Smooth Trajectory Research Articles

Autoregressive GAN for Semantic Unconditional Head Motion Generation

In this work, we address the task of unconditional head motion generation to animate still human faces in a low-dimensional semantic space from a single reference pose. Different from traditional audio-conditioned talking head generation that seldom puts emphasis on realistic head motions, we devise a GAN-based architecture that learns to synthesize rich head motion sequences over long duration while maintaining low error-accumulation levels. In particular, the autoregressive generation of incremental outputs ensures smooth trajectories, while a multi-scale discriminator on input pairs drives generation toward better handling of high- and low-frequency signals and less mode collapse. We experimentally demonstrate the relevance of the proposed method and show its superiority compared to models that attained state-of-the-art performances on similar tasks.

Kinematic Analysis and Trajectory Planning Based on a Six-Axis Robotic Arm

Kinematic analysis and time-optimal trajectory planning are applied to the robot in order to enhance its operational efficiency and preserve its continuous, smooth running trajectory. In this paper, the robot kinematics model is established based on the D-H parametric method with the Daqi Elfin series E05 six-axis robot as the research object. After that, forward and inverse kinematic analysis is carried out. And the segmented polynomial interpolation trajectory planning model of robotic arm is optimized in time based on the improved particle swarm algorithm. And MATLAB robot toolbox is used to build the robotic arm simulation model. From there, the trajectory planning simulation experiments are performed. As well as the experimental results show that the improved particle swarm algorithm effectively reduces the trajectory planning time. In the simulation experiment the time is reduced by 40.78% compared to the initial setting. The effectiveness of the robotic arm is greatly increased by this research.

Safe motion planning and formation control of quadruped robots

This paper introduces a motion planning and cooperative formation control approach for quadruped robots and multi-agent systems. First, in order to improve the efficiency and safety of quadruped robots navigating in complex environments, this paper proposes a new planning method that combines the dynamic model of quadruped robots and a gradient-optimized obstacle avoidance strategy without Euclidean Signed Distance Field. The framework is suitable for both static and slow dynamic obstacle environments, aiming to achieve multiple goals of obstacle avoidance, minimizing energy consumption, reducing impact, satisfying dynamic constraints, and ensuring trajectory smoothness. This approach differs in that it reduces energy consumption throughout the movement from a new perspective. Meanwhile, this method effectively reduces the impact of the ground on the robot, thus mitigating the damage to its structure. Second, we combine the dynamic control barrier function and the virtual leader-follower model to achieve efficient and safe formation control through model predictive control. Finally, the proposed algorithm is validated through both simulations and real-world scenarios testing.

Robot Task-Constrained Optimization and Adaptation with Probabilistic Movement Primitives

Enabling a robot to learn skills from a human and adapt to different task scenarios will enable the use of robots in manufacturing to improve efficiency. Movement Primitives (MPs) are prominent tools for encoding skills. This paper investigates how to learn MPs from a small number of human demonstrations and adapt to different task constraints, including waypoints, joint limits, virtual walls, and obstacles. Probabilistic Movement Primitives (ProMPs) model movements with distributions, thus providing the robot with additional freedom for task execution. We provide the robot with three modes to move, with only one human demonstration required for each mode. We propose an improved via-point generalization method to generalize smooth trajectories with encoded ProMPs. In addition, we present an effective task-constrained optimization method that incorporates all task constraints analytically into a probabilistic framework. We separate ProMPs as Gaussians at each timestep and minimize Kullback–Leibler (KL) divergence, with a gradient ascent–descent algorithm performed to obtain optimized ProMPs. Given optimized ProMPs, we outline a unified robot movement adaptation method for extending from a single obstacle to multiple obstacles. We validated our approach with a 7-DOF Xarm robot using a series of movement adaptation experiments.

Analysis of static-dynamic global path planning for the rosa roxburghii picking robot

Abstract In the context of the Rosa Roxburghii picking robot operating in the Rosa Roxburghii park, path planning represents a critical challenge and a key area of study. To address this, a globally optimized A* algorithm has been developed, which integrates A* (A-star) with the dynamic window approach (DWA) for local optimization. The process begins by incorporating the robot’s positional information into the traditional evaluation function, along with establishing a weight function that balances both cost and heuristic factors. Following this, the conventional eight search directions are reduced to seven, enhancing the efficiency of the path search. To increase the smoothness of the path, unnecessary turning points are eliminated while retaining essential ones for node optimization. A safety domain value is also introduced to further minimize extraneous turns, ensuring comprehensive global path optimization. For effective realtime dynamic obstacle avoidance. The combination of the two algorithms enables online path planning, resulting in a smooth trajectory based on the globally optimal path. Simulation outcomes demonstrate that this approach significantly reduces path length, average turning angle, and execution time, with its effectiveness validated through additional simulation experiments.

Intelligent Perception and Seam Tracking System for Thick Plate Weldments Based on Constant-Focus Optical Path

To achieve efficient and accurate thick plate welding, as well as to precisely extract and plan the paths of complex three-dimensional weld seams in large steel structures, this study introduces a novel vision-guided approach for robotic welding systems utilizing a constant-focus laser sensor. This methodology specifically targets and mitigates several critical shortcomings inherent in conventional vision-guided welding techniques, including limited detection ranges, diminished precision in both detection and tracking, and suboptimal real-time performance. For preprocessed weld images, an improved grayscale extreme centroid method was developed to extract the center of the light stripe. Furthermore, a sophisticated feature point extraction algorithm, which integrates a maximum distance search strategy with a least-squares fitting procedure, was developed to facilitate the precise and timely identification of weld seam characteristic points. To further optimize the outcomes, a cylindrical filtering mechanism was employed to eliminate substantial discrepancies, whereas local Non-Uniform Rational B-Spline (NURBS) curve interpolation was utilized for the generation of smooth and accurate trajectory plans. A spatial vector-based pose adjustment strategy was then implemented to provide robust guidance for the welding robot, ensuring the successful execution of the welding operations. The experimental results indicated that the proposed algorithm achieved a tracking error of 0.3197 mm for welding workpieces with a thickness of 60 mm, demonstrating the method’s substantial potential in the manufacturing sector, especially in the domain of automated welding.

Deep reinforcement learning-based local path planning in dynamic environments for mobile robot

Path planning for robots in dynamic environments is a challenging task, as it requires balancing obstacle avoidance, trajectory smoothness, and path length during real-time planning.This paper proposes an algorithm called Adaptive Soft Actor–Critic (ASAC), which combines the Soft Actor–Critic (SAC) algorithm, tile coding, and the Dynamic Window Approach (DWA) to enhance path planning capabilities. ASAC leverages SAC with an automatic entropy adjustment mechanism to balance exploration and exploitation, integrates tile coding for improved feature representation, and utilizes DWA to define the action space through parameters such as target heading, obstacle distance, and velocity In this framework, the action space is defined by DWA’s three weighting parameters: target heading deviation, distance to the nearest obstacle, and velocity. To facilitate the learning process, a non-sparse reward function is designed, incorporating factors such as Time-to-Collision (TTC), heading, and velocity. To validate the effectiveness of the algorithm, experiments were conducted in four different environments, and the algorithm was evaluated based on metrics such as trajectory deviation, smoothness, and time to reach the end point. The results demonstrate that ASAC outperforms existing algorithms in terms of trajectory smoothness, arrival time, and overall adaptability across various scenarios, effectively enabling path planning in dynamic environments.

Real-time position path smoothing for robotic manipulators by constructing Composite Trajectory Spline

Aiming at smoothing discontinuous corners in robotic tool paths, a novel spline named “Composite Trajectory Spline”(CT-Spline) is proposed in this paper. Based on CT-Spline, the real-time position path smoothing for robotic manipulators is realized. CT-Spline enables analytical trajectory planning and interpolation without curve length computation, significantly enhancing trajectory generation efficiency and avoiding numerical errors. By directly controlling resultant trajectory acceleration, CT-Spline avoids decomposing it into tangential and normal accelerations, ensuring adherence to the maximum acceleration constraint while fully utilizing acceleration potential. The geometric shape of CT-Spline is determined by three control points and a trajectory model. This paper further develops C1 and C3 continuous CT-Splines based on two different trajectory models, combined with a velocity look-ahead algorithm to achieve real-time local smoothing of path corners. Additionally, an adaptive control algorithm of smoothing error is introduced to dynamically maximize trajectory velocity. Simulations and experiments validate the effectiveness of CT-Spline, and demonstrate that the proposed C3 continuous trajectory smoothing method has several advantages over the method based on Pythagorean-hodograph splines in terms of kinematic constraints, velocity, smoothing errors, and real-time performance.

A Five-Axis Toolpath Corner-Smoothing Method Based on the Space of Master–Slave Movement

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.

Smooth and Time-Optimal Trajectory Planning for Robots Using Improved Carnivorous Plant Algorithm

To improve the safety and reliability of robotic manipulators during high-speed precision movements, this paper proposes a method for smooth and time-optimal trajectory planning incorporating kinodynamic constraints. The primary objective is to use an evolutionary algorithm to determine a trajectory by considering time and jerk within the feasible path-pseudo-velocity phase plane region. Firstly, the path parameterization theory extracted the maximum pseudo-velocity projection curve from the kinodynamic constraints. Subsequently, the feasible region in the phase plane was defined through reachability analysis of discrete linear systems. Thereafter, we constructed the trajectory function using a cubic B-spline curve, optimizing its control points with an improved carnivorous plant optimization algorithm. Finally, the effectiveness and practicality of this method were verified through simulations on a 6-DOF manipulator.

Piecewise Time Polynomials-Based Control Methods for Obstacle Avoidance and Precision Positioning of Tower Crane Systems with Varying Cable Lengths

During the hoisting and lowering operations of a tower crane, dynamic variations in cable lengths significantly influence the oscillation frequency and amplitude of the load. These variations complicate the oscillation characteristics, heightening the challenge of balancing obstacle avoidance with precise positioning. To tackle this issue, we propose a trajectory planning and tracking control method that integrates hoisting control to reduce the impact of varying cable lengths on load swinging and achieve accurate positioning during obstacle navigation. A novel definition of swing angle is introduced to model the crane’s rigid and swinging components separately, enhancing model accuracy while simplifying complexity. A piecewise polynomial constructs the load trajectory in a low-dimensional flat space, which is then mapped to a high-dimensional generalized state space through a homeomorphic transformation, ensuring trajectory smoothness and traceability. A fractional-order sliding mode controller is employed to facilitate rapid and precise tracking of the actuated degrees of freedom, suppressing load oscillation while maintaining positioning accuracy. Experimental validation on a tower crane platform shows that the proposed strategy enables smooth obstacle avoidance and precise target point reaching, even with varying cable lengths.

Multi-objective optimal trajectory planning for manipulators based on CMOSPBO

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 Novel Robust Hybrid Control Strategy for a Quadrotor Trajectory Tracking Aided with Bioinspired Neural Dynamics

This paper introduces a novel hybrid control strategy for quadrotor UAVs inspired by neural dynamics. Our approach effectively addresses two common issues: the velocity jump problem in traditional backstepping control and the control signal chattering in conventional sliding mode control. The proposed system combines an outer-loop bioinspired backstepping controller with an inner-loop bioinspired sliding mode controller, ensuring smooth trajectory tracking even under external disturbances. We rigorously analyzed the system’s stability using Lyapunov stability theory. To validate our algorithm’s effectiveness, we conducted trajectory tracking experiments in both disturbance-free and step-disturbance conditions, comparing it with the traditional backstepping control, conventional sliding mode control, and saturated sliding mode control. The results demonstrate that our algorithm not only tracks trajectories more effectively but also significantly outperforms these methods in suppressing velocity jumps and signal chattering.

Enhancing unmanned vehicle navigation safety: real-time visual mapping with CNNs with optimized Bezier trajectory smoothing

Enhancing unmanned vehicle navigation safety: real-time visual mapping with CNNs with optimized Bezier trajectory smoothing

Cooperative Adaptive Cruise Control Platoon Fleet Formation Model Considering Efficiency and Stability

In the existing formation model, vehicles in the same lane or adjacent lane are regarded as the structure, and the driving behavior of vehicles is studied from the perspectives of safety, speed consistency, and stability, and the speed control model is proposed from the perspective of vehicles themselves, to obtain a stable fleet with the same distance and speed. However, in this process, the initial condition of the vehicle, the traffic flow environment, and the efficiency of the fleet formation are less considered. Therefore, based on summarizing the existing fleet building model, this paper puts forward the rapid construction model and algorithm of a cooperative adaptive cruise control platoon fleet. One of the important goals of forming a team is to enter the team with the smoothest trajectory in the shortest time. Therefore, this chapter studies the trajectory optimization of the vehicle formation process from the perspective of vehicle dynamics.

An optimized method for AUV trajectory model in benthonic hydrothermal area based on improved slime mold algorithm

The optimization of the desired autonomous underwater vehicle (AUV) trajectory modeling and AUV trajectory tracking control in the benthonic hydrothermal area were studied. In the conventional trajectory tracking model construction methods, the time points were roughly combined with the position points of the planned path, making it difficult to produce a smooth trajectory. Although the spline interpolation method was an ideal option for smooth curves, a great number of points were needed for a complex desired trajectory mode. In response to the demanding requirements of AUV trajectory tracking control in the benthonic hydrothermal area, an under-actuated test platform was first established, and the cubic spline interpolation was adopted to process the preset path points for a smooth desired trajectory. An improved slime mold algorithm (SMA) was put forward to optimize the interpolating points used in the trajectory modeling. The Levy flight technology and the compactness technique to speed up the search process and increase the search accuracy. The simulation experiments were conducted in comparison with the artificial fish swarm algorithm (AFSA), the particle swarm optimization (PSO), and the compact cuckoo search (CCS). The results showed that the improved SMA shortened the search process, effectively avoided the local extreme values, and generated a high-precision desired trajectory model in a shorter time. The pool test also verified the feasibility and effectiveness of the proposed method. The method proposed in this study can satisfy the modeling of benthonic hydrothermal trajectory with a fewer number of nodes, faster search progress and search accuracy.

An Eco-Driving Strategy at Multiple Fixed-Time Signalized Intersections Considering Traffic Flow Effects

To encourage energy saving and emission reduction and improve traffic efficiency in the multiple signalized intersections area, an eco-driving strategy for connected and automated vehicles (CAVs) considering the effects of traffic flow is proposed for the mixed traffic environment. Firstly, the formation and dissipation process of signalized intersection queues are analyzed based on traffic wave theory, and a traffic flow situation estimation model is constructed, which can estimate intersection queue length and rear obstructed fleet length. Secondly, a feasible speed set calculation method for multiple signalized intersections is proposed to enable vehicles to pass through intersections without stopping and obstructing the following vehicles, adopting a trigonometric profile to generate smooth speed trajectory to ensure good riding comfort, and the speed trajectory is optimized with comprehensive consideration of fuel consumption, emissions, and traffic efficiency costs. Finally, the effectiveness of the strategy is verified. The results show that traffic performance and fuel consumption benefits increase as the penetration rate of CAVs increases. When all vehicles on the road are CAVs, the proposed strategy can increase the average speed by 9.5%, reduce the number of stops by 78.2%, reduce the stopped delay by 82.0%, and reduce the fuel consumption, NOx, and HC emissions by 20.4%, 39.4%, and 46.6%, respectively.

Ship Trajectory Extraction Using Python Vessel Tracking Interpolation Method

A deep understanding of ship trajectory movements has essential implications for maritime applications, including navigation, monitoring, and marine traffic analysis. Efficient and accurate extraction techniques are necessary to extract valuable information from ship trajectory data. One commonly used approach is the interpolation method, which allows the reconstruction of smooth trajectories from recorded data points. This research is focused on analyzing the extraction of ship trajectories using the interpolation method provided by the Python Vessel Tracking (PyVT) library. This method allows interpolation of ship trajectory data based on various algorithms available in the library. This research aims to evaluate the effectiveness and accuracy of interpolation methods from PyVT in reconstructing ship trajectories from incomplete or disturbed data. Within this research's framework, several test scenarios were implemented to examine different types of ship trajectory data, including data with missing points and speed variations. Evaluation metrics RMSE (root mean Squared Error), which includes reconstruction accuracy, will be utilized from the interpolation algorithm in PyVT.

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

Trajectory planning of robotic manipulators in complex environments involves generating smooth and collision-free paths, and key aspects to consider include dynamic environment perception, path planning, trajectory smoothing and optimization, and obstacle avoidance. This paper discusses different algorithms and finally proposes a fusion of the improved Dung Beetle Optimizer (IDBO) algorithm using chaotic mapping, sinusoidal random mutation, and nonlinear convergence strategies with the bidirectional Rapidly exploring Random Tree (RRT) algorithm to achieve manipulator trajectory planning and minimum jerk optimization trajectory. In the experiment, the IDBO algorithm was compared with other heuristic algorithms. The path obtained was shortened by 9.18% on average, and the calculation time was shortened by 33.81% on average. Then, the paper explored Cartesian coordinate space trajectory planning and joint space trajectory planning when the robot was working in 3D space, and verified the superiority of the latter. In controlling the movement of the robot, by combining the minimum angle jerk planning and the bidirectional RRT obstacle avoidance algorithm to drive the joint angle parameters obtained by the spatial trajectory planning, the trajectory of the robot manipulator can be smoother, more efficient, and avoid obstacles in complex 3D space. This research helps improve the performance, safety, and technical support of robots, and is of great research significance.

Online Trajectory Replanning for Avoiding Moving Obstacles Using Fusion Prediction and Gradient-Based Optimization

In this study, we introduce a novel method for an online trajectory replanning approach for fixed-wing Unmanned Aerial Vehicles (UAVs). Our method integrates moving obstacle predictions within a gradient-based optimization framework. The trajectory is represented by uniformly discretized waypoints, which serve as the optimization variables within the cost function. This cost function incorporates multiple objectives, including obstacle avoidance, kinematic and dynamic feasibility, similarity to the reference trajectory, and trajectory smoothness. To enhance prediction accuracy, we combine physics-based and pattern-based methods for predicting obstacle movements. These predicted movements are then integrated into the online trajectory replanning framework, significantly enhancing the system’s safety. Our approach provides a robust solution for navigating dynamic environments, ensuring both optimal and secure UAV operation.