Trajectory Planning of Cable-Suspended Parallel Robots Using Interval Positive-Definite Polynomials

2012 ◽  
Author(s):  
Ping Ren ◽  
Clément Gosselin
Keyword(s):  
Trajectory Planning ◽  
Inequality Constraints ◽  
Positive Definite ◽  
Parallel Robots ◽  
Planning Problem ◽  
Final States ◽  
Time Duration ◽  
Algebraic Investigation ◽  
Point To Point ◽  
Parametric Polynomials

In this paper, the dynamic point-to-point trajectory planning of cable-suspended robots is investigated. A simple planar two-degree-of-freedom (2-dof) robot is used to demonstrate the technique. In order to maintain the cables’ positive tension, a set of algebraic inequalities is derived from the dynamic model of the 2-dof robot. The trajectories are defined using parametric polynomials with the coefficients determined by the prescribed initial and final states, and the variable time duration. With the polynomials substituted into the inequality constraints, the planning problem is then converted into an algebraic investigation on how the coefficients of the polynomials will affect the number of real roots over a given interval. An analytical approach based on a polynomial’s Discrimination Matrix and Discriminant Sequence is proposed to solve the problem. It is shown that, by adjusting the time duration within appropriate ranges, it is possible to find positive-definite polynomials such that the polynomial-based trajectories always satisfy the inequality constraints of the dynamic system. Feasible dynamic trajectories that are able to travel both beyond and within the static workspace will exploit more potential of the cable-suspended robotic platform.

Dynamic Point-To-Point Trajectory Planning for Three Degrees-of-Freedom Cable-Suspended Parallel Robots Using Rapidly Exploring Random Tree Search

2020 ◽  
Vol 12 (4) ◽  
Author(s):  
Sheng Xiang ◽  
Haibo Gao ◽  
Zhen Liu ◽  
Clément Gosselin
Keyword(s):  
Trajectory Planning ◽  
Degrees Of Freedom ◽  
Parallel Robots ◽  
Tree Search ◽  
Planning Techniques ◽  
Motion Primitive ◽  
Planning Technique ◽  
Point To Point ◽  
Three Degrees Of Freedom ◽  
Specific Distance

Abstract This paper proposes a dynamic point-to-point trajectory planning technique for three degrees-of-freedom (DOFs) cable-suspended parallel robots. The proposed technique is capable of generating feasible multiple-swing trajectories that reach points beyond the footprint of the robot. Tree search algorithms are used to automatically determine a sequence of intermediate points to enhance the versatility of the planning technique. To increase the efficiency of the tree search, a one-swing motion primitive and a steering motion primitive are designed based on the dynamic model of the robot. Closed-form expressions for the motion primitives are given, and a corresponding rapid feasibility check process is proposed. An energy-based metric is used to estimate the distance in the Cartesian space between two points of a dynamic point-to-point task, and this system’s specific distance metric speeds up the coverage. The proposed technique is evaluated using a series of Monte Carlo runs, and comparative statistics results are given. Several example trajectories are presented to illustrate the approach. The results are compared with those obtained with the existing state-of-the-art methods, and the proposed technique is shown to be more general compared to previous analytical planning techniques while generating smoother trajectories than traditional rapidly exploring randomized tree (RRT) methods.

Smooth point-to-point trajectory planning for robot manipulators by using radial basis functions

Robotica ◽  
2018 ◽  
Vol 37 (3) ◽  
pp. 539-559 ◽  
Author(s):  
Taha Chettibi
Keyword(s):  
Radial Basis Functions ◽  
Trajectory Planning ◽  
Robot Manipulators ◽  
Smooth Point ◽  
Basis Functions ◽  
Minimum Time ◽  
Planning Problem ◽  
Planning Techniques ◽  
Radial Basis ◽  
Point To Point

SUMMARYThe paper introduces the use of radial basis functions (RBFs) to generate smooth point-to-point joint trajectories for robot manipulators. First, Gaussian RBF interpolation is introduced taking into account boundary conditions. Then, the proposed approach is compared with classical planning techniques based on polynomial and trigonometric models. Also, the trajectory planning problem involving via-points is solved using the proposed RBF interpolation technique. The obtained trajectories are then compared with those synthesized using algebraic and trigonometric splines. Finally, the proposed method is tested for the six-joint PUMA 560 robot in two cases (minimum time and minimum time-jerk) and results are compared with those of other planning techniques. Numerical results demonstrate the advantage of the proposed technique, offering an effective solution to generate trajectories with short execution time and smooth profile.

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.

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.

scholarly journals Trajectory optimization of UAV based on Hp-adaptive Radau pseudospectral method

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yi Cui ◽  
Xintong Fang ◽  
Gaoqi Liu ◽  
Bin Li
Keyword(s):  
Trajectory Planning ◽  
Trajectory Optimization ◽  
Optimization Problem ◽  
Tracking Error ◽  
Pseudospectral Method ◽  
Planning Problem ◽  
A Algorithm ◽  
Planning Scheme ◽  
Path Search ◽  
Simulation Results

<p style='text-indent:20px;'>Unmanned Aerial Vehicles (UAVs) have been extensively studied to complete the missions in recent years. The UAV trajectory planning is an important area. Different from the commonly used methods based on path search, which are difficult to consider the UAV state and dynamics constraints, so that the planned trajectory cannot be tracked completely. The UAV trajectory planning problem is considered as an optimization problem for research, considering the dynamics constraints of the UAV and the terrain obstacle constraints during flight. An hp-adaptive Radau pseudospectral method based UAV trajectory planning scheme is proposed by taking the UAV dynamics into account. Numerical experiments are carried out to show the effectiveness and superior of the proposed method. Simulation results show that the proposed method outperform the well-known RRT* and A* algorithm in terms of tracking error.</p>

Trajectory Planning for Concrete Pump Truck Based on Intelligent Hill Climbing and Genetic Algorithm

2011 ◽  
Vol 127 ◽  
pp. 360-367 ◽  
Author(s):  
Xiao Dong Kang ◽  
Gang Huang ◽  
Xian Li Cao ◽  
Xiang Zhou
Keyword(s):  
Genetic Algorithm ◽  
Trajectory Planning ◽  
Performance Comparison ◽  
Hill Climbing ◽  
Planning Problem ◽  
Online Planning ◽  
And Performance ◽  
Concrete Pump Truck ◽  
Concrete Pump ◽  
Constrained Conditions

This paper takes the five –link concrete pump boom as the research object, and transforms its trajectory planning issue into a multi-object optimization problem. Using intelligent hill climbing algorithm and genetic algorithm, and integrating them closely to ensure real-time online planning for the pump truck effectively, and make the planned motion trajectory for the boom is global optimized under particular constrained conditions. Simulation and performance comparison experiments show that this hybrid algorithm is practical and effective, which offers a new approach for the trajectory planning problem of concrete pump truck.

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