Robot Manipulator Minimum Jerk Trajectory Planning Based on the Improved Dung Beetle Optimizer Algorithm

A new method for smooth trajectory planning of robot manipulators

The simultaneous achievement of high accuracy and productivity in robotics has been extensively investigated using the trajectory planning approach. We propose a smooth and proximate time-optimal trajectory planning method. First, we generated the velocity limit curve by expressing joint torque and joint velocity constraints as a function of the path coordinate. Then, we calculated the time-optimal trajectory using a dynamic programming technique and fitted the smooth cubic spline. The smoothing factor of the cubic spline curve was optimized by applying a binary recursive. The proposed method can guarantee the continuity and smoothness of joint torque. The simulation results showed that the proposed method can reduce joint-jerk and improve the tracking accuracy of the controller.

A new approach based on genetic algorithm (GA) and autonomous mental development for trajectory planning of robot manipulator is presented in this paper. The trajectory for the manipulator is optimized by the GA. To make the trajectory planning used in real time application, a developmental learning algorithm is proposed to generate an incremental hierarchical discriminating regression (IHDR) tree to form the mapping from the state space to the action space. Just like the human brain from infancy to adulthood, the algorithm develops its cognitive and behavioral skills through online learning from the samples obtained from the GA-based method. When the IHDR tree is generated, it can perform the trajectory planning in real time by retrieving in its knowledge database.

Identifying feasible pathways for safe endovascular tool navigation is necessary for preoperative planning, intraoperative guidance, and robotic-assisted procedures. However, current path-planning approaches do not guarantee that optimal paths can be found due to limitations in path exploration. As such, this paper proposes a novel approach using Bi-directional Rapidly Exploring Random Trees (BiRRT) with a Genetic Algorithm (GA) to generate optimal paths in vascular environments. This approach initializes a population of Bi-RRT paths and performs GA to arrive at the optimal path in terms of path length, smoothness, and safety. Path planning simulations were performed across three 2D representations of aortic arches to model path planning in endovascular surgery. Results indicate that the algorithm produced optimal paths compared to a standalone Bi-RRT and a centerline-based path planning algorithm for endovascular surgery. The resulting paths also demonstrate that the proposed method produced shorter, smoother, and safer paths across different environments than other algorithms. These findings demonstrate that combining Bi-RRT with GA is a promising approach for improving path planning in endovascular surgery, potentially leading to safer and more efficient procedures.

This paper presents two different strategies for the problem of the optimal trajectory planning of robot manipulators in the presence of fixed obstacles. The first strategy is related to the situation where the trajectory must pass through a given number of points. The second strategy corresponds to the case where only the initial and final points are given. The optimal traveling time and the minimum mechanical energy of the actuators are considered together to build a multiobjective function. The trajectories are defined using spline functions and are obtained through offline computation for online operation. Sequential unconstrained minimization techniques (SUMT) have been used for the optimization. The obstacles are considered as three-dimensional objects sharing the same workspace performed by the robot. The obstacle avoidance is expressed in terms of the distances between potentially colliding parts. Simulation results are presented and show the efficiency of the general methodology used in this paper.

Sampling-based search algorithms such as Rapidly-Exploring Random Trees (RRT) have been utilized for mobile robot path planning and motion planning in high dimensional continuous spaces. This paper presents a path planning method for a planetary exploration rover in rough terrain. The proposed method exploits the framework of a sampling-based search, the optimal RRT (RRT*) algorithm. The terrain geometry used for planning is composed of point cloud data close to continuous space captured by a light detection and ranging (LIDAR) sensor. During the path planning phase, the proposed RRT*algorithm directly samples a point (node) from the LIDAR point cloud data. The path planner then considers the rough terrain traversability of the rover during the tree expansion process of RRT*. This process improves conventional RRT*in that the generated path is safe and feasible for the rover in rough terrain. In this paper, simulation study on the proposed path planning algorithm in various real terrain data confirms its usefulness.

As a sampling based path planning method, Rapidly-exploring Random Tree (RRT) is powerful for its high efficiency in finding feasible solutions. Optimal RRT (RRT*) improves RRT by asymptotically searching the optimal solution, however, at the cost of time consuming. This paper proposes an efficient optimal planning algorithm based on RRT* with adaptive restricted sampling space, which is inspired by the tropism of plants and named as tropistic RRT*. Tropistic RRT* improves the efficiency of the path planning by restricting the sampling space to approach the goal position just like the phototropism of plants. To validate our proposed algorithm, we carry out both path planning and motion planning experiments in 2D environments. In the path planning experiments, we compare the proposed algorithm with RRT* and Informed RRT* and experimental results show that our method outperforms the other two in the convergence rate, final solution cost and robustness. Furthermore, we also implement our algorithm in solving motion planning problem for a nonholonomic mobile robot and compare the time cost in the robot navigation process. Compared results exhibit that the time cost of our algorithm is much less than that of Real-Time RRT* in both static and dynamic environments.

Trajectory planning is essential for self-driving vehicles and has stringent requirements for accuracy and efficiency. The existing trajectory planning methods have limitations in the feasibility of planned trajectories and computational efficiency. This paper proposes a life-long learning framework to achieve effective and high-accuracy direct trajectory planning (DTP) tasks. Based on generative adversarial networks (GANs), this study develops a lightweight GDTP model to map the initial/final states and the control action sequence. Additionally, by embedding the GDTP into the rapidly-exploring random tree (RRT), a GDTP-RRT algorithm is further designed for long-distance and multi-stage planning tasks. Taking the tractor-trailer as an application case, we test the proposed method in multiple scenarios with varying characteristics. The experimental results show that the method can plan highly feasible trajectories in a short time, compared with the most applied algorithm – the cubic curve RRT* (CCRRT*). It is found that the tracking errors of our method are 29.1% and 44.1% lower than the CCRRT* in terms of position and heading angle. This paper provides an effective and stable vehicle trajectory planning method for complex self-driving tasks.

Path planning and obstacle avoidance involve planning a feasible path from the initial to goal conflgurations while avoiding obstacles. This paper presents a vision-based three dimensional navigation frame mapping and path planning technique for collision avoidance for Micro Air Vehicles (MAVs) using a forward-looking onboard camera. Using computer vision algorithms, a depth map representing the range and bearing to obstacles is obtained. Based on the depth map, we use the extended Kalman Filter (EKF) to estimate the range and azimuth to obstacles and the height of obstacles and use the joint compatibility branch and bound (JCBB) algorithm to associate the camera measurements with the existing obstacles. A three dimensional map, constructed in cylindrical coordinates, is then created in the navigation frame of the MAV. We employ the Rapidly-Exploring Random Tree (RRT) algorithm to flnd collision-free Dubins paths in the navigation frame. The simulation results show that the proposed technique is successful in solving path planning and multiple obstacles avoidance problems for MAVs.

PurposeThe purpose of this paper is to present a new nested rapidly‐exploring random tree (RRT) algorithm for fault tolerant motion planning of robotic manipulators.Design/methodology/approachAnother RRT algorithm is nested within the general RRT algorithm. This second nested level is used to check whether the new sampled node in the first nested level is fault tolerant. If a solution can be found in the second nested RRT, the reduced manipulator after failures at the new sampled node can still fulfill the remaining task and this new sampled node is added into the nodes of RRT in the first level. Thus, the nodes in the first level RRT algorithm are all fault tolerant postures. The final trajectory joined by these nodes is also obviously fault tolerant. Besides fault tolerance, this new nested RRT algorithm also can fulfill some secondary tasks such as improvement of dexterity and obstacle avoidance. Sufficient simulations and experiments of this new algorithm on fault tolerant motion planning of robotic manipulators are implemented.FindingsIt is found that the new nested RRT algorithm can fulfill fault tolerance and some other secondary tasks at the same time. Compared to other existing fault tolerant algorithms, this new algorithm is more efficient.Originality/valueThe paper presents a new nested RRT algorithm for fault tolerant motion planning.

The online cooperative path planning problem is discussed for multi-quadrotor maneuvering in an unknown dynamic environment. Based on the related basic concepts, typical three-dimensional obstacle models, such as spherical and cubic, and their collision checking criteria are presented in this article. An improved rapidly exploring random tree (RRT) algorithm with goal bias and greed property is proposed based on the heuristic search strategy to overcome the shortcomings of the classical RRT algorithm. Not only are the kinematic constraints of the quadrotor established but the time and space coordination strategy matching with the improved RRT algorithm is also presented in this article. Furthermore, a novel online collision avoidance strategy according to the partial information of the surrounding environment is proposed. On the basis of the above work, a distributed online path planning strategy is proposed to obtain the feasible path for each quadrotor. Numerical simulation results show that the improved RRT algorithm has better search efficiency than the classical RRT algorithm. And the satisfactory path planning and path tracking results prove that the above model and related planning strategies are reasonable and effective.

In this paper, an improved APF-GFARRT* (artificial potential field-guided fuzzy adaptive rapidly exploring random trees) algorithm based on APF (artificial potential field) guided sampling and fuzzy adaptive expansion is proposed to solve the problems of weak orientation and low search success rate when randomly expanding nodes using the RRT (rapidly exploring random trees) algorithm for disinfecting robots in the dense environment of disinfection operation. Considering the inherent randomness of tree growth in the RRT* algorithm, a combination of APF with RRT* is introduced to enhance the purposefulness of the sampling process. In addition, in the context of RRT* facing dense and restricted environments such as narrow passages, adaptive step-size adjustment is implemented using fuzzy control. It accelerates the algorithm’s convergence and improves search efficiency in a specific area. The proposed algorithm is validated and analyzed in a specialized environment designed in MATLAB, and comparisons are made with existing path planning algorithms, including RRT, RRT*, and APF-RRT*. Experimental results show the excellent exploration speed of the improved algorithm, reducing the average initial path search time by about 46.52% compared to the other three algorithms. In addition, the improved algorithm exhibits faster convergence, significantly reducing the average iteration count and the average final path cost by about 10.01%. The algorithm’s enhanced adaptability in unique environments is particularly noteworthy, increasing the chances of successfully finding paths and generating more rational and smoother paths than other algorithms. Experimental results validate the proposed algorithm as a practical and feasible solution for similar problems.

In this paper a novel combination of data structures and algorithms is presented as a fast and efcient practical approach to path planning for unmanned vehicles. This approach utilizes an architecture that integrates effective obstacle representation using an efcient Quadtree data structure, with path planning based on a modied Rapidly-exploring Random Tree (RRT) algorithm, and a path pruning technique based on Dijkstra’s algorithm, resulting in rapid discovery of sub-optimal feasible paths. One of the computationally expensive steps of the RRT algorithm is checking RRT segments for collision with obstacles. To address this problem, an efcient obstacle representation using Quadtrees is implemented enabling fast segment checks. While the RRT approach is guaranteed to nd a feasible path through complex obstacle elds with the probability of discovery approaching one as the number of iterations increases, the resulting paths may be far from optimal as the only criterion embedded in the RRT search is feasibility. For this reason, the paths generated by the RRT algorithm are passed through Dijkstra algorithm that nds a shortest obstacle-free path among the points on the path. Dijkstra algorithm that re-samples the segments of the path and nds the shortest path among the new points is implemented resulting in paths that are very close to the optimal ones. To speed up the computation, the basic search algorithm is implemented as a dual RRT from the initial and nal points. To account for motion transients along the path, a suitable size corridor is introduced, assuring that the vehicle has enough room for maneuvering among the obstacles. This computationally efcient architecture lends itself to real-time implementation for both pre-planning with known obstacles as well as rapid reactive re-planning in the presence of new pop-up obstacles. The proposed technique is evaluated using several challenging path-planning examples characterized by a large number of non-convex constraints arising in cluttered obstacle elds with known and unknown obstacles. A modication that allows an easy way to introduce vehicle dynamics constraints or actuation failures is also implemented. Algorithms have been implemented for two as well as three dimensional path planning applications.

This paper presents a method for planning a motion for a humanoid robot performing manipulation tasks in a high dimensional space such that the energy consumption of the robot is minimized. While sampling-based path planning algorithms, such as rapidly-exploring random tree (RRT) and its variants, have been highly effective for complex path planning problems, it is still difficult to find the minimum cost path in a high dimensional space since RRT-based algorithms extend a search tree locally, requiring a large number of samples to find a good solution. This paper presents an efficient nonmyopic motion planning algorithm for finding a minimum cost path by combining RRT* and cross entropy (CE). The proposed method constructs two RRT trees: the first tree is a standard RRT tree which is used to determine the nearest node in the tree to a randomly chosen point and the second tree contains the first tree with additional long extensions. By maintaining two separate trees, we can grow the search tree non-myopically to improve efficiency while ensuring the asymptotic optimality of RRT*. We first identify and demonstrate the limitation of RRT* when it is applied to energy-efficient path planning in a high dimensional space. Results from experiments show that the proposed method consistently achieves the lowest energy consumption against other algorithms.

Robot path planning is a cornerstone of precision agriculture, enabling safe and efficient operations for agricultural robots. However, complex field environments—characterized by static and dynamic obstacles, dense vegetation, and unstructured terrain—pose significant challenges to effective path planning. Conventional methods, such as A*, Dijkstra, and rapidly exploring random tree (RRT), exhibit limitations in efficiency and adaptability to dynamic conditions. To address these challenges, this study introduces AgriPath, a robust multi-objective path planning framework that integrates an improved convolutional neural network (CNN), an improved A* algorithm, and an improved whale optimization algorithm (IWOA) to optimize pathfinding, convergence efficiency, and obstacle avoidance in complex agricultural settings. Key innovations include an improved CNN leveraging causal convolution and multi-head self-attention mechanisms to improve temporal modeling for short-term trajectory prediction, augmented by Gaussian perturbations to enhance initial solution diversity; an improved A* algorithm incorporating dynamic heuristic functions based on Normalized Difference Vegetation Index (NDVI), combined with Kalman filtering, to bolster global path adaptability; IWOA employing non-linear convergence factors and differential evolution mechanisms to dynamically balance path length, smoothness, and planning time; and an improved Douglas–Peucker algorithm paired with cubic B-spline smoothing and navigation command modules to ensure path simplification and real-time execution. Experiments conducted in the Modern Agricultural Demonstration Zone at Chengdu, Sichuan Province, China, across simple, moderate, and complex scenarios, demonstrate that AgriPath outperforms advanced algorithms—SBREA*, Ant Colony A*, Orchard A*, and Greedy A*—in path length, smoothness, planning time, and dynamic obstacle avoidance success rate, indicative of superior multi-objective optimization balance. This study significantly enhances the efficiency and robustness of agricultural robot path planning, offering a more adaptive solution for autonomous navigation in precision agriculture while providing new theoretical and practical directions for the field of path planning.