scholarly journals Numerical Aspects and Performances of Trajectory Planning Methods of Flexible Axes

2006 ◽  
Vol 1 (4) ◽  
pp. 35 ◽  
Author(s):  
Jean-Yves Dieulot ◽  
Issam Thimoumi ◽  
Frédéric Colas ◽  
Richard Béarée
Keyword(s):  
Optimal Control ◽  
Path Planning ◽  
Natural Frequency ◽  
Trajectory Planning ◽  
Input Shaping ◽  
Robot Arm ◽  
Frequency Mismatch ◽  
Planning Methods ◽  
Real Robot ◽  
Theoretical Results

Adequate Path Planning design is an important stage for controlling flexible axes because it may allow to cancel vibrations induced by oscillating modes. Among bang-bang profiles which are linked to optimal control, jerk assignment (acceleration derivative) and input shapers have been investigated. Theoretical results show the performance and robustness with respect to natural frequency mismatch. Practical validations on a real robot arm show the relevance of the jerk algorithm which is more robust with the same productivity performances as input shaping techniques.

3D Curve Generation Using Spherical Polar Piecewise Interpolation in CAD and CAM

2020 ◽  
Vol 896 ◽  
pp. 224-228
Author(s):  
Mihai Dupac
Keyword(s):  
Path Planning ◽  
Coordinate System ◽  
Numerical Simulations ◽  
Trajectory Planning ◽  
Robot Arm ◽  
Polar Plane ◽  
Spherical Coordinate ◽  
Manufacturing Efficiency ◽  
Planning Approach ◽  
Design And Manufacturing

In this paper a newly 3D path planning approach and curve generation for design and manufacturing efficiency is considered. The 3D path is generated by a combination of piecewise interpolating curves - along a given number of via-points - created via a spherical coordinate system specified by the polar angles, radial distances and the associated azimuthal angles. Each piecewise interpolating curve is constructed using Hermite polar interpolation in the projective polar plane and the rotating azimuthal plane. To verify the proposed approach, numerical simulations for the generation of a helix design, a 4 and 6 leaf design and a trajectory planning of a picking robot arm are conducted.

Trajectory Planning of Quadrotor Systems for Various Objective Functions

Robotica ◽  
2020 ◽  
Vol 39 (1) ◽  
pp. 137-152
Author(s):  
Hamidreza Heidari ◽  
Martin Saska
Keyword(s):  
Optimal Control ◽  
Path Planning ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Trajectory Planning ◽  
Minimum Principle ◽  
Optimal Path ◽  
Necessary Condition ◽  
Objective Functions ◽  
Wide Range

SUMMARYQuadrotors are unmanned aerial vehicles with many potential applications ranging from mapping to supporting rescue operations. A key feature required for the use of these vehicles under complex conditions is a technique to analytically solve the problem of trajectory planning. Hence, this paper presents a heuristic approach for optimal path planning that the optimization strategy is based on the indirect solution of the open-loop optimal control problem. Firstly, an adequate dynamic system modeling is considered with respect to a configuration of a commercial quadrotor helicopter. The model predicts the effect of the thrust and torques induced by the four propellers on the quadrotor motion. Quadcopter dynamics is described by differential equations that have been derived by using the Newton–Euler method. Then, a path planning algorithm is developed to find the optimal trajectories that meet various objective functions, such as fuel efficiency, and guarantee the flight stability and high-speed operation. Typically, the necessary condition of optimality for a constrained optimal control problem is formulated as a standard form of a two-point boundary-value problem using Pontryagin’s minimum principle. One advantage of the proposed method can solve a wide range of optimal maneuvers for arbitrary initial and final states relevant to every considered cost function. In order to verify the effectiveness of the presented algorithm, several simulation and experiment studies are carried out for finding the optimal path between two points with different objective functions by using MATLAB software. The results clearly show the effect of the proposed approach on the quadrotor systems.

Cosine Second Order Robot Trajectory Planning Method

2011 ◽  
Vol 80-81 ◽  
pp. 1075-1080
Author(s):  
Zong Wu Xie ◽  
Cao Li ◽  
Hong Liu
Keyword(s):  
Path Planning ◽  
Trajectory Planning ◽  
Trajectory Tracking ◽  
Joint Space ◽  
Planning Method ◽  
Robot Trajectory ◽  
Great Performance ◽  
Planning Methods ◽  
Planning Algorithm ◽  
Path Planning Algorithm

A new joint space trajectory planning method for the series robot is proposed. Comparing with the traditional path planning methods which can only guarantee the planned trajectory velocity or acceleration continuous, the proposed trajectory planning algorithm can also ensure the derivative of acceleration (Jerk) continuous within a limit threshold. At the end of this paper, the proposed path planning algorithm is validated of having a great performance on robot trajectory tracking.

A Novel Static Path Planning Method for Mobile Anchor-Assisted Localization in Wireless Sensor Networks

2020 ◽  
Vol 10 ◽  
Author(s):  
Abdelhady M. Naguib ◽  
Shahzad Ali
Keyword(s):  
Wireless Sensor Networks ◽  
Sensor Networks ◽  
Path Planning ◽  
Sensor Node ◽  
Large Scale ◽  
Performance Metrics ◽  
Wireless Sensor ◽  
Anchor Node ◽  
Mobile Anchor ◽  
Planning Methods

Background: Many applications of Wireless Sensor Networks (WSNs) require awareness of sensor node’s location but not every sensor node can be equipped with a GPS receiver for localization, due to cost and energy constraints especially for large-scale networks. For localization, many algorithms have been proposed to enable a sensor node to be able to determine its location by utilizing a small number of special nodes called anchors that are equipped with GPS receivers. In recent years a promising method that significantly reduces the cost is to replace the set of statically deployed GPS anchors with one mobile anchor node equipped with a GPS unit that moves to cover the entire network. Objectives: This paper proposes a novel static path planning mechanism that enables a single anchor node to follow a predefined static path while periodically broadcasting its current location coordinates to the nearby sensors. This new path type is called SQUARE_SPIRAL and it is specifically designed to reduce the collinearity during localization. Results: Simulation results show that the performance of SQUARE_SPIRAL mechanism is better than other static path planning methods with respect to multiple performance metrics. Conclusion: This work includes an extensive comparative study of the existing static path planning methods then presents a comparison of the proposed mechanism with existing solutions by doing extensive simulations in NS-2.

scholarly journals On the optimal control of coronavirus (2019-nCov) mathematical model; a numerical approach

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
N. H. Sweilam ◽  
S. M. Al-Mekhlafi ◽  
A. O. Albalawi ◽  
D. Baleanu
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Weighted Average ◽  
Necessary Optimality Conditions ◽  
Numerical Approach ◽  
Population Number ◽  
Infected People ◽  
The Stability ◽  
Novel Coronavirus ◽  
Theoretical Results

Abstract In this paper, a novel coronavirus (2019-nCov) mathematical model with modified parameters is presented. This model consists of six nonlinear fractional order differential equations. Optimal control of the suggested model is the main objective of this work. Two control variables are presented in this model to minimize the population number of infected and asymptotically infected people. Necessary optimality conditions are derived. The Grünwald–Letnikov nonstandard weighted average finite difference method is constructed for simulating the proposed optimal control system. The stability of the proposed method is proved. In order to validate the theoretical results, numerical simulations and comparative studies are given.

scholarly journals Adaptive Optimal Robust Control for Uncertain Nonlinear Systems Using Neural Network Approximation in Policy Iteration

2021 ◽  
Vol 11 (5) ◽  
pp. 2312
Author(s):  
Dengguo Xu ◽  
Qinglin Wang ◽  
Yuan Li
Keyword(s):  
Neural Network ◽  
Optimal Control ◽  
Robust Control ◽  
Nonlinear Systems ◽  
Policy Iteration ◽  
Control Law ◽  
Globally Asymptotically Stable ◽  
Control Approach ◽  
Input Uncertainties ◽  
Theoretical Results

In this study, based on the policy iteration (PI) in reinforcement learning (RL), an optimal adaptive control approach is established to solve robust control problems of nonlinear systems with internal and input uncertainties. First, the robust control is converted into solving an optimal control containing a nominal or auxiliary system with a predefined performance index. It is demonstrated that the optimal control law enables the considered system globally asymptotically stable for all admissible uncertainties. Second, based on the Bellman optimality principle, the online PI algorithms are proposed to calculate robust controllers for the matched and the mismatched uncertain systems. The approximate structure of the robust control law is obtained by approximating the optimal cost function with neural network in PI algorithms. Finally, in order to illustrate the availability of the proposed algorithm and theoretical results, some numerical examples are provided.

Robot Trajectory Planning Using Rational Frenet-Serret Curves

Volume 2 ◽  
2004 ◽  
Author(s):  
Reza Ravani ◽  
Ali Meghdari
Keyword(s):  
Trajectory Planning ◽  
Computer Animation ◽  
Rational Curves ◽  
Robot Arm ◽  
Robot Trajectory ◽  
Arm Motion ◽  
Sweep Surface ◽  
And Robotics ◽  
Rotation Minimizing Frame ◽  
Robot Trajectory Planning

The aim of this paper is to demonstrate that the techniques of Computer Aided Geometric Design such as spatial rational curves and surfaces could be applied to Kinematics, Computer Animation and Robotics. For this purpose we represent a method which utilizes a special class of rational curves called Rational Frenet-Serret (RF) [8] curves for robot trajectory planning. RF curves distinguished by the property that the motion of their Frenet-Serret frame is rational. We describe an algorithm for interpolation of positions by a rational Frenet-Serret motion. Further more we provide an analysis on spatial frames (Frenet-Serret frame and Rotation Minimizing frame) for smooth robot arm motion and investigate their applications in sweep surface modeling.

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