Distance Calculations in Motion Planning Problems With Interference Situations

1990 ◽  
Author(s):  
C. Y. Liu ◽  
R. W. Mayne
Keyword(s):  
Quadratic Form ◽  
Convex Polyhedron ◽  
Linear Inequality ◽  
Convex Bodies ◽  
Three Dimensional ◽  
Robot Path Planning ◽  
Contact Distance ◽  
Swept Volume ◽  
Planning Problems ◽  
Robot Path

Abstract This paper discusses distance calculations for three dimensional polyhedra with the assumption of convex bodies. An n-surface convex polyhedron is viewed as the intersection of n half-spaces and is represented by n linear inequality equations while the square of the distance between two points is of a quadratic form in terms of two sets of x-y-z coordinates. The static distance-to-contact between two non-interfering convex polyhedral shapes is then directly solvable by quadratic programming. Based on the concept of distance-past-contact, distance calculations for situations with interference are presented and tested in optimization based robot path planning examples. The distance evaluation is further investigated for the dynamic situations by a swept volume computation strategy. The approach is illustrated in examples with a moving robot link and a fixed obstacle.

An Approach to Dynamic Distance Calculations for Obstacle Avoidance Problems

1991 ◽  
Author(s):  
C. Y. Liu ◽  
W. R. Chen ◽  
R. W. Mayne
Keyword(s):  
Motion Planning ◽  
Calculation Method ◽  
Two Dimensional ◽  
Robot Path Planning ◽  
Distance Calculation ◽  
Approach Distance ◽  
Quadratic Programming Method ◽  
Swept Volume ◽  
Planning Problems ◽  
Robot Path

Abstract This paper presents a distance calculation method which can be used in machine motion planning optimizations where interference is a concern. Dynamic distance calculations are discussed which use the quadratic programming method combined with an approximate swept volume approach. Distance-to-contact calculations can be obtained for both interference and non-interference situations. The swept volume of a moving polygon is constructed through a series of overlapped swept volume segments. Each of the swept volume segments is efficiently developed by checking the inner products of polygon outward boundary normals with velocity vectors for polygon vertices. Two dimensional examples of distance-to-contact computations and robot path planning problems are presented for a sample three link robot with three rotational joints.

Robot Path Planning and Obstacle Avoidance: A Design Optimization Approach

1989 ◽  
Author(s):  
E. Sandgren ◽  
S. Venkataraman
Keyword(s):  
Path Planning ◽  
Design Optimization ◽  
Dynamic Programming Algorithm ◽  
Three Dimensional ◽  
Programming Algorithm ◽  
Optimization Approach ◽  
Robot Arm ◽  
Robot Path Planning ◽  
Real Time Control ◽  
Robot Path

Abstract A design optimization approach to robot path planning in a two dimensional workplace is presented. Obstacles are represented as a series of rectangular regions and collision detection is performed by an operation similar to clipping in computer graphics. The feasible design space is approximated by a discrete set of robot arm and gripper positions. Control is applied directly through the angular motion of each link. Feasible positions which are located between the initial and final robot link positions are grouped into stages. A dynamic programming algorithm is applied to locate the best state within each stage which minimizes the overall path length. An example is presented involving a three link planar manipulator. Extensions to three dimensional robot path planning and real time control in a dynamically changing workplace are discussed.

Three Dimensional Robot Path Planning With Workspace Considerations

1992 ◽  
Author(s):  
C. Y. Liu ◽  
R. W. Mayne
Keyword(s):  
Path Planning ◽  
Three Dimensional ◽  
Optimization Methods ◽  
Planning Problem ◽  
Robot Path Planning ◽  
Recursive Quadratic Programming ◽  
Six Degree Of Freedom ◽  
Nonlinear Programming Method ◽  
Path Planning Problem ◽  
Robot Path

Abstract This paper considers the problem of robot path planning by optimization methods. It focuses on the use of recursive quadratic programming (RQP) for the optimization process and presents a formulation of the three dimensional path planning problem developed for compatibility with the RQP selling. An approach 10 distance-to-contact and interference calculations appropriate for RQP is described as well as a strategy for gradient computations which are critical to applying any efficient nonlinear programming method. Symbolic computation has been used for general six degree-of-freedom transformations of the robot links and to provide analytical derivative expressions. Example problems in path planning are presented for a simple 3-D robot. One example includes adjustments in geometry and introduces the concept of integrating 3-D path planning with geometric design.

Path Planning in a Mobile Robot

2019 ◽  
pp. 582-608
Author(s):  
Diego Alexander Tibaduiza Burgos ◽  
Maribel Anaya Vejar
Keyword(s):  
Genetic Algorithms ◽  
Path Planning ◽  
Mobile Robot ◽  
Fitness Function ◽  
Experimental Setup ◽  
Robot Path Planning ◽  
Natural Evolution ◽  
On Line ◽  
Planning Problems ◽  
Robot Path

This chapter presents the development and implementation of three approaches that contribute to solving the mobile robot path planning problems in dynamic and static environments. The algorithms include some items regarding the implementation of on-line and off-line situations in an environment with static and mobile obstacles. A first technique involves the use of genetic algorithms where a fitness function and the emulation of the natural evolution are used to find a free-collision path. The second and third techniques consider the use of potential fields for path planning using two different ways. Brief descriptions of the techniques and experimental setup used to test the algorithms are also included. Finally, the results applying the algorithms using different obstacle configurations are presented and discussed.

Pigeon-inspired optimization: a new swarm intelligence optimizer for air robot path planning

2014 ◽  
Vol 7 (1) ◽  
pp. 24-37 ◽  
Author(s):  
Haibin Duan ◽  
Peixin Qiao
Keyword(s):  
Path Planning ◽  
Swarm Intelligence ◽  
Implementation Process ◽  
Robot Path Planning ◽  
Operator Model ◽  
Content Type ◽  
De Algorithm ◽  
The Mathematical Model ◽  
Planning Problems ◽  
Robot Path

Purpose – The purpose of this paper is to present a novel swarm intelligence optimizer — pigeon-inspired optimization (PIO) — and describe how this algorithm was applied to solve air robot path planning problems. Design/methodology/approach – The formulation of threat resources and objective function in air robot path planning is given. The mathematical model and detailed implementation process of PIO is presented. Comparative experiments with standard differential evolution (DE) algorithm are also conducted. Findings – The feasibility, effectiveness and robustness of the proposed PIO algorithm are shown by a series of comparative experiments with standard DE algorithm. The computational results also show that the proposed PIO algorithm can effectively improve the convergence speed, and the superiority of global search is also verified in various cases. Originality/value – In this paper, the authors first presented a PIO algorithm. In this newly presented algorithm, map and compass operator model is presented based on magnetic field and sun, while landmark operator model is designed based on landmarks. The authors also applied this newly proposed PIO algorithm for solving air robot path planning problems.

Path Planning in a Mobile Robot

2013 ◽  
pp. 123-147
Author(s):  
Diego Alexander Tibaduiza Burgos ◽  
Maribel Anaya Vejar
Keyword(s):  
Genetic Algorithms ◽  
Path Planning ◽  
Mobile Robot ◽  
Fitness Function ◽  
Experimental Setup ◽  
Robot Path Planning ◽  
Natural Evolution ◽  
On Line ◽  
Planning Problems ◽  
Robot Path

This chapter presents the development and implementation of three approaches that contribute to solving the mobile robot path planning problems in dynamic and static environments. The algorithms include some items regarding the implementation of on-line and off-line situations in an environment with static and mobile obstacles. A first technique involves the use of genetic algorithms where a fitness function and the emulation of the natural evolution are used to find a free-collision path. The second and third techniques consider the use of potential fields for path planning using two different ways. Brief descriptions of the techniques and experimental setup used to test the algorithms are also included. Finally, the results applying the algorithms using different obstacle configurations are presented and discussed.

Dynamic direct subspaces for robot path planning

Robotica ◽  
1987 ◽  
Vol 5 (1) ◽  
pp. 29-36 ◽  
Author(s):  
W. E. Red ◽  
K. H. Kim
Keyword(s):  
Path Planning ◽  
Machine Tools ◽  
Three Dimensional ◽  
Joint Space ◽  
Automated Guided Vehicles ◽  
Robot Path Planning ◽  
Configuration Point ◽  
Dynamic Objects ◽  
Robot Configuration ◽  
Robot Path

SUMMARYA direct subspace of a dynamic three-dimensional joint space is found to be useful for robot path planning in workspaces comprised of both static and dynamic objects. Dynamic descriptions permit positioning tables, automated guided vehicles, conveyors and cycling machine tools to be modeled by elements which translate or cycle along rectilinear paths. Graphical path planning procedures use cursor indicators to move the robot configuration point between the desired starting and final configurations while avoiding both the static and dynamic joint space obstacles.

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