Optimal Path Planning of Redundant Cooperative Robots Under Equality and Inequality Constraints

2003 ◽  
Author(s):  
Ali Hosseini ◽  
Mehdi Keshmiri
Keyword(s):  
Path Planning ◽  
Optimization Problem ◽  
Search Algorithm ◽  
Minimum Principle ◽  
Optimal Path ◽  
Inequality Constraints ◽  
Optimal Path Planning ◽  
Nonlinear Inequality ◽  
Nonlinear Inequality Constraints ◽  
Cooperative Manipulators

Using kinematic resolution, the optimal path planning for two redundant cooperative manipulators carrying a solid object on a desired trajectory is studied. The optimization problem is first solved with no constraint. Consequently, the nonlinear inequality constraints, which model obstacles, are added to the problem. The formulation has been derived using Pontryagin Minimum Principle and results in a Two Point Boundary Value Problem (TPBVP). The problem is solved for a cooperative manipulator system consisting of two 3-DOF serial robots jointly carrying an object and the results are compared with those obtained from a search algorithm. Defining the obstacles in workspace as functions of joint space coordinates, the inequality constrained optimization problem is solved for the cooperative manipulators.

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.

Target Estimate PDF-Based Optimal Path Planning Algorithm With Application to UAV Systems

2010 ◽  
Author(s):  
Jared G. Wood ◽  
Benjamin Kehoe ◽  
J. Karl Hedrick
Keyword(s):  
Path Planning ◽  
Optimization Problem ◽  
Optimal Path ◽  
Finite Horizon ◽  
Path Optimization ◽  
Optimal Path Planning ◽  
Planning Algorithm ◽  
Local Path ◽  
Path Planning Algorithm ◽  
Insight Into

Companies are starting to explore investing in UAV systems that come with standard autopilot trackers. There is a need for general cooperative local path planning algorithms that function with these types of systems. We have recently finished a project in which algorithms for autonomously searching for, detecting, and tracking ground targets was developed for a fixed-wing UAV with a visual spectrum gimballed camera. A set of scenarios are identified in which finite horizon path optimization results in a non-optimal ineffective path. For each of these scenarios, an appropriate path optimization problem is defined to replace finite horizon optimization. An algorithm is presented that determines which path optimization should be performed given a UAV state and target estimate probability distribution. The algorithm was implemented and thoroughly tested in flight experiments. The experimental work was successful and gave insight into what is required for a path planning algorithm to robustly work with standard waypoint tracking UAV systems. This paper presents the algorithm that was developed, theory supporting the algorithm, and experimental results.

scholarly journals Optimal Path Planning using Informed Probabilistic Road Map Algorithm

2021 ◽  
Author(s):  
Muhammad Aria ◽  
Keyword(s):  
Path Planning ◽  
Local Search ◽  
Search Algorithm ◽  
Optimal Path ◽  
Local Search Algorithm ◽  
Optimal Path Planning ◽  
Road Map ◽  
Planning Algorithm ◽  
Sample Points ◽  
Path Planning Algorithm

This study aims to propose a new path planning algorithm that can guarantee the optimal path solution. The method used is to hybridize the Probabilistic Road Map (PRM) algorithm with the Information Search Algorithm. This hybridization algorithm is called the Informed-PRM algorithm. There are two informed search methods used. The first method is the informed sampling through an ellipsoid subset whose eccentricity is dependent on the length of the shortest current solution that is successfully planned in that iteration. The second method is to use a local search algorithm. The basic PRM algorithm will be run in the first iteration. Since the second iteration, the generation of sample points in the PRM algorithm will be carried out based on information. The informed sampling method will be used to generate 50% of the sampling points. Meanwhile, the remaining number of sample points will be generated using a local search algorithm. Using several benchmark cases, we compared the performance of the Informed-PRM algorithm with the Rapidly Exploring Random Tree* (RRT*) and informed RRT* algorithm. The test results show that the Informed-PRM algorithm successfully constructs the nearly optimal path for all given cases. In producing the path, the time and path cost of the Informed-PRM algorithm is better than the RRT* and Informed RRT* algorithm. The Friedman test was then performed to check for the significant difference in performance between Informed-PRM with RRT* and Informed RRT*. Thus, the Informed-PRM algorithm can be implemented in various systems that require an optimal path planning algorithm, such as in the case of medical robotic surgery or autonomous vehicle systems.

scholarly journals Time-optimal Path Planning of Multi-axis CNC Processes Using Variability of Orientation

Procedia CIRP ◽  
2021 ◽  
Vol 96 ◽  
pp. 324-329
Author(s):  
Frederik Wulle ◽  
Max Richter ◽  
Christoph Hinze ◽  
Alexander Verl
Keyword(s):  
Path Planning ◽  
Optimal Path ◽  
Optimal Path Planning ◽  
Time Optimal

scholarly journals A CNN-based scheme for COVID-19 detection with emergency services provisions using an optimal path planning

2021 ◽  
Author(s):  
Ahmed Barnawi ◽  
Prateek Chhikara ◽  
Rajkumar Tekchandani ◽  
Neeraj Kumar ◽  
Mehrez Boulares
Keyword(s):  
Path Planning ◽  
Emergency Services ◽  
Optimal Path ◽  
Optimal Path Planning
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