the machining efficiency and surface quality. To solve these problems, a novel corner smoothing method based on error feasible area and curvature optimization is proposed in this paper. Compared with most traditional corner smoothing methods using higher-order curves with all control points lying in the straight segment and inside of the tool path, the proposed method constructs B-spline transition curves with smaller curvatures to smooth the corners by reasonably distributing the curve control points inside and outside the straight line segment of the tool path (i.e., error feasible area). Furthermore, the corner transition curve is optimized by the minimum curve curvature extreme to improve the smoothness of the corner transition curve and reduce fluctuation in the kinematic profiles while respecting the G3 continuity (i.e., curvature-smooth), transition length limits and the uniqueness of curvature extremum. Finally, the simulation results show that the proposed method can reduce the curvature value and improve the smoothness of the curve and the minimum transitional velocity of the corner, which means that it can enhance machining efficiency and weaken machining vibration. The feasibility and effectiveness of the method are also verified.

Real-Time Directed Rapidly Exploring Random Tree Path Planning for Air Collision Avoidance

In this paper, a path planning algorithm is proposed for dynamic obstacle avoidance by improving a rapidly exploring random tree (RRT) algorithm, a sampling-based path-planning algorithm. Although guaranteeing a globally optimal path is impossible when using RRT algorithm, it is advantageous because it can generate the path quickly. Considering this advantage of the RRT algorithm, the directed RRT (DRRT) algorithm was developed, which reduces the generation time and supplements optimality by improving node generation and tree expansion process. It is also added the path smoothing method for the flight. The anytime DRRT algorithm is based on the DRRT algorithm and repeats path generation within the time limit considering the direction of movement of the obstacle and selects the shortest path for the flight. Air collision avoidance between unmanned aerial vehicles (UAVs) considering the intruders as a dynamic obstacle was simulated using the Gazebo simulator. Based on the simulation, the performance of the proposed anytime DRRT algorithm was verified with varying the host UAV and intruder conditions, and its applicability to UAVs was affirmed.

An Effective Dynamic Path Planning Approach for Mobile Robots Based on Ant Colony Fusion Dynamic Windows

To further improve the path planning of the mobile robot in complex dynamic environments, this paper proposes an enhanced hybrid algorithm by considering the excellent search capability of the ant colony optimization (ACO) for global paths and the advantages of the dynamic window approach (DWA) for local obstacle avoidance. Firstly, we establish a new dynamic environment model based on the motion characteristics of the obstacles. Secondly, we improve the traditional ACO from the pheromone update and heuristic function and then design a strategy to solve the deadlock problem. Considering the actual path requirements of the robot, a new path smoothing method is present. Finally, the robot modeled by DWA obtains navigation information from the global path, and we enhance its trajectory tracking capability and dynamic obstacle avoidance capability by improving the evaluation function. The simulation and experimental results show that our algorithm improves the robot’s navigation capability, search capability, and dynamic obstacle avoidance capability in unknown and complex dynamic environments.

An Analytical Method for Decoupled Local Smoothing of Linear Paths in Industrial Robots

The linear-format path is widely adopted to approximate the continuous contour in robot controllers. The tangential discontinuity of the linear paths usually causes the discontinuity of the joint velocity. To comply with the joint kinematics limits, the robots have to stop at each corner point, resulting in a great loss of efficiency. To achieve a smooth motion, this paper presents an analytical decoupled C3 continuous local path smoothing method for industrial robots. The tool position path is smoothed in the reference frame while the tool orientation is smoothed in the rotation parametric space based on the exponential coordinates of rotations. The quintic B-splines are inserted at the corners of the linear segments to achieve the G3 continuity of the tool position path and tool orientation path. The orientation smoothing error is constrained analytically. By reparameterization of the remaining linear segments using specially constructed B-splines, the C3 continuity of the tool position path and tool orientation path is achieved. Then, the synchronization of the tool orientation path and tool position path can be guaranteed by sharing the same curve parameter. Besides, to improve the smoothness of the angular motion on the remaining linear segments during parameter synchronization, the transition lengths of the inserted B-splines are optimized. The proposed local smoothing method guarantees that the generated smooth orientation path in the rotation space is invariant with the selection of the reference frame and the orientation of the tool frame, and ensures the jerk-continuous motion with a smoother angular motion on the remaining linear segments, which could improve the motion smoothness of the tool path and tracking accuracy. The effectiveness of the proposed method is validated through simulation and experiments.

HPA* Enhancements

In video games, pathfinding must be done quickly and accurately. Not much computational time is allowed for pathfinding, but realistic looking paths are required. One approach to pathfinding which attempts to satisfy both of these constraints is to perform pathfinding on abstractions of the map. Botea et al.'s Hierarchical Pathfinding A* (HPA*) does this by dividing the map into square sectors and defining entrances between them. Although HPA* performs quick pathfinding which produces near-optimal paths, some improvements can be introduced. Here we discuss a faster path smoothing method, an alternative way to compute the weights of abstract edges, and lazy edge weight computations.

A G3 continuous tool path smoothing method for 5-axis CNC machining

The chain of short linear tool path segments is the most common form for the five-axis machining by Computer Numerical Control (CNC) machines. The connection points of the linear path segments lead to the discontinuities in position, velocity, acceleration, and jerk, resulting in fluctuation of machine motion which leaves undesired marks on the finished surface. This paper presents a geometric smoothing algorithm by enforcing the continuity of first, second, and third geometric derivatives of the splined path segments at their meeting points for the five-axis machining of curved surfaces. The linear tool path segments are first smoothed by Bezier splines while constraining the path errors within a set tolerance. The tool path segments, that cannot be smoothed within the path error limit, are smoothly connected at the connection points. The tooltip position and tool axis orientation displacements are synchronized to avoid discontinuous displacements along the tool axis. The proposed algorithms are demonstrated with simulations and experiments in following a five-axis, curved tool path on a CNC machine tool. It is shown that the proposed G3 continuous tool path algorithm gives smoother tool-tip and tool axis orientation, reduces the tracking errors, contour errors and amplitudes of jounce at the connections of segments along the tool path, leading to the smoother surface for the precision five-axis machining of sculptured surfaces.

A postprocessing and path optimization based on nonlinear error for multijoint industrial robot-based 3D printing

Multijoint industrial robots can be used for 3D printing to manufacture the complex freeform surfaces. The postprocessing is the basis of the precise printing. Due to the nonlinear motion of the rotational joint, nonlinear error is inevitable in multijoint industrial robots. In this article, the postprocessing and the path optimization based on the nonlinear errors are proposed to improve the accuracy of the multijoint industrial robots-based 3D printing. Firstly, the kinematics of the multijoint industrial robot for 3D printing is analyzed briefly based on product of exponential (POE) theory by considering the structure parameters. All possible groups of joint angles for one tool pose in the joint range are obtained in the inverse kinematics. Secondly, the nonlinear error evaluation based on the interpolation is derived according to the kinematics. The nonlinear error of one numerical control (NC) code or one tool pose is obtained. The principle of minimum nonlinear error of joint angle is proposed to select the appropriate solution of joint angle for the postprocessing. Thirdly, a path smoothing method by inserting new tool poses adaptively is proposed to reduce the nonlinear error of the whole printing path. The smooth level in the smoothing is proposed to avoid the endless insertion near the singular area. Finally, simulation and experiments are carried out to testify the effectiveness of the proposed postprocessing and path optimization method.

An open‐source system for vision‐based micro‐aerial vehicle mapping, planning, and flight in cluttered environments

AbstractWe present an open‐source system for Micro‐Aerial Vehicle (MAV) autonomous navigation from vision‐based sensing. Our system focuses on dense mapping, safe local planning, and global trajectory generation, especially when using narrow field‐of‐view sensors in very cluttered environments. In addition, details about other necessary parts of the system and special considerations for applications in real‐world scenarios are presented. We focus our experiments on evaluating global planning, path smoothing, and local planning methods on real maps made on MAVs in realistic search‐and‐rescue and industrial inspection scenarios. We also perform thousands of simulations in cluttered synthetic environments, and finally validate the complete system in real‐world experiments.

Six-dimensional B-spline fitting method for five-axis tool paths

Piecewise linear segments (presented by a sequence of G01 G-Codes) are the widely adopted tool path format for five-axis computer numerical control (CNC) machining. Nevertheless, the G01 tool path has only G0 continuity, which may lead to feedrate and acceleration fluctuation, and produce machinery vibration and unexpected slowdowns during the process. Thus, tool path smoothing method such as B-spline fitting is developed to increase the continuity of the tool paths. This work proposes a six-dimensional B-spline fitting method with arc-length parameterization and quality evaluation/refinement for five-axis tool paths. First, establish the relationship of cutter contact (CC) error, and cutter location (CL) error and tool-axis error to ensure that the CC error of five-axis B-spline tool path can be accurately computed. Second, six-dimensional B-spline tool paths generated by three-axis B-spline fitting method in six-dimensional space are parameterized with arc-length, satisfying the stability condition of tool axis. Third, the chord errors of the fitted six-dimensional B-spline tool paths are computed using the Hausdorff distance. The chord error computation, smoothness assessment, and refinement algorithm are performed together to ensure the fitting quality. The simulation result demonstrates that the proposed six-dimensional fitting method is effective and suitable for five-axis blade machining, and the evaluation/refinement algorithm can ensure that the five-axis B-spline tool paths are shape-preserving strictly and satisfy the chord error constraint. The experimental results show that the proposed six-dimensional fitting method improves the machining quality and is suitable for industrial applications.

A tolerance constrained G2 continuous path smoothing and interpolation method for industrial SCARA robots

Abstract Piecewise-linear robot paths lack G1 and G2 continuity. The discontinuity results in feedrate reduction and fluctuation during real-time execution. State-of-art linear path smoothing methods have issues such as lack of data or chord tolerance constraints, numerical instability, and lack of synchronized position and orientation parameterization. This study proposes a robot path smoothing method for SCARA (Selective Compliance Assembly Robot Arm) robots. The smoothing method simultaneously satisfies requirements of G2 continuity, tolerance constraints (target point interpolation and chord tolerance constrained), shape-preserving (free of self-intersection), unified parameterization, and real-time performance. A global geometric iteration method combined with local corner transition scheme is used to generate smooth path. A convex combination presentation is proposed to simplify the formulation, which also makes it possible to unify various smoothing schemes into one extensible framework. Simulations with data analysis and actual experiments are performed for the verification of quality and efficiency. Comparisons with other solutions are included to evaluate the advantages of the proposed robot path smoothing method.

Double-DQN based path smoothing and tracking control method for robotic vehicle navigation

Automatically tracking paths with large curvatures smoothly and tightly is an acknowledged challenge in robotic vehicle navigation. This is particularly true for some navigation applications in which pre-defined paths such as crop rows in agricultural applications must be followed accurately. This article presents a novel path smoothing and tracking control method based on Double Deep Q-Network (Double DQN) for an automated robotic vehicle. This Double-DQN-based controller utilized a deep reinforcement learning method that scored all potential actions at the current state according to their performance index and selected the best performer as the output of the network. In this study, a path-tracking algorithm was self-developed with a deep Q-network trained by driving a rover in a simulated virtual environment. The algorithm was tested in both simulation and on a grass field to follow paths with multiple sharp turns. The performance was compared with that of the Pure-Pursuit Control (PPC) algorithm. The results showed that the Double DQN-based control dramatically reduced the settling time and the overshoot at the corner at higher forward speeds at a minor expense of slightly increased rise time and steady state error.

Dual NURBS Path Smoothing for 5-Axis Linear Path of Flank Milling

Linear path is still widely used to describe the five-axis machining trajectory. Five-axis tool path consists of two parts, one trajectory describes the tool tip position, and the other one represents the second point on tool axis to define the tool orientation. The natural disadvantages of G01 path are tangential and curvature discontinuities at freeform surface, which will lead to feedrate fluctuation and accuracy decrease due to the drive constraints of machine tool. In this study, a path smoothing method is proposed to smooth and optimize the linear path by using dual NURBS curves. Firstly, according to the accuracy requirements, the tool tip spline can be fitted. Secondly, the tool orientation spline can also be obtained by a coordinate system mapping method. Then, the synchronization equation of the two spline parameters is established to achieve interpolation synchronization of cutter location points. Finally, the smoothing dual NURBS tool path can be obtained with continuous curvature to improve the surface quality, motion stability and machining efficiency. Simulations and experiments validate its practicability and reliability. This method is no need to upgrade the CAM, and also could be integrated into CAM system to perform the 5-axis path smoothing.