Search Results (42)

To address the challenges of unstable motion and insufficient detection accuracy in robotic scanning trajectories, particularly under high curvature and irregular shape conditions during ultrasonic testing of complex free-form surface workpieces, this paper proposes a G³ continuous trajectory planning and optimization method based on quintic B-spline curves. First, the scanning trajectory of the robot is represented by a parametric curve, with explicit expressions for position, velocity, acceleration, and jerk derived in the form of quintic B-splines. These expressions ensure continuity in position, velocity, acceleration, and jerk (C³/G³ continuity), thus maintaining high-order geometric continuity and motion stability of the trajectory. Second, to achieve the dual optimization objectives of trajectory smoothness and surface fitting, this paper constructs a composite objective function that incorporates both the integral of acceleration squared and the surface fitting error. The smoothness index is weighted by the sum of the square integrals of the second and third derivatives of the trajectory, thereby suppressing high-order oscillations, while the fitting index is based on the mean square error between the robot end-effector path and the target surface. Finally, a numerical optimization algorithm is utilized to solve the objective function, resulting in an optimal scanning trajectory that ensures both motion stability and fitting accuracy, while maintaining G³ continuity. Simulation and experimental results demonstrate that this method effectively mitigates trajectory mutations and oscillations, enabling efficient and high-precision automatic ultrasonic testing, and provides a reliable trajectory planning strategy for online non-destructive testing of complex curved workpieces. Full article

The Rapidly-exploring Random Tree Star (RRT*) algorithm is widely applied in robotic manipulator path planning, yet it does not directly consider motion control, where abrupt changes may cause shocks and vibrations, reducing accuracy and stability. To overcome this limitation, this paper proposes the Kinematically Smoothed, dynamically Biased Bidirectional Potential-guided RRT* (KSBB-P-RRT*) algorithm, which unifies path planning and motion control and introduces three main innovations. First, a fast path search strategy on the basis of Bi-RRT* integrates adaptive sampling and steering to accelerate exploration and improve efficiency. Second, a triangle-inequality-based optimization reduces redundant waypoints and lowers path cost. Third, a kinematically constrained smoothing strategy adapts a Jerk-Continuous S-Curve scheme to generate smooth and executable trajectories, thereby integrating path planning with motion control. Simulations in four environments show that KSBB-P-RRT* achieves at least 30% reduction in planning time and at least 3% reduction in path cost, while also requiring fewer iterations compared with Bi-RRT*, confirming its effectiveness and suitability for complex and precision-demanding applications such as agricultural robotics. Full article

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. Full article

This research describes a multi-objective trajectory planning method for robotic arms based on time, energy, and impact. The quintic Non-Uniform Rational B-Spline (NURBS) curve was employed to interpolate the trajectory in joint space. The quintic NURBS interpolation curve can make the trajectory become constrained within the kinematic limits of velocity, acceleration, and jerk while also satisfying the continuity of jerk. Then, based on the Parrot Optimization (PO) algorithm, through improvements to reduce algorithmic randomness and the introduction of appropriate multi-objective strategies, the algorithm was extended to the Multi-Objective Parrot Optimization (MOPO) algorithm, which better balances global search and local convergence, thereby more effectively solving multi-objective optimization problems and reducing the impact on optimization results. Subsequently, by integrating interpolation curves, the multi-objective optimization of joint trajectories could be performed under robotic kinematic constraints based on time–energy-jerk criteria. The obtained Pareto optimal front can provide decision-makers in industrial robotic arm applications with flexible options among non-dominated solutions. Full article

This paper proposes a robot trajectory planning method focused on time and jerk optimization under compound constraints. First, the robot path-tracking task is parameterized by incorporating both kinematic and dynamic constraints in joint and Cartesian spaces, establishing a time-optimal trajectory optimization model. To achieve C³ continuity in joint motion, joint-motion continuity conditions are analyzed, and optimization variables are reconstructed using piecewise cubic splines with corresponding continuity constraints. Considering the nonlinear and nonconvex characteristics of jerk constraints, the time-optimal planning model is decomposed into two second-order cone programming (SOCP) subproblems, achieving linear convexification of the original problem. Additionally, the objective function is improved to optimize both time and joint jerk simultaneously. Experimental results confirm that the proposed method effectively improves robot efficiency and trajectory smoothness. Full article

Trajectory planning and tracking control strategies have a significant impact on the fast and stable operation of high-precision position servo permanent magnet synchronous motors (PMSMs). Therefore, this paper proposes an active disturbance rejection control (ADRC) strategy for high-precision position servo PMSMs based on jerk- and time-optimal trajectory planning. Firstly, in order to meet the requirement of continuous jerk in the positioning process of precision loads, the seventh-degree Chebyshev polynomial is adopted to establish the point-to-point trajectory planning function. Based on the dynamic boundary conditions under the short-term overload of PMSMs, and with the positioning time as the optimization objective, the optimal coefficient of the polynomial is solved through the fast particle swarm optimization (FPSO) algorithm to obtain the trajectory planning function that takes into account both jerk and time performance. Then, the trajectory plan is used as the position loop reference signal to construct a non-cascade second-order ADRC strategy, leading to a position servo PMSM control strategy that combines a second-order disturbance observer and feedback control law. Finally, the experimental platform is set up to verify the proposed method. The results show that, compared with the traditional control methods, the steady-state positioning time of the control strategy proposed under typical working conditions is reduced by 12.5%, and the jerk continuity during the positioning process has also been significantly improved. Full article

This article presents an alternative variant of motion planning techniques for autonomous vehicles (AVs) centered on an inverse approach that concurrently optimizes both trajectory and speed. This method emphasizes searching for a trajectory and distributing its speed within a single road segment, regarded as a final element. The references for the road lanes are represented by splines that interpolate the path length, derivative, and curvature using Cartesian coordinates. This approach enables the determination of parameters at the final node of the road segment while varying the reference length. Instead of directly modeling the trajectory and velocity, the second derivatives of curvature and speed are modeled to ensure the continuity of all kinematic parameters, including jerk, at the nodes. A specialized inverse numerical integration procedure based on Gaussian quadrature has been adapted to reproduce the trajectory, speed, and other key parameters, which can be referenced during the motion tracking phase. The method emphasizes incorporating kinematic, dynamic, and physical restrictions into a set of nonlinear constraints that are part of the optimization procedure based on sequential quadratic optimization. The objective function allows for variation in multiple parameters, such as speed, longitudinal and lateral jerks, final time, final angular position, final lateral offset, and distances to obstacles. Additionally, several motion planning variants are calculated simultaneously based on the current vehicle position and the number of lanes available. Graphs depicting trajectories, speeds, accelerations, jerks, and other relevant parameters are presented based on the simulation results. Finally, this article evaluates the efficiency, speed, and quality of the predictions generated by the proposed method. The main quantitative assessment of the results may be associated with computing performance, which corresponds to time costs of 0.5–2.4 s for an average power notebook, depending on optimization settings, desired accuracy, and initial conditions. Full article

The human knee joint is crucial for mobility, especially in older adults who are susceptible to conditions like osteoarthritis (OA). Traditionally, assessing knee health requires complex gait analysis in clinical settings, which limits opportunities for convenient and continuous monitoring. This study leverages advancements in wearable technology to explore the adaptation of models based on in-shoe motion sensors (IMS), initially trained on young adults, for evaluating knee function in older populations, both healthy and with OA. Data were collected from 44 older OA patients, presenting various levels of severity, and 20 healthy older adults, with a focus on key knee indicators: knee angle measures (S1 to S3), temporal gait parameters (S4 and S5), and knee angular jerk cost metrics (S6 to S8). The models effectively identified trends and differences across these indicators between the healthy group and the OA group. Notably, in indicators S1, S2, S3, S7, and S8, the models exhibited a large effect size in correlation with true values. These findings suggest that gait models derived from younger, healthy individuals are possible to be robustly adapted for non-invasive, everyday monitoring of knee health in older adults, offering valuable insights for the early detection and management of knee impairments. However, limitations such as fixed biases due to differences in measurement systems and sensor placement inaccuracies were identified. Future research will aim to enhance model precision by addressing these limitations through domain adaptation techniques and improved sensor calibration. Full article

In addition to the widely recognized benefits of reducing carbon emissions and protecting the environment, the authors believe that bus electrification has potential advantages in enhancing driving safety, improving passenger comfort, and reducing driver fatigue—areas that have not yet been sufficiently studied and emphasized. Safety and comfort are fundamental objectives in the continuous development of transportation systems. They are directly and closely related to both passengers and drivers and are among the top priorities when individuals choose their mode of transportation. Therefore, these aspects deserve broader and more in-depth attention and research. This study aims to identify the potential advantages of route bus electrification in terms of safety and comfort. The results of a passive experiment on the speed profile of buses operating on actual routes are presented here. Firstly, we focus on the acceleration/deceleration at the starting/stopping stops, specifically for regular-route buses, and obtain the following information: I. Starting acceleration from a bus stop is particularly strong in the second half of the acceleration process, being suitable for motor-driven vehicles. II. The features of the stopping deceleration at a bus stop are “high intensity” and “low dispersion”, with the latter enabling the refinement of regenerative settings and significantly lowering electricity economy during electrification. And we compare the speed profile of an electric bus with those of a diesel bus and obtain the following information: III. Motor-driven vehicles offer the advantages of “high acceleration performance” and “no gear shifting”, making them particularly suitable for the high-intensity acceleration required when route buses depart from stations. This not only simplifies driving operations but also enhances lane-changing safety. And by calculating and analyzing the jerk amount, we could quantitatively demonstrate the comfortable driving experience while riding on this type of bus where there is no shock due to gear shifting. IV. While the “high acceleration performance” of motor-driven vehicles produces “individual differences in the speed change patterns”, this does not translate to “individual differences in electricity consumption”, owing to the characteristics of this type of vehicle. With engine-driven vehicles, measures such as “slow acceleration” and “shift up early” are strongly encouraged to realize eco-driving, and any driving style that deviates from these measures is avoided. However, with motor-driven vehicles, the driver does not need to be too concerned about the speed change patterns during acceleration. This characteristic also suggests a benefit in terms of the electrification of buses. Full article

The manipulator has been widely used in the wood processing industry; the main problem currently faced is optimizing the motion trajectory to enhance the processing efficiency and operational stability of the woodworking manipulator and worktable. A 5-7-5 piecewise polynomial interpolation method is proposed to construct the spatial trajectories of each joint. An improved non-dominated sorting genetic algorithm (INSGA-II) is proposed to achieve a time–jerk multi-objective trajectory planning that can meet the dual requirements of minimal processing time and reduced motion impact. In order to address the limitations of the standard NSGA-II algorithm, which is prone to local optima and exhibits slow convergence, we propose a good point set method for multi-objective optimization population initialization and a linear ranking selection method to refine the parent selection process within the genetic algorithm. The improved NSGA-II algorithm markedly enhanced both the uniformity of the population distribution and convergence speed. In practical applications, selecting suitable weightings to construct a normalized weight function can identify the optimal solution from the Pareto frontier curve. A high-order continuous and smooth optimal trajectory without abrupt changes can be obtained. The simulation results demonstrated that the 5-7-5 piecewise polynomial interpolation curve effectively constructed a high-order smooth processing trajectory with continuous and smooth velocity, acceleration, and jerk, free from discontinuities. Moreover, the INSGA-II algorithm outperforms the original algorithm in terms of convergence and distribution, enabling the optimal time–jerk multi-objective trajectory planning that adheres to constraint conditions. Optimized by the improved NSGA-II algorithm, the optimal total running time is 4.5400 s, and the optimal jerk is 17.934 $\mathrm{m}\left(\mathrm{r}\mathrm{a}\mathrm{d}\right)/{\mathrm{s}}^3$. This provides a novel approach to solving the inefficiencies and operational instability prevalent in traditional woodworking equipment. Full article

The three performance indexes of the space robot, travel time, energy consumption, and smoothness, are the key to its important role in space exploration. Therefore, this paper proposes a multi-objective trajectory planning method for robots. Firstly, the kinematics and dynamics of the Puma560 robot are analyzed to lay the foundation for trajectory planning. Secondly, the joint space trajectory of the robot is constructed with fifth-order B-spline functions, realizing the continuous position, velocity, acceleration, and jerk of each joint. Then, the improved multi-objective particle swarm optimization (MOPSO) algorithm is used to optimize the trajectory, and the distribution uniformity, convergence, and diversity of the obtained Pareto front are good. The improved MOPSO algorithm can realize the optimization between multiple objectives and obtain the trajectory that meets the actual engineering requirements. Finally, this paper implements the visualization of the robot’s joints moving according to the optimal trajectory. Full article

In rehabilitation, physicians plan lower-limb exercises via linear guidance. Ensuring efficacy and safety, they design patient-specific paths, carefully plotting smooth trajectories to minimize jerks. Replicating their precision in robotics is a major challenge. This study introduces a linear rehabilitation motion planning method designed for physicians to use a multi-posture lower-limb rehabilitation robot, encompassing both path and trajectory planning. By subdividing the lower limb’s action space into four distinct training sections and classifying this space, we articulate the correlation between linear trajectories and key joint rehabilitation metrics. Building upon this foundation, a rehabilitative path generation system is developed, anchored in joint rehabilitation indicators. Subsequently, high-order polynomial curves are employed to mimic the smooth continuity of traditional rehabilitation trajectories and joint motions. Furthermore, trajectory planning is refined through the resolution of a constrained quadratic optimization problem, aiming to minimize the abrupt jerks in the trajectory. The optimized trajectories derived from our experiments are compared with randomly generated trajectories, demonstrating the suitability of trajectory optimization for real-time rehabilitation trajectory planning. Additionally, we compare trajectories generated based on the two groups of joint rehabilitation indicators, indicating that the proposed path generation system effectively assists clinicians in executing efficient and precise robot-assisted rehabilitation path planning. Full article

The smoothing of linear toolpaths plays is critical in improving machining quality and efficiency in five-axis CNC machining. Existing corner-smoothing methods often overlook the impact of spline curvature fluctuations, which may lead to acceleration variations, hindering surface quality improvements. The paper presents a five-axis toolpath corner-smoothing method based on the space of master–slave movement (SMM), aiming to minimize curvature fluctuations in five-axis machining and improve surface quality. The concept of movement space in master–slave cooperative motion is introduced, where the tool tip position and tool orientation are decoupled into a main motion trajectory and two master–slave movement space trajectories. By deriving the curvature monotony conditions of a dual Bézier spline, a G2-continuous tool tip corner-smoothing curve with minimal curvature fluctuations is constructed in real-time. Subsequently, using the SMM and the asymmetric dual Bézier spline, a high-order continuous synchronization relationship between the tool tip position and tool orientation is established. Simulation tests and machining experiments show that with our smoothing algorithm, maximum acceleration values for each axis were reduced by 21.05%, while jerk was lowered by 22.31%. These results indicate that trajectory smoothing significantly reduces mechanical vibrations and improves surface quality. Full article

This paper proposes a method for solving the path planning problem for a collaborative robot. The time-optimal, smooth, collision-free B-spline path is obtained by the application of a nature-inspired optimization algorithm. The proposed approach can be especially useful when moving items that are delicate or contain a liquid in an open container using a robotic arm. The goal of the optimization is to obtain the shortest execution time of the production cycle, taking into account the velocity, velocity and jerk limits, and the derivative continuity of the final trajectory. For this purpose, the velocity profiling algorithm for B-spline paths is proposed. The methodology has been applied to the production cycle optimization of the pick-and-place process using a collaborative robot. In comparison with point-to-point movement and the solution provided by the RRT* algorithm with the same velocity profiling to ensure the same motion limitations, the proposed path planning algorithm decreased the entire production cycle time by 11.28% and 57.5%, respectively. The obtained results have been examined in a simulation with the entire production cycle visualization. Moreover, the smoothness of the movement of the robotic arm has been validated experimentally using a robotic arm. Full article

For hybrid direct sequence/frequency hopping (DS/FH) spread spectrum signals, even if the relative motion speed between the transmitter and receiver remains constant, the Doppler frequency will vary due to the continuous hopping of the carrier frequency. Under high dynamic conditions, the first-order and second-order change rates of the Doppler frequency attached to the received signal further increase the Doppler frequency agility, making it difficult for the carrier tracking loop to maintain steady-state tracking. To address these issues, a high dynamic velocity locked loop (HD-VLL) is proposed in this paper. Specifically, the accumulated phase tracking error caused by acceleration and jerk is first analyzed. Subsequently, to compensate for this phase tracking error with the system clock, the proposed loop adds an acceleration compensation module and a jerk compensation module. However, this results in the output of the high dynamic loop filter being updated with the system clock, which contradicts the multiplexing design of a traditional loop filter for parallel signal processing, making the hardware implementation of an HD-VLL impractical. Therefore, this contradiction leads us to design an HD-VLL-based multi-carrier NCO (HD-VLL-NCO). The HD-VLL and HD-VLL-NCO are simulated, revealing the HD-VLL’s superior dynamic adaptability and steady-state tracking, while the HD-VLL-NCO achieves comparable accuracy with the appropriate truncation bit width. Full article