Manipulator Trajectory Research Articles

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.

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.

Analysis of Polynomial Interpolation Characteristics Based on 6DOF Manipulator Trajectory Planning

Aiming at the problems of choosing and using polynomials of different times and mixed polynomials in the process of manipulator trajectory planning, such as difficulty, wide range of light and low accuracy, in this paper, the application of different polynomials in manipulator trajectory planning is systematically analyzed by using MATLAB Robot Toolbox simulation platform and Polynomial interpolation algorithm. Using a 6-dof robotic arm Puma560 as a simulation object, the effects of three-, five-, and seven-Polynomial interpolation on joint position and pose in joint space trajectory planning were analyzed, a preliminary understanding of the application of different polynomials, and secondly, the more complex application of the fifth and seventh degree polynomials in Descartes space for the trajectory planning of the manipulator, the influence of trajectory planning with different degree polynomials on the position and pose of manipulator joint is clarified. The results show that the higher the number of polynomials, the smoother the transition of the joint at the critical path points, but the greater the maximum angular velocity and angular acceleration of the joint, the Polynomial interpolation of joint space and Descartes space trajectory planning are 14% and 23% lower than the average of absolute maximum angular velocity and absolute maximum angular acceleration of the Polynomial interpolation, respectively. Based on the analysis of the research results, this paper presents the applicable conditions and applications of Polynomial interpolation method in trajectory planning, and further summarizes the application conditions and methods of mixed polynomials.

Trajectory control and optimization of PID controller parameters for dual-arms with a single-link underwater robot manipulator

ABSTRACT This paper focuses on the modeling, simulation, and control of the trajectories of a dual-arm single-link underwater robot manipulator (DS-URM), having dual arms (left and right) with a single link each. The dynamic coupling between the base and the dual arms makes trajectory control of the end effector difficult. This study attempts to simulate and control dual arms with a single-link underwater robotic manipulator using a hybrid controller. To reduce the error for a sinusoidal wave and a cycloid trajectory, a hybrid controller is the combination of the Proportional-Integral-Derivative (PID) controller and overwhelm controller. The underwater dynamic’s buoyancy, gravity, and hydrostatic forces acting on the underwater robot are modeled in an integrated SIMULINK model, including the DS-URM. The DS-URM has been investigated, revealing some significant trajectories of the left and right tips. Effective tuning methods include Ziegler-Nicholas (Z-N), genetic algorithms, Ant Colony Optimization (ACO), and Particle Swarm Optimization (PSO). The Integral of Time multiplied by Absolute Error (ITAE) criteria has been used to improve trajectory tracking via particle swarm optimization. Results show significant improvements in trajectory tracking, with ITAE error reduction by 96.44% and 98.6% for left and right arms, respectively, achieving stability in 0.000645s.

Design of Optimal STSMC Method Based on FPGA to Track the Trajectory of 2-DOF Robot Manipulator

Design of Optimal STSMC Method Based on FPGA to Track the Trajectory of 2-DOF Robot Manipulator

Trajectory Analysis of 6-DOF Industrial Robot Manipulators by Using Artificial Neural Networks.

Robot manipulators are robotic systems that are frequently used in automation systems and able to provide increased speed, precision, and efficiency in the industrial applications. Due to their nonlinear and complex nature, it is crucial to optimize the robot manipulator systems in terms of trajectory control. In this study, positioning analyses based on artificial neural networks (ANNs) were performed for robot manipulator systems used in the textile industry, and the optimal ANN model for the high-accuracy positioning was improved. The inverse kinematic analyses of a 6-degree-of-freedom (DOF) industrial denim robot manipulator were carried out via four different learning algorithms, delta-bar-delta (DBD), online back propagation (OBP), quick back propagation (QBP), and random back propagation (RBP), for the proposed neural network predictor. From the results obtained, it was observed that the QBP-based 3-10-6 type ANN structure produced the optimal results in terms of estimation and modeling of trajectory control. In addition, the 3-5-6 type ANN structure was also improved, and its root mean square error (RMSE) and statistical R2 performances were compared with that of the 3-10-6 ANN structure. Consequently, it can be concluded that the proposed neural predictors can successfully be employed in real-time industrial applications for robot manipulator trajectory analysis.

Two types of anti-noise integral enhanced recurrent neural networks for solving time-varying complex quadratic programming

The time-varying complex quadratic programming problem plays an important role in scientific research and engineering applications, and has received extensive attention. In this paper, by solving the problem in different number domains, two types of novel anti-noise integral enhanced recurrent neural networks (IERNNs) are proposed and analyzed. Specifically, the IERNN-A model solves the problems in the complex number domain, while the IERNN-B model solves the problems by converting the problems from the complex number domain into the real number domain. Both the IERNN-A and IERNN-B have the same design paradigm, i.e., an integral-type error function is first defined to obtain good anti-noise capability, and then substitute it into a differential-driven design formula to ensure convergence. Theory analysis and simulation results verify the global convergence and robustness of the proposed IERNNs. Furthermore, if a linear activation is used, the exponential convergence rate is obtained. Meanwhile, when time-varying bounded noise exists, the IERNNs are input-to-state stable. In addition, compared with other art-of-the-state methods, the proposed methods have faster convergence speed, stronger noise-suppression ability, and no overshoot, which are verified by the simulation and application of manipulator trajectory tracking.

A Novel Cost Calculation Method for Manipulator Trajectory Planning.

It is worthwhile to calculate the execution cost of a manipulator for selecting a planning algorithm to generate trajectories, especially for an agricultural robot. Although there are various off-the-shelf trajectory planning methods, such as pursuing the shortest stroke or the smallest time cost, they often do not consider factors synthetically. This paper uses the state-of-the-art Python version of the Robotics Toolbox for manipulator trajectory planning instead of the traditional D-H method. We propose a cost function with mass, iteration, and residual to assess the effort of a manipulator. We realized three inverse kinematics methods (NR, GN, and LM with variants) and verified our cost function's feasibility and effectiveness. Furthermore, we compared it with state-of-the-art methods such as Double A* and MoveIt. Results show that our method is valid and stable. Moreover, we applied LM (Chan λ = 0.1) in mobile operation on our agricultural robot platform.

Enhancing aero-engine thrust response: Accounting for combustion delays

In scenarios like aircraft landing, Rapid Thrust Modulation (RTM) is required to achieve high-precision attitude and trajectory manipulations. However, the traditional manipulated variable in aero-engines, specifically the fuel flow, experiences sluggishness in adjusting thrust (Fn) due to combustion delays. In contrast, geometric variable areas, like the nozzle throat area (A8), offer rapid responsiveness but have limited thrust-adjusting capacity. Hence, the proposal of an innovative parallel Valve Position Control (VPC) scheme, combining redundant control inputs, emerges as a groundbreaking solution to enable RTM. In the pursuit of achieving RTM, the non-minimum phase thrust responses are first addressed, which has not been recognized previously to the best of the author's knowledge. This includes the implementation of a new valve position control (VPC) structure, incorporating a dual input Single Output (DISO) system, which is vital for optimizing response time and minimizing the delayed effects in combustion processes. After proper selection of operating conditions, the synthesis process of VPC is outlined by three key requirements, including: 1) realizing the 10 rad/s thrust bandwidth despite the combustion delay; 2) ensuring continuous modulation capability by mid-ranging the A8; 3) decoupling the A8 and thrust during flights. The VPC controller is implemented and compared with the classical Edmond algorithm in a turbofan engine. Results emphasize VPC's robustness in handling combustion delays, meeting specified requirements, and showcasing its potential as an effective RTM solution. Practically, the VPC system's architecture allows for critical rapid thrust changes within a 10 rad/s bandwidth, essential for operations like VSTOL aircraft maneuvers.

Optimized Proportional-derivative Feedback-assisted Iterative Learning Control for Manipulator Trajectory Tracking

Optimized Proportional-derivative Feedback-assisted Iterative Learning Control for Manipulator Trajectory Tracking

Fixed-time solution of inequality constrained time-varying linear systems via zeroing neural networks

Zeroing neural network (ZNN) has been explored and applied in a variety of time-varying problems solving. However, ZNN models for inequality constrained time-varying linear equation (ICTVLE) solving are rarely reported. Generally, numerous practical problems can be mathematically modeled as ICTVLE problems. Motivated by the above mentioned issue, a nonlinear tunable activation function activated ZNN (NTAF-ZNN) model is constructed to effectively solve ICTVLE problems. To further improve the performances of NTAF-ZNN model, a fuzzy nonlinear tunable activation function (FNTAF) is also designed. Based on the FNTAF, a fuzzy nonlinear tunable activation function-based ZNN (FNTAF-ZNN) model is realized. Firstly, the fixed-time convergence property and disturbance rejection ability of the NTAF-ZNN and FNTAF-ZNN models are proved by theoretical analysis. Then, comparative simulation results of the two models with other existing ZNN models for solving the ICTVLE problem are provided to further verify their robustness and effectiveness. Additionally, the two models and other existing ZNN models are also employed to realize inequality constrained manipulator trajectory tracking under ideal and noisy environments for further comparisons. Finally, the superior performances of the FNTAF-ZNN model for manipulator trajectory tracking are further verified by physical experiment results.

An asymmetric S-curve trajectory planning based on an improved jerk profile

AbstractIn this paper, a method of planning the expanded S-curve trajectory of robotic manipulators is proposed to minimize the execution time as well as to achieve the smoother trajectory generation in the deceleration stage for point-to-point motions. An asymmetric parameter is added to the piecewise sigmoid function for an improved jerk profile. This asymmetric profile is continuous and infinitely differentiable. Based on this profile, two analytical algorithms are presented. One is applied to determine the suitable time intervals of trajectory satisfying the time optimality under the kinematic constraints, and the other is to determine the asymmetric parameter generating the minimum execution time. Also, the calculation procedure for the time-scaled synchronization for all joints is given to decrease unnecessary loads onto the actuators. The velocity, acceleration, jerk and snap (the derivative of jerk) of the joints and the end-effector are equal to zero at two end points of motion. The simulation results through 3 DOF and 6 DOF robotic manipulators show that our approach reduces the jerk and snap of the deceleration stage effectively while decreasing the total execution time. Also, the analysis for a single DOF mass-spring-damper system indicates that the residual vibration could be reduced to 10% more than the benchmark techniques in case velocity, acceleration and jerk are limited to 1.24 m/s, 6 m/s2 and 80 m/s3, respectively and displacement is set to 0.8m. These results manifest that the performance of reducing residual vibrations is good and demonstrate an important characteristic of the proposed profile suitable for point-to-point motion.

Generation, manipulation, and detection of snake-state trajectories of a neutral atom in a ring cavity

Generation, manipulation, and detection of snake-state trajectories of a neutral atom in a ring cavity

Multi-objective optimal trajectory planning for robot manipulator attention to end-effector path limitation

Abstract In the process of trajectory optimization for robot manipulator, the path that is generated may deviate from the intended path because of the adjustment of trajectory parameters, if there is limitation of end-effector path in Cartesian space for specific tasks, this phenomenon is dangerous. This paper proposes a methodology that is based on the Pareto front to address this issue, and the methodology takes into account both the multi-objective optimization of robotic arm and the quality of end-effector path. Based on dung beetle optimizer, this research proposes improved non-dominated sorting dung beetle optimizer. This paper interpolates manipulator trajectory with quintic B-spline curves, achieves multi-objective trajectory optimization that simultaneously optimizes traveling time, energy consumption, and mean jerk, proposes a trajectory selection strategy that is based on Pareto solution set by introducing the concept of Fréchet distance, and the strategy enables the end-effector to approach the desired path in Cartesian space. Simulation and experimental results validate the effectiveness and practicability of the proposed methodology on the Sawyer robot manipulator.

Jerk and Energy Issues in Optimal Trajectory Planning for Robot Manipulators

Objective: One of the important objectives in industrial applications is minimizing the consumed energy due to the unsecured supply lines because of the international crisis and the sudden increase in the prices of the crude oil as well. It is the objective of this research to investigate the effect of jerk and the minimum energy consumption per cycle of the manipulator’s actuators on the optimal trajectory of industrial manipulator. Methods: The design for optimal trajectory for industrial robots has a primary importance in attaining mass production with accurate performance. Optimal trajectory can be designed from start to goal positions to achieve certain criterion optimally such as minimum time, minimum distance and / or minimum energy consumption while avoiding obstacles during the course of motion. Results: The proposed analysis will consider also the jerk which is the time derivative of the acceleration to guarantee that the end-effector will not vibrate at the start and goal of each stroke. A polynomial of seven-degree is proposed to investigate how the jerk affects the optimality of the trajectory and the torques of the joints as well. Conclusion: From the presented parametric study and analysis, it is recommended to apply energy per cycle as a criterion for minimum kinetic energy of an industrial manipulator trajectory in spatial manoeuvring.

Application of the crow search algorithm to achieve an optimal solution for a double link manipulator

Robotic manipulators are mechanical devices that are electronically controlled and have several linkages that allow them to do specific jobs under specified situations. Here, a double-link manipulator is explored and modified using uncertainty factors that impact the robot manipulator's performance in monitoring the angular position. Unlike, the standard Lagrangian technique is employed to derive the motion equations and calculate the performance of the Two Link Robot Manipulator. Because the motion equation involves a nonlinear system of ordinary differential equations, getting to the target place is challenging. Meta-heuristic search algorithms were standard methodologie to solve any optimization problem, mainly real-time problems. Meta-heuristic algorithms depend upon the natural behaviour of the animals or birds. This paper uses a Crow search algorithm to minimize the trajectory and position of the double link manipulator. It also demonstrates how the Crow search algorithm can easily be used to solve optimal control problems (OCP) with constraints in MATLAB simulation. The Crow search algorithm depends on the crow's behaviour of keeping their excess food in a safe place and getting it as needed. The Crow search algorithm (CSA) was compared with particle swarm optimization (PSO), differential evolution (DE), and Grey Wolf Optimization (GWO). The double link manipulator's fundamental Model's performance is computed to find a solution. The Crow search method has produced notable results in terms of performance, i.e. 25 % to 98 % better, compared to other algorithms such as DE, PSO, and GWO.

A Two-Layer Trajectory Tracking Control Scheme of Manipulator Based on ELM-SMC for Autonomous Robotic Vehicle

With the development of autonomous driving technology, some special vehicles should also be developed into autonomous driving vehicles. The robotic vehicles are widely used in engineering operations, and the robotic manipulator is a common tool mounted on robotic vehicles. The autonomous driving of robotic vehicles requires not only automatic movement, but also the automation of the robotic manipulator drive system. Therefore, this paper proposes an adaptive trajectory tracking control of manipulator based on sliding mode control (SMC), which can more accurately describe the joint space movement of the manipulator system under multi task coupling and external interference. Considering the multi-tasking situation, the influence of obstacle avoidance and base tilt on the trajectory of manipulator is investigated by using extreme learning machine (ELM), and the framework of machine learning is established. The output based on ELM-SMC is used as the bottom-layer control. Then an effective trajectory compensation method is proposed as the top-level control to avoid the error accumulation in the periodic repeated operation of the manipulator. Finally, the application effect of trajectory error tracking and compensation of manipulator in complex tasks of dynamic environment is verified by simulation and experiments, which lays a foundation for the stability control of manipulator in practical complex engineering applications. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The motivation of this paper is to solve the problem of poor trajectory tracking control accuracy of the manipulator caused by the change of the direction of the manipulator base. It is suitable for the high-precision position control of the manipulator assembled on the mobile robotic vehicle. Nowadays, the autonomous driving technology is developing rapidly, and the automation of traffic will be widely popularized in the future. Therefore, we should not only pay attention to the autonomous driving function of passenger vehicles, but also give consideration to the autonomous driving technology of robotic vehicles applied in engineering. It not only needs to complete the driving function, but also needs to ensure the reliable operation of the manipulator. In this paper, we mathematically deduce the control model of the manipulator. Then, we use SMC as the trajectory tracking control method of the manipulator, and use ELM to estimate the trajectory error caused by the end trajectory of the manipulator in the non-horizontal state of the base. Furthermore, we propose an optimization algorithm to optimize the compensation coefficient of cubic spline and give a reasonable compensation scheme. Through simulation and experiments, it is preliminarily verified that the schemes proposed in this paper are feasible, but they lack the application verification in the actual robotic vehicles, and the model fitting part of machine learning is completed with the help of the host computer, and the calculation ability of the controller of the actual manipulator may also be the limitation of completing this scheme.

Parameters identification and trajectory optimization of free-floating space robots

There is a strong dynamic coupling between the base of free-floating space robot and the space manipulator. In order to reduce the interference of the movement of the space manipulator on the robot's base, the trajectory of the space manipulator needs to be optimized. In this paper, the joint path of space manipulators is optimized by using the pseudo-spectral method to reduce the impact of the arm movement on the base. For space robots, parameters identification is the premise of trajectory planning. A parameters identification method is proposed, which only needs to measure the base's angular speed. Numerical simulation results verify the validity of the proposed method. The attitude angle of floating base returns to the initial state after maneuvers of space manipulators.

An Enhanced Activated Zeroing Neural Dynamics for Solving Complex Matrix Inverse and Tracking Trajectory of Robotic Manipulator

An Enhanced Activated Zeroing Neural Dynamics for Solving Complex Matrix Inverse and Tracking Trajectory of Robotic Manipulator

Neural Optimal Control for Constrained Visual Servoing via Learning From Demonstration

This paper proposes a novel optimal control scheme for constrained image based visual servoing of a robot manipulator. For a robot manipulator with an eye-on-hand configuration, visibility constraint is an essential requirement to avoid servo failure, while robot’s actuator limits must also be satisfied. To ensure this, the constraints are modelled implicitly via learning the task and defining safe regions using expert human demonstrations via mixture of Dynamic Movement Primitives (DMPs). The visual servoing problem is then formulated as a closed-loop optimal control problem using these constraint model where a desired target (possibly time-varying) is obtained by acting upon the feedback from the real-time visual sensors. The visual servo control loop consists of a single network adaptive critic optimal tracking control scheme whose weights are tuned using Lyapunov stability criteria. The stability and the performance of the proposed control scheme is shown theoretically via Lyapunov approach and also verified experimentally using a seven degree of freedom (DOF) Franka Emika and six DOF Universal Robot (UR) 10 manipulator. The approach is also demonstrated on a use case scenarios in mock-up convenience store and warehouse setup. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The applications of robots in busy warehouses, healthcare sectors and convenience store, has a big societal impact. The scenarios in these real-world problems often consist of a dynamic environment. Therefore, sensor-based localization and planning, along with satisfying robot and task constraints are needed. These naturally adds up to the programming costs in addition to the robot platform and actuation. However, modern robots need intuitive and easy programming for more pervasive in a practical societal application. In our proposed method, this sensor-based planning with environmental constraints is modelled implicitly using the Programming by Demonstration framework. The user needs to catch the robot arm by his hand and teach the task at hand, and the framework captures the task and robot constraints while generalizing to new goals. This modelling, along with cost optimal controller, generates real-time constraint aware robot manipulation trajectories for the demonstrated task in dynamic environments.