Path Generation Research Articles

Predefined-time control design for tracking chaotic trajectories around a contour with an UAV

The surveillance or monitoring of places is crucial to ensuring security, protecting people and assets, preventing crimes, and detecting emergencies, to mention some. Unmanned Aerial Vehicles (UAVs) play a vital role in these applications, offering versatility, agility, and aerial vision. A crucial step for such tasks is to protect the UAV path ahead. This paper focuses on a methodology harnessing the unpredictable nature of chaotic systems to generate trajectories around a closed area or contour. However, although a vast quantity of research papers mention the use of chaotic path generation, they have yet to learn about the control system and the dynamics affecting the UAV, where developing the control theory is challenging. In this paper, we design controllers based on predetermined-time stability, ensuring the achievement of the desired trajectory before a specified time. Additionally, adjusting control parameters is a crucial step during the control design, impacting the control performance. Hence, we present a method to optimize and adapt controller parameters through evolutionary optimization, demonstrating precision enhancement. We validate the proposed system’s performance and the controllers through numerical simulations, indicating that the UAV effectively and accurately follows some types of chaotic trajectories like a square contour, aiming at the feasibility of this methodology in real UAV surveillance applications.

Continuous fiber path optimization in additive manufacturing: A gradient-based B-spline finite element approach

Additive manufacturing of continuous fiber enables the control of local material distribution and mechanical characteristics. This localized control is realized through fiber path generation and optimization, which is one of the core problems in the additive manufacturing of continuous fiber. Current fiber path generation and optimization methods mostly try to infill topology-optimized parts or align the fiber with the maximum stress directions, which may lead to sub-optimality or time-consuming computations. This paper provides a different approach to optimize the fiber path directly by parameterizing it with B-splines and manipulating its control points. A finite element model with B-spline fiber parameterization is established, with an analytical fiber-in-element probability. This framework streamlines the computation of local and global stiffness and mass matrices, enabling effective and efficient prediction of loading responses, stiffness, and natural frequencies. The probability framework also allows efficient calculation of the gradients of the stiffness and mass matrices, leading to a gradient-based fiber path optimization. The effectiveness and accuracy of both the finite element and optimization methods are verified with simulation and experiment case studies. Results demonstrate enhancements in stiffness and strength with less fiber usage compared to a commonly adopted principal stress direction method.

Genetic Algorithm-Based Framework for Optimization of Laser Beam Path in Additive Manufacturing

In this study, a genetic algorithm-based laser beam (LB) path optimization method is presented to improve laser-based additive manufacturing (LBAM). To emulate the LBAM process, LB irradiation of a thin metal substrate is applied. The LB path generation is formulated as the search for the optimal sequence of LB irradiation into the cells on the substrate that minimizes the fitness function, which is composed of two components, i.e., thermal fitness and process fitness. The thermal fitness is expressed by the average thermal gradient, and a simple thermal model is developed to simulate the effects of laser-induced heat input on the temperature distribution in the substrate. The process fitness regulates the suitability of the proposed LB path for the implementation of the LBAM process. In addition to standardized tool paths (i.e., raster, spiral, etc.), novel LB path generators are proposed to define the initial population of LB path solutions. To implement a genetic algorithm-based LB path optimization, a framework is proposed, and custom initialization, crossover, and mutation operators are developed for application in LBAM. The effectiveness of the proposed approach is demonstrated through a simulation case study aiming to identify LB paths that minimize the fitness function and thus provide more suitable LB path solutions with respect to the defined fitness function. Compared with the traditional trial-and-error LB path formulations, the proposed approach provides an improved and automated method for an efficient laser beam path selection in LBAM.

Fabrication of the freeform Fresnel lens by swinging-rotating diamond ruling

Freeform optics are widely applied across various industries, encompassing both imaging and non-imagining optical systems. To compact the freeform surface, the freeform Fresnel lens has been devised by optical designers. However, conventional slow slide servo techniques cannot effectively fabricate the intricate lens, due to its asymmetry and discontinuity. In this paper, a novel swinging-rotating diamond ruling method is proposed to fabricate a biconical freeform Fresnel lens, with the synchronized motions of X-, Z-, C- and A-axes. The morphed Archimedean driving spiral based on contour lines is constructed to avoid the tool-microstructure interference. The tool path generation algorithm is proposed to generate smooth and accurate tool path, encompassing an adaptive projection principle, a transition tool path interpolation method and a postprocessing method. Finally, the feasibility and superiority of the proposed method is validated through two case studies. It is demonstrated that the precise and efficient fabrication of the freeform Fresnel lens can be realized by swinging-rotating diamond ruling method.

Position Checking-Based Sampling Approach Combined with Attraction Point Local Optimization for Safe Flight of UAVs.

Trading off the allocation of limited computational resources between front-end path generation and back-end trajectory optimization plays a key role in improving the efficiency of unmanned aerial vehicle (UAV) motion planning. In this paper, a sampling-based kinodynamic planning method that can reduce the computational cost as well as the risks of UAV flight is proposed. Firstly, an initial trajectory connecting the start and end points without considering obstacles is generated. Then, a spherical space is constructed around the topological vertices of the environment, based on the intersections of the trajectory with the obstacles. Next, some unnecessary sampling points, as well as node rewiring, are discarded by the designed position-checking strategy to minimize the computational cost and reduce the risks of UAV flight. Finally, in order to make the planning framework adaptable to complex scenarios, the strategies for selecting different attraction points according to the environment are designed, which further ensures the safe flight of the UAV while improving the success rate of the front-end trajectory. Simulations and real-world experiment comparisons are conducted on a vision-based platform to verify the performance of the proposed method.

Fixed-Time Path-Following-Based Underactuated Unmanned Surface Vehicle Dynamic Positioning Control

The development of dynamic positioning (DP) algorithms for an unmanned surface vehicle (USV) is attracting great interest, especially in support of complex missions such as sea rescue. In order to improve the simplicity of the algorithm, a DP algorithm based on its own path following control ability is proposed. The algorithm divides the DP problem into two parts: path generation and path following. The key contribution is that the DP ability can be realized only by designing the path generation method, rather than a whole complex independent DP controller. This saves the computing power of the USV onboard computer and can effectively reduce the complexity of the algorithm. In addition, the fixed-time LOS guidance law is designed to improve the convergence rate of the system state in path-following control. The reasonable selection of speed and a heading controller ensures that the number of design parameters to be determined is at a low level. The above algorithms have been thoroughly evaluated and validated through extensive computer simulations, demonstrating their effectiveness in simulated and real marine environments. The simulation results verify the ability of the proposed algorithm to realize the dynamic positioning of USVs, and provide a practical scheme for the design of the dynamic positioning controller of USVs.

Learning and generalization of task-parameterized skills through few human demonstrations

In the field of robotics, the demand for adaptable skills capable of effectively handling diverse situations has surpassed the reliance on repetitive tasks. To enhance the generalization of motion policies, task-parameterized learning has emerged as a valuable approach, as it encodes pertinent contextual information in task parameters, facilitating the flexible execution of tasks. This process requires the collection of multiple demonstrations in various situations. Generate a set of diverse situations covering all possible cases is a complex task. Due to this, the search for training with fewer demonstrations becomes highly desirable. In this article, we present a novel algorithm focused on generating synthetic information to facilitate the generalization of parameterized tasks. This algorithm makes use of Kinesthetic Fast Marching Learning, a Learning from Demonstration (LfD) algorithm that allows obtaining optimal movement paths based on velocity fields. The algorithm enables autonomous data generation, producing demonstrations that are equal to or more optimal than those generated by users themselves. Evaluation is done through a metric based on Wasserstein distance that takes into account the probabilistic data of the generated paths. The algorithm has been evaluated through tests in simulated environments, comparing its efficiency against two widely used algorithms (where it has shown greater efficiency in generalization and the generation of more optimal paths) and with real-world tests in a task-oriented environment (sweeping) carried out by the ADAM robot.

Chaotic Path-Planning Algorithm Based on Courbage–Nekorkin Artificial Neuron Model

Developing efficient path-planning algorithms is an essential topic in modern robotics and control theory. Autonomous rovers and wheeled and tracked robots require path generators that can efficiently cover the explorable space with minimal redundancy. In this paper, we present a new path-planning algorithm based on the chaotic behavior of the Courbage–Nekorkin neuron model with a coverage control parameter. Our study aims to reduce the number of iterations required to cover the chosen investigated area, which is a typical efficiency criterion for this class of algorithms. To achieve this goal, we implemented a pseudorandom bit generator (PRBG) based on a Courbage–Nekorkin chaotic map, which demonstrates chaotic behavior and successfully passes all statistical tests for randomness. The proposed PRBG generates a bit sequence that can be used to move the tracked robot in four or eight directions in an operation area of arbitrary size. Several statistical metrics were applied to evaluate the algorithm’s performance, including the percentage of coverage of the study area and the uniformity of coverage. The performance of several competing path-planning algorithms was analyzed using the chosen metrics when exploring two test areas of the sizes 50 × 50 cells and 100 × 100 cells, respectively, in four and eight directions. The experimental results indicate that the proposed algorithm is superior compared to known chaotic path-planning methods, providing more rapid and uniform coverage with the possibility of controlling the covered area using tunable parameters. In addition, this study revealed the high dependence of the coverage rate on the starting point. To investigate how the coverage rate depends on the choice of chaotic map, we implemented six different PRBGs using various chaotic maps. The obtained results can be efficiently used for solving path-planning tasks in both real-life and virtual (e.g., video games) applications.

More Quickly-RRT*: Improved Quick Rapidly-exploring Random Tree Star algorithm based on optimized sampling point with better initial solution and convergence rate

RRT* (Rapidly-exploring Random Tree Star), as a variant of RRT (Rapidly-exploring Random Tree), is widely used to solve path planning problems because of its asymptotic optimality. However, the algorithm is inefficient due to the high initial path cost and the slow convergence rate. In this paper, we propose a More Quickly-RRT* (MQ-RRT*) path planning algorithm based on optimized sampling points to solve the problems. A sparse sampling mechanism is proposed in MQ-RRT* to improve the global search efficiency by reducing repetitive sampling. To make the random tree oriented when expanding, a dynamic goal-biased strategy is proposed, which can reduce the sampling time. Like Q-RRT* (Quick-RRT*), MQ-RRT* expands the set of possible parent nodes in the ChooseParent and Rewire phases, which reduces the path cost. On this basis, a method for creating a new parent node close to the obstacle is proposed. The creation process can be divided into two steps: Remove-tips and CreateNodes, which further reduces the cost of path generation and makes the path smoother by using the triangle inequality principle. Finally, numerical simulations are used to compare the proposed algorithm with RRT*, Q-RRT*, GuILD (Guided Incremental Local Densification), and F-RRT* (Fast-RRT*), which verifies that the proposed algorithm has certain advantages in path cost, convergence rate, and path smoothness.

Adaptation of Symbolic Discrete Control Synthesis for Energy-Efficient Multi-Pocket Milling

In engineering, cost minimization, especially in Computer Numerical Control (CNC) machining like pocket milling, is crucial. Existing tool path definition software often lacks optimization, particularly at critical starting and ending points. This study optimizes CNC machine tool paths for energy-efficient multi-pocket milling, utilizing the Symbolic Discrete Control Synthesis (SDCS) method for formal correctness. In our work, the tool path generation is formulated as a traveling salesman problem. We introduce a modeling framework to adapt SDCS to multi-pocket-milling processes, aiming to enhance precision and efficiency for potential cost savings, including energy and time, in engineering applications. This study reports experimental and comparative results, where comparative evaluations were made using metaheuristic algorithms. Our proposed approach improves CNC machining processes for multi-pocket milling. We experimentally evaluate our control algorithms and demonstrate and validate our approach through case studies.

Non-monotonic Generation of Knowledge Paths for Context Understanding

Knowledge graphs can be used to enhance text search and access by augmenting textual content with relevant background knowledge. While many large knowledge graphs are available, using them to make semantic connections between entities mentioned in the textual content remains to be a difficult task. In this work, we therefore introduce contextual path generation (CPG), which refers to the task of generating knowledge paths, contextual path , to explain the semantic connections between entities mentioned in textual documents with given knowledge graph. To perform the CPG task well, one has to address its three challenges, namely, path relevance, incomplete knowledge graph, and path well-formedness. This article designs a two-stage framework comprised of the following: (1) a knowledge-enabled embedding matching and learning-to-rank with multi-head self-attention context extractor to determine a set of context entities relevant to both the query entities and context document, and (2) a non-monotonic path generation method with pretrained transformer to generate high-quality contextual paths. Our experiment results on two real-world datasets show that our best performing CPG model successfully recovers 84.13% of ground truth contextual paths, outperforming the context window baselines. Finally, we demonstrate that the non-monotonic model generates more well-formed paths compared to the monotonic counterpart.

Data model-based toolpath generation techniques for CNC milling machines

Introduction: With the development of computer technology and data modeling, the use of point cloud models to generate tool paths is particularly important for improving productivity and accuracy.Methods: This study proposes a new method that first preprocesses the point cloud data using four-point denoising and octree methods to improve processing efficiency. Subsequently, roughing tool paths were analyzed using the layer slicing method and finishing paths using the residual height method.Results and Discussion: The experimental results show that the layer slicing method has a minimum error close to 10% on the roughing path generation and the computation time is reduced to 35 s, while the residual height method has an error rate of 10.17% on the finishing path and the computation time is only 11.82 s, which reflects a high trajectory smoothness and accuracy. The above results show that the study not only optimizes the tool path generation process and improves the machining efficiency and accuracy, but also demonstrates the potential application of point cloud models in the machining of complex parts.Conclusion: The novel tool roughing and finishing methods provide more reliable path planning for actual machining operations, and future research will be devoted to further improving the performance of the data processing algorithms and exploring more efficient path planning strategies to facilitate automated production.

Investigating Suitable Combinations of Dynamic Models and Control Techniques for Offline Reinforcement Learning Based Navigation: Application of Universal Omni-Wheeled Robots

Abstract Omnidirectional locomotion provides wheeled mobile robots (WMR) with better maneuverability and flexibility, which enhances their energy efficiency and dexterity. Universal omni-wheels are one of the best categories of wheels that can be used to develop a WMR (Amarasiri et al., 2022, “Robust Dynamic Modeling and Trajectory Tracking Controller of a Universal Omni-Wheeled Mobile Robot,” ASME Letters Dyn. Sys. Control., 2(4), p. 040902. 10.1115/1.4055690). We study dynamic modeling and controllers for mobile robots to train in a reinforcement learning (RL)-based navigation algorithm. RL tasks require copious amounts of learning iteration episodes, which makes training very time consuming. The choice of dynamic model and controller has a significant impact on training time. In this paper, we compare a traditional Kane’s equations model to a non-holonomic canonical momenta model (Barhorst, 2019, “Generalized Momenta in Constrained Non-Holonomic Systems—Another Perspective on the Canonical Equations of Motion,” Int. J. Non-Linear Mech., 113, pp. 128–145.). We implemented four controllers: proportional integral derivative, linear quadratic regulator with integral action, pole placement, and a full nonlinear sliding mode controller. We summarize the pros and cons of each of the modeling techniques, and control laws implemented. The outcomes of our analysis will improve RL training time for path generation in unstructured environments.

DBVS-APF-RRT*: A global path planning algorithm with ultra-high speed generation of initial paths and high optimal path quality

During the last decade, RRT* algorithm has been widely concerned by researchers because of its asymptotic optimality. However, the slow convergence rate of the RRT* algorithm leads to poor quality of the optimal paths at small number of iterations. Meanwhile, searching the initial path slowly limits its application scenarios. To overcome these problems, a directionally biased variable step APF-RRT* (DBVS-APF-RRT*) algorithm is proposed in this paper. Firstly, a novel directionally biased variable step sampling strategy is used in RRT* algorithm to quickly generate the initial path. Then, global random sampling and key region sampling strategies are added to improve global search ability and optimal path quality. At the same time, an artificial potential field (APF) method is introduced to improve the ability of obstacle avoidance. In addition, we propose a pruning strategy based on triangular inequality with direct connection of goal points to reduce the number of redundant nodes and shorten the path length. Finally, DBVS-APF-RRT* algorithm is compared with RRT*, Bias-RRT*, Informed-RRT* and Bias-P-RRT* algorithms to verify its superiority of optimal path quality, stability of the algorithm and its rapidity of finding the initial path.

Advanced Path Planning for Autonomous Street-Sweeper Fleets under Complex Operational Conditions

In recent years, autonomous mobile platforms have seen an increase in usage in several applications. One of which is street-sweeping. Although street-sweeping is a necessary process due to health and cleanliness, fleet operations are difficult to plan optimally. Since each vehicle has several constraints (battery, debris, and water), path planning becomes increasingly difficult to perform manually. Additionally, in real-world applications vehicles may become inactive due to a breakdown, which requires real-time scheduling technology to update the paths for the remaining vehicles. In this paper, the fleet street-sweeping problem can be solved using the proposed lower-level and higher-level path generation methods. For the lower level, a Smart Selective Navigator algorithm is proposed, and a modified genetic algorithm is used for the higher-level path planning. A case study was presented for Uchi Park, South Korea, where the proposed methodology was validated. Specifically, results generated from the ideal scenario (all vehicles operating) were compared to the breakdown scenario, where little to no difference in the overall statistics was observed. Additionally, the lower-level path generation could yield solutions with over 94% area coverage.

Gas concentration mapping and source localization for environmental monitoring through unmanned aerial systems using model-free reinforcement learning agents.

There are three primary objectives of this work; first: to establish a gas concentration map; second: to estimate the point of emission of the gas; and third: to generate a path from any location to the point of emission for UAVs or UGVs. A mountable array of MOX sensors was developed so that the angles and distances among the sensors, alongside sensors data, were utilized to identify the influx of gas plumes. Gas dispersion experiments under indoor conditions were conducted to train machine learning algorithms to collect data at numerous locations and angles. Taguchi's orthogonal arrays for experiment design were used to identify the gas dispersion locations. For the second objective, the data collected after pre-processing was used to train an off-policy, model-free reinforcement learning agent with a Q-learning policy. After finishing the training from the training data set, Q-learning produces a table called the Q-table. The Q-table contains state-action pairs that generate an autonomous path from any point to the source from the testing dataset. The entire process is carried out in an obstacle-free environment, and the whole scheme is designed to be conducted in three modes: search, track, and localize. The hyperparameter combinations of the RL agent were evaluated through trial-and-error technique and it was found that ε = 0.9, γ = 0.9 and α = 0.9 was the fastest path generating combination that took 1258.88 seconds for training and 6.2 milliseconds for path generation. Out of 31 unseen scenarios, the trained RL agent generated successful paths for all the 31 scenarios, however, the UAV was able to reach successfully on the gas source in 23 scenarios, producing a success rate of 74.19%. The results paved the way for using reinforcement learning techniques to be used as autonomous path generation of unmanned systems alongside the need to explore and improve the accuracy of the reported results as future works.

Automatic computation of bending sequences for double-head wire bending machines

ABSTRACT Determining a feasible bending sequence for a double-head bending machine is a challenging and time-consuming task, even for an expert operator. An automatic bending sequence computation algorithm for a single-head bending machine was proposed in a previous work, exploiting A ⋆ graph search algorithm and the representation of the workpiece as an equivalent manipulator. This paper extends that approach to the case of a double-head bending machine, whose complexity, in terms of number of possible solutions to the problem of computing the feasible bending sequences, and of determination of the better sequences, that should exploit parallelism thanks to the execution of simultaneous bends on the two heads, is definitely higher. In this case, the wire has been modelled using two serial-link manipulators with a common base, and the A ⋆ cost function has been modified to promote simultaneous bends. An axes reachability-based path generator and the possibility of partial sequence search have been incorporated as well, to manage the run-time challenges due to an increased number of bends. In this way, an efficient bending sequence computation algorithm for a double-head wire bending machine has been devised, whose performance has been assessed on two industrial test cases, demonstrating its effectiveness and usefulness.

Tool path generation with a uniform residual error distribution considering tool contour error for ultra-precision diamond turning

Tool path generation strategy plays a crucial role in improving the efficiency and surface quality of ultra-precision diamond turning mainly by influencing residual errors. However, current approaches in tool path generation have not achieved a uniform distribution of residual error due to the unexplored and significant impact of tool contour error on residual error. Therefore, this study introduces a novel tool path generation algorithm for ultra-precision diamond turning, aiming for a uniform residual error distribution with consideration of tool contour error. The tool contour is measured off-machine, fitted, and modeled to achieve its actual cutting-edge contour at a submicron scale. An estimation model is established to calculate residual error on the machined surface considering the tool contour error. A tool path generation approach is then proposed to achieve uniform residual error distribution by adaptively controlling stepovers. Then the proposed stepover is smoothed by cubic Hermite polynomial interpolation to avoid undesired tool path fluctuations. To further improve the machining accuracy, a spiral tool path is generated with proper discretization parameters to control chord error. Finally, a prototype software system is developed to optimize the tool path as well as predict the residual and machining error across the entire machined surface. Experiment results demonstrate a significant reduction of approximately 40 % in both residual error and machining error compared to unoptimized results.

Utilizing Deep Reinforcement Learning, EGO-Swarm Parameter Control determines the path of the drone

The recent attention garnered by the EGO-Swarm system is due to its successful generation of smooth drone flight paths in complex real-world environments. Among the various parameter values utilized by EGO-Swarm for path generation, the maximum speed and maximum acceleration of the drone play a critical role in enhancing flight performance. However, in the current EGO-Swarm setup, these parameter values remain fixed during path creation, despite the potential need for real-time adjustments in dynamic environments. Therefore, there is a need to dynamically adapt these values to the evolving real-time environment. This paper proposes a novel algorithm that dynamically adjusts the maximum speed and maximum acceleration using hierarchical deep reinforcement learning in response to real-time environmental changes. To assess the effectiveness of the proposed method, a comparative experiment is conducted between the existing EGO-Swarm algorithm and the proposed algorithm in a ROS simulation. The experimental results reveal that the proposed algorithm surpasses the existing EGO-Swarm algorithm in terms of average speed improvement and path length.(Zhou et al., 2021)

Efficient Path Planning Algorithm for Mobile Robots Performing Floor Cleaning Like Operations

In this paper, we introduce an efficient path planning algorithm designed for floor cleaning applications, utilizing the concept of Spanning Tree Coverage (STC). We operate under the assumption that the environment, i.e., the floor, is initially unknown to the robot, which also lacks knowledge regarding obstacle positions, except for the workspace boundaries. The robot executes alternating phases of exploration and coverage, leveraging the local map generated during exploration to construct a STC tree, which then guides the subsequent coverage (cleaning) phase. The extent of exploration is determined by the range of the robot's sensors. The path generation algorithms for cleaning fall within the broader category of coverage path planning (CPP) algorithms. A key advantage of this algorithm is that the robot returns to its initial position upon completing the operation, minimizing battery usage since sensors are only active during the exploration phase. We classify the proposed algorithm as an offline-online scheme. To validate the effectiveness and non-repetitive nature of the algorithm, we conducted simulations using VRep/MATLAB environments and implemented real-time experiments using Turtlebot in the ROS-Gazebo environment. The results substantiate the completeness of coverage and underscore the algorithm's significance in applications akin to floor cleaning.