scholarly journals Minimum-jerk trajectory planning pertaining to a translational 3-degree-of-freedom parallel manipulator through piecewise quintic polynomials interpolation

2020 ◽  
Vol 12 (3) ◽  
pp. 168781402091366 ◽  
Author(s):  
Song Lu ◽  
Bingxiao Ding ◽  
Yangmin Li
Keyword(s):  
Trajectory Planning ◽  
Virtual Work ◽  
Angular Position ◽  
Programming Algorithm ◽  
Planning Problem ◽  
Typical Application ◽  
Parallel Kinematic Manipulator ◽  
Minimum Jerk ◽  
Planning Approach ◽  
Parallel Kinematic

This article aims to present a minimum-jerk trajectory planning approach to address the smooth trajectory generation problem of 3-prismatic-universal-universal translational parallel kinematic manipulator. First, comprehensive kinematics and dynamics characteristics of this 3-prismatic-universal-universal parallel kinematic manipulator are analyzed by virtue of the accepted link Jacobian matrices and proverbial virtual work principle. To satisfy indispensable continuity and smoothness requirements, the discretized piecewise quintic polynomials are employed to interpolate the sequence of joints’ angular position knots which are transformed from these predefined via-points in Cartesian space. Furthermore, the trajectory planning problem is directly converted into a constrained nonlinear multi-variables optimization problem of which objective function is to minimize the maximum of the joints’ angular jerk throughout the whole trajectory. Finally, two typical application simulations using the reliable sequential quadratic programming algorithm demonstrate that this proposed minimum-jerk trajectory planning approach is of explicit feasibility and appreciable effectiveness.

Minimum jerk for trajectory planning and control

Robotica ◽  
1994 ◽  
Vol 12 (2) ◽  
pp. 109-113 ◽  
Author(s):  
K.J. Kyriakopoulos ◽  
G.N. Saridis
Keyword(s):  
Trajectory Planning ◽  
Tracking Control ◽  
Optimization Problem ◽  
Control Algorithms ◽  
Planning Problem ◽  
Cartesian Space ◽  
Planning And Control ◽  
Minimum Jerk ◽  
And Control ◽  
Trajectory Planning And Control

SUMMARYIt has been experimentally verified that the jerk of the desired trajectory adversely affects the performance of the tracking control algorithms for robotic manipulators. In this paper, we investigate the reasons behind this effect, and state the trajectory planning problem as an optimization problem that minimizes a norm of joint jerk over a prespecified Cartesian space trajectory. The necessary conditions are derived and a numerical algorithm is presented.

scholarly journals Human-Machine Cooperative Trajectory Planning for Semi-Autonomous Driving Based on the Understanding of Behavioral Semantics

Electronics ◽  
2021 ◽  
Vol 10 (8) ◽  
pp. 946
Author(s):  
Bohan Jiang ◽  
Xiaohui Li ◽  
Yujun Zeng ◽  
Daxue Liu
Keyword(s):  
Decision Making ◽  
Trajectory Planning ◽  
Autonomous Driving ◽  
Planning Problem ◽  
Decision Level ◽  
Planning Approach ◽  
Decision Making Problem ◽  
Generation Level ◽  
High Level ◽  
Real Vehicle

This paper presents a novel cooperative trajectory planning approach for semi-autonomous driving. The machine interacts with the driver at the decision level and the trajectory generation level. To minimize conflicts between the machine and the human, the trajectory planning problem is decomposed into a high-level behavior decision-making problem and a low-level trajectory planning problem. The approach infers the driver’s behavioral semantics according to the driving context and the driver’s input. The trajectories are generated based on the behavioral semantics and driver’s input. The feasibility of the proposed approach is validated by real vehicle experiments. The results prove that the proposed human–machine cooperative trajectory planning approach can successfully help the driver to avoid collisions while respecting the driver’s behavior.

Optimal Trajectory Planning for Redundant Manipulators Based on Minimum Jerk

2008 ◽  
Author(s):  
Jingzhou Yang ◽  
Joo Kim ◽  
Esteban Pena Pitarch ◽  
Karim Abdel-Malek
Keyword(s):  
Trajectory Planning ◽  
Degrees Of Freedom ◽  
Initial Point ◽  
Planning Problem ◽  
Optimization Approach ◽  
Control Points ◽  
Unknown Parameters ◽  
Spline Curve ◽  
Minimum Jerk ◽  
Optimal Trajectory Planning

This paper presents an optimization-based method to solve the smooth trajectory planning problem where the user knows only the start and end points of the end-effector or the via point plus the start and end target points. For the start and end target points, we use an optimization approach to determine the manipulator configurations. Having obtained the desired minimum jerk path in the Cartesian space using the minimum jerk theory and having represented each joint motion by the third-degree B-spline curve with unknown parameters (i.e., control points), an optimization approach, rather than the pseudoinverse technique for inverse kinematics, is used to calculate the control points of each joint spline curve. The objective function includes several parts: (a) dynamic effort; (b) the inconsistency function, which is the joint rate change (first derivative) and predicted overall trend from the initial point to the end point; and (c) the nonsmoothness function of the trajectory, which is the second derivative of the joint trajectory. This method can be used for robotic manipulators with any number of degrees of freedom. Minimum jerk trajectories are desirable for their similarity to human joint movements, for their amenability to limit robot vibrations, and for their control (i.e., enhancement of control performance). Illustrative examples are presented to demonstrate the method.

Minimum Jerk Trajectory Planning of PUMA560 with Intelligent Computation using ANN

2021 ◽  
Author(s):  
M Aruna Devi ◽  
C P S Prakash ◽  
Praveen D Jadhav ◽  
Prajwal S Hebbar ◽  
Mohammed Mohsin ◽  
...  
Keyword(s):  
Trajectory Planning ◽  
Minimum Jerk

Optimum Path Planning for Mechanical Manipulators

1981 ◽  
Vol 103 (2) ◽  
pp. 142-151 ◽  
Author(s):  
J. Y. S. Luh ◽  
C. S. Lin
Keyword(s):  
Path Planning ◽  
Feasible Solution ◽  
Computing Time ◽  
Inequality Constraints ◽  
Programming Algorithm ◽  
Planning Problem ◽  
Linear Inequality Constraints ◽  
Nonlinear Inequality ◽  
Angular Velocities ◽  
Nonlinear Inequality Constraints

To assure a successful completion of an assigned task without interruption, such as the collision with fixtures, the hand of a mechanical manipulator often travels along a preplanned path. An advantage of requiring the path to be composed of straight-line segments in Cartesian coordinates is to provide a capability for controlled interaction with objects on a moving conveyor. This paper presents a method of obtaining a time schedule of velocities and accelerations along the path that the manipulator may adopt to obtain a minimum traveling time, under the constraints of composite Cartesian limit on linear and angular velocities and accelerations. Because of the involvement of a linear performance index and a large number of nonlinear inequality constraints, which are generated from physical limitations, the “method of approximate programming (MAP)” is applied. Depending on the initial choice of a feasible solution, the iterated feasible solution, however, does not converge to the optimum feasible point, but is often entrapped at some other point of the boundary of the constraint set. To overcome the obstacle, MAP is modified so that the feasible solution of each of the iterated linear programming problems is shifted to the boundaries corresponding to the original, linear inequality constraints. To reduce the computing time, a “direct approximate programming algorithm (DAPA)” is developed, implemented and shown to converge to optimum feasible solution for the path planning problem. Programs in FORTRAN language have been written for both the modified MAP and DAPA, and are illustrated by a numerical example for the purpose of comparison.

scholarly journals A New Methodology for Solving Trajectory Planning and Dynamic Load-Carrying Capacity of a Robot Manipulator

2016 ◽  
Vol 2016 ◽  
pp. 1-28 ◽  
Author(s):  
Wanjin Guo ◽  
Ruifeng Li ◽  
Chuqing Cao ◽  
Xunwei Tong ◽  
Yunfeng Gao
Keyword(s):  
Trajectory Planning ◽  
Dynamic Load ◽  
Carrying Capacity ◽  
Robot Manipulator ◽  
Time Interval ◽  
Planning Problem ◽  
Load Carrying Capacity ◽  
Objective Functions ◽  
Decision Variables ◽  
Load Carrying

A new methodology using a direct method for obtaining the best found trajectory planning and maximum dynamic load-carrying capacity (DLCC) is presented for a 5-degree of freedom (DOF) hybrid robot manipulator. A nonlinear constrained multiobjective optimization problem is formulated with four objective functions, namely, travel time, total energy involved in the motion, joint jerks, and joint acceleration. The vector of decision variables is defined by the sequence of the time-interval lengths associated with each two consecutive via-points on the desired trajectory of the 5-DOF robot generalized coordinates. Then this vector of decision variables is computed in order to minimize the cost function (which is the weighted sum of these four objective functions) subject to constraints on joint positions, velocities, acceleration, jerks, forces/torques, and payload mass. Two separate approaches are proposed to deal with the trajectory planning problem and the maximum DLCC calculation for the 5-DOF robot manipulator using an evolutionary optimization technique. The adopted evolutionary algorithm is the elitist nondominated sorting genetic algorithm (NSGA-II). A numerical application is performed for obtaining best found solutions of trajectory planning and maximum DLCC calculation for the 5-DOF hybrid robot manipulator.

Optimization in Trajectory Planning of Multi-Jointed Fingers in Dextrous Hand Designs

1991 ◽  
Author(s):  
A. Meghdari ◽  
H. Sayyaadi
Keyword(s):  
Dynamic Programming ◽  
Motion Control ◽  
Trajectory Planning ◽  
Degrees Of Freedom ◽  
Optimization Technique ◽  
Dynamic Programming Algorithm ◽  
Programming Algorithm ◽  
Kinematics And Dynamics ◽  
Feasible Solutions ◽  
Dextrous Hand

Abstract An optimization technique based on the well known Dynamic Programming Algorithm is applied to the motion control trajectories and path planning of multi-jointed fingers in dextrous hand designs. A three fingered hand with each finger containing four degrees of freedom is considered for analysis. After generating the kinematics and dynamics equations of such a hand, optimum values of the joints torques and velocities are computed such that the finger-tips of the hand are moved through their prescribed trajectories with the least time or/and energy to reach the object being grasped. Finally, optimal as well as feasible solutions for the multi-jointed fingers are identified and the results are presented.

scholarly journals Trajectory Planning in UAV Emergency Networks with Potential Underlaying D2D Communication Based on K-means

2021 ◽  
Author(s):  
Shuo Zhang ◽  
Shuo Shi ◽  
Tianming Feng ◽  
Xuemai Gu
Keyword(s):  
Trajectory Planning ◽  
Communication Systems ◽  
High Speed ◽  
Large Scale ◽  
High Reliability ◽  
Base Station ◽  
Planning Problem ◽  
Communication Signal ◽  
User Coverage ◽  
Trajectory Length

Abstract Unmanned aerial vehicles (UAVs) have been widely used in communication systems due to excellent maneuverability and mobility. The ultra-high speed, ultra-low latency, and ultra-high reliability of 5th generation wireless systems (5G) have further promoted vigorous development of UAVs. Compared with traditional means of communication, UAV can provide services for ground terminal without time and space constraints, so it is often used as air base station (BS). Especially in emergency communications and rescue, it provides temporary communication signal coverage service for disaster areas. In the face of large-scale and scattered user coverage tasks, UAV's trajectory is an important factor affecting its energy consumption and communication performance. In this paper, we consider a UAV emergency communication network where UAV aims to achieve complete coverage of potential underlying D2D users (DUs). The trajectory planning problem is transformed into the deployment and connection problem of stop points (SPs). Aiming at trajectory length and sum throughput, two trajectory planning algorithms based on K-means are proposed. Due to the non-convexity of sum throughput optimization, we present a sub-optimal solution by using the successive convex approximation (SCA) method. In order to balance the relationship between trajectory length and sum throughput, we propose a joint evaluation index which is used as an objective function to further optimize trajectory. Simulation results show the validity of the proposed algorithms which have advantages over the well-known benchmark scheme in terms of trajectory length and sum throughput.

Sign in / Sign up

Export Citation Format

Share Document