An optimal and smooth trajectory for industrial robots has a positive impact on reducing the execution time in an operation and the vibration in their joints. In this paper, a methodology for the time-optimal and jerk-continuous trajectory planning of industrial robots is proposed. The entire trajectory is interpolated in the joint space utilizing fifth-order B-splines and then optimized by a hybrid whale optimization algorithm and genetic algorithm (WOA-GA). Two objective functions, including the integral of the squared jerk along the entire trajectory and the total execution time, are minimized to obtain the optimal entire trajectory. A fifth-order B-spline interpolation technique enables the achievement of a jerk-continuous trajectory, while respecting the kinematic limits of jerk, acceleration and velocity. WOA-GA is utilized to solve the time-jerk optimal trajectory planning problem with nonlinear constraints. The proposed hybrid optimization algorithm yielded good results and achieved the time-jerk optimal trajectory better under kinematic constraints compared to the genetic algorithm, whale optimization algorithm, improved whale optimization algorithm with particle swarm optimization and adaptive cuckoo search algorithm. The numerical results show the competent performances of the proposed methodology to generate trajectories with high smooth curves and short total execution time.

Suitable trajectories with minimum execution time are essential for an industrial robot to enhance productivity in pick and place operations. A novel point-to-point trajectory planning algorithm (PTPA) is proposed to improve the motion efficiency of industrial robots. The jerk profile for a trajectory model is determined by five intervals and the jerk constraint. According to the kinematic constraints and two shape coefficients, a velocity threshold and three displacement thresholds are calculated for an individual joint to transfer the proposed jerk motion profile into four specific profiles. The optimal trajectory model of the joint is developed for the minimum-time and jerk-continuous trajectory via the performance evaluation with the input displacement and three displacement thresholds. Moreover, time-based motion synchronization for all joints is taken into account in PTPA to decrease unnecessary burdens on the actuators. The simulations illustrate that the execution time by PTPA is more efficient than that by other techniques. The experiments of a point-to-point application on a real six-axis industrial robot show that the absolute errors at the end of the motion for all joints are within 0.04°. These results prove that PTPA can be an effective point-to-point trajectory planner for industrial robots

Feasible, smooth, and time-jerk optimal trajectory is essential for manipulators utilized in manufacturing process. A novel technique to generate trajectories in the joint space for robotic manipulators based on quintic B-spline and constrained multi-objective student psychology based optimization (CMOSPBO) is proposed in this paper. In order to obtain the optimal trajectories, two objective functions including the total travelling time and the integral of the squared jerk along the whole trajectories are considered. The whole trajectories are interpolated by quintic B-spline and then optimized by CMOSPBO, while taking into account kinematic constraints of velocity, acceleration, and jerk. CMOSPBO mainly includes improved student psychology based optimization, archive management, and an adaptive ε-constraint handling method. Lévy flights and differential mutation are adopted to enhance the global exploration capacity of the improved SPBO. The ε value is varied with iterations and feasible solutions to prevent the premature convergence of CMOSPBO. Solution density estimation corresponding to the solution distribution in decision space and objective space is proposed to increase the diversity of solutions. The experimental results show that CMOSPBO outperforms than SQP, and NSGA-II in terms of the motion efficiency and jerk. The comparison results demonstrate the effectiveness of the proposed method to generate time-jerk optimal and jerk-continuous trajectories for manipulators.

A multi-objective optimal trajectory planning method is proposed for manipulators in this paper to enhance motion efficiency and to reduce component wear while ensuring motion smoothness. The trajectory is initially interpolated in the joint space by using quintic non-uniform B-splines with virtual points, achieving the C⁴ continuity of joint motion and satisfying dynamic, kinematic, geometric, synchronization, and boundary constraints. The interpolation reformulates the trajectory planning problem into an optimization problem, where the time intervals between desired adjacent waypoints serve as variables. Travelling time and the integral of the squared jerk along the entire trajectories comprise the multi-objective functions. A constrained multi-objective dream optimization algorithm is designed to solve the time–jerk optimal trajectory planning problem and generate Pareto solutions for optimized trajectories. Simulations conducted on 6-DOF manipulators validate the effectiveness and superiority of the proposed method in comparison with existing typical trajectory planning methods.

It is necessary to determine the location and number of leaks in a pipeline in time to repair it, thus reducing economic losses. A multizone leakage detection method based on the YOLOv5 and OMD-ViBe algorithm is proposed to detect the metal hose’s location and leakage rate. The deep learning model of YOLOv5 is used to accurately recognize the zone of the metal hose for the region of interest rectification. The multiframe averaging method is applied to construct the initial background of the video frames. The OTSU algorithm based on the background difference method and the adaptive threshold of the maximum intraclass and interclass variance ratio method is used to improve the recognition rate of bubbles and reduce the influence of illumination change. In a comparison with the existing algorithms, the experimental results showed that OMD-ViBe improves the F-measure by 1.79–16.41% and the percentage of misclassification by 0.003–0.165%. Analysis of the pressure data indicated a comprehensive leakage error reduction of 1.53–25.19%, which can meet the requirements of metal hose leakage detection.