An approach to time-optimal, smooth and collision-free path planning in a two robot arm environment

Robotica ◽  
1996 ◽  
Vol 14 (1) ◽  
pp. 61-70 ◽  
Author(s):  
Bailin Cao ◽  
Gordon I. Dodds ◽  
George W. Irwin
Keyword(s):  
Path Planning ◽  
Free Path ◽  
Industrial Robot ◽  
Planning Problem ◽  
Robot Arm ◽  
Rates Of Change ◽  
Time Optimal ◽  
Time Optimality ◽  
Path Planning Problem ◽  
Effective Collision

SummaryAn approach to time-optimal smooth and collision-free path planning for two industrial robot arms is presented, where path planning and joint trajectory generation are integrated. A suitable objective function, combining the requirements of time optimality and path smoothness, is proposed, which is subject to the continuity of joint trajectories, limits on their rates of change and collision-free constraints. Fast and effective collision detection for the arms is achieved using the Kuhn- Tucker conditions along with the convexity of the distance function and relying on geometrical relationships between cylinders. Nonlinear optimization is used to solve this path planning problem. The feasibility of this method is illustrated both by simulation and by experimental results.

Path Planning for Spheres in Three Dimensional Environments With Low Interference Index

1994 ◽  
Author(s):  
Duane W. Storti ◽  
Debasish Dutta
Keyword(s):  
Path Planning ◽  
Free Path ◽  
Configuration Space ◽  
Local Knowledge ◽  
Three Dimensional ◽  
Target Point ◽  
Planning Problem ◽  
Spherical Object ◽  
Starting Point ◽  
Path Planning Problem

Abstract We consider the path planning problem for a spherical object moving through a three-dimensional environment composed of spherical obstacles. Given a starting point and a terminal or target point, we wish to determine a collision free path from start to target for the moving sphere. We define an interference index to count the number of configuration space obstacles whose surfaces interfere simultaneously. In this paper, we present algorithms for navigating the sphere when the interference index is ≤ 2. While a global calculation is necessary to characterize the environment as a whole, only local knowledge is needed for path construction.

A Collision-Free Path Planning Method for an Articulated Mobile Robot in a Free Environment

2005 ◽  
Author(s):  
Patricia Quintero-Alvarez ◽  
Gabriel Ramirez ◽  
Sai¨d Zeghloul
Keyword(s):  
Path Planning ◽  
Mobile Robot ◽  
Free Path ◽  
Velocity Space ◽  
Control Law ◽  
Planning Problem ◽  
Optimization Approach ◽  
Reference Velocity ◽  
Free Environment ◽  
Path Planning Problem

In our previous work, we have treated the collision-free path-planning problem for a nonholonomic mobile robot in a cluttered environment. The method we have used is based on a representation of the obstacles in the robot’s velocity space, called Feasible Velocities Polygon (FVP). Every obstacle in the robot’s influence zone is represented by a linear constraint over the robot’s velocities such that it could not be collision between the robot and the obstacle. These constraints define a convex subset in the velocity space, the FVP. Every velocity vector of the FVP ensures a safe motion for the given obstacle configuration. The path-planning problem is solved by an optimization approach between the FVP and a reference velocity to reach the goal. In this paper, we have extended our work to an articulated mobile robot. This robot is composed of a differential mobile robot as tractor and a trailer, linked by off-center joints. We have modified the reference velocity in order to consider the constraints imposed by the trailer over the robot’s velocities. The control law is a nonlinear control law, which is asymptotically stable to the goal. We use the virtual robot concept, to solve the stability problem when the robot and its trailer move backwards. An articulated mobile robot is a strongly constrained system. Even in a free environment, under some circumstances, the robot may get blocked by its trailer in its progression towards the goal. To solve these situations, we have developed a heuristic algorithm. This algorithm is based in human experience: when a blocking situation is detected, a forward-backward maneuver is made, in order to increase the distance between the tows until a maximal value. After this maneuver, the robot takes the path to the original goal. Some numerical results show that our method leads the robot and the trailer to the final position in a stable way.

Rough level path planning method for a robot using SOFM neural network

Robotica ◽  
1998 ◽  
Vol 16 (4) ◽  
pp. 415-423 ◽  
Author(s):  
Kimmo Pulakka ◽  
Veli Kujanpää
Keyword(s):  
Neural Network ◽  
Path Planning ◽  
Industrial Robot ◽  
Planning Method ◽  
Planning Problem ◽  
Test Results ◽  
Feature Map ◽  
Working Environments ◽  
Path Planning Problem

In this paper a path planning method for off-line programming of a joint robot is described. The method can automatically choose the easiest and safest route for an industrial robot from one position to another. The method is based on the use of a Self Organised Feature Map (SOFM) neural network. By using the SOFM neural network the method can adapt to different working environments of the robot. According to test results one can conclude that the SOFM neural network is a useful tool for the path planning problem of a robot.

scholarly journals A Collision-Free Path-Planning Method for an Articulated Mobile Robot

2007 ◽  
Vol 4 (2) ◽  
pp. 71-81 ◽  
Author(s):  
P. Quintero-Alvarez ◽  
G. Ramirez ◽  
S. Zeghloul
Keyword(s):  
Path Planning ◽  
Mobile Robot ◽  
Free Path ◽  
Planning Problem ◽  
Minimal Distance ◽  
Final Position ◽  
Cluttered Environment ◽  
Distance Calculation ◽  
Articulated Robot ◽  
Path Planning Problem

In previous works, we treated the collision-free path-planning problem for a nonholonomic mobile robot in a cluttered environment. We used a method based on a representation of the obstacles on the robot's velocity space. This representation is called Feasible Velocities Polygon (FVP). Every obstacle in the robot's influence zone is represented by a linear constraint on the robot's velocities such that a collision between the robot and the obstacle could be avoided. These constraints define a convex subset in the velocity space, the FVP. Every velocity vector in the FVP ensures a safe motion for the given obstacle configuration. The path-planning problem is solved by an optimization approach between the FVP and a reference velocity to reach the goal. In this paper, we have extended our work to an articulated mobile robot evolving in a cluttered environment. This robot is composed of a differential mobile robot and one or several modules that together form the trailer which are linked by off-center joints. This kind of robot is a strongly constrained system. Even in a free environment, under some circumstances, the robot may be blocked by its trailers in its progression towards the goal. The proposed approach, compared to other methods, has the main advantage of integrating anti-collision constraints between the articulated robot itself and the environment, in order to avoid and resolve dead-lock situations. For moving to the final position, the articulated mobile robot uses the FVP and a reference control law, to formulate the constraints method as a problem of minimal distance calculation. This formulation is then solved with the algorithm of minimal distance calculation proposed by Zeghloul (Zeghloul and Rambeaud, 1996). When a dead-locking situation arises and according to the robot–obstacle configuration, we have developed three different modules to solve these conditions. Each module uses a different approach to resolve the blocking situation. In order to show the capabilities of our method to lead the articulated robot to the final position in a stable way, a numerical result is presented.

Optimum path planning of robot arms

Robotica ◽  
1987 ◽  
Vol 5 (4) ◽  
pp. 323-331 ◽  
Author(s):  
V. Braibant ◽  
M. Geradin
Keyword(s):  
Path Planning ◽  
Industrial Robot ◽  
Planning Problem ◽  
Numerical Application ◽  
Optimum Path ◽  
On Line ◽  
Physical Limitations ◽  
Line Path ◽  
Path Planning Problem ◽  
Mixed Nature

SUMMARYThe optimum control of an industrial robot can be achieved by splitting the problem into two tasks: off-line programming of an optimum path, followed by an on-line path tracking.The aim of this paper is to address the numerical solution of the optimum path planning problem. Because of its mixed nature, it can be expressed either in terms of Cartesian coordinates or at joint level.Whatever the approach adopted, the optimum path planning problem can be formulated as the problem of minimizing the overall time (taken as objective function) subject to behavior and side constraints arising from physical limitations and deviation error bounds. The paper proposes a very general optimization algorithm to solve this problem, which is based on the concept of mixed approximation.A numerical application is presented which demonstrates the computational efficiency of the proposed algorithm.

scholarly journals An Exact Geometry–Based Algorithm for Path Planning

2018 ◽  
Vol 28 (3) ◽  
pp. 493-504 ◽  
Author(s):  
Hassan Jafarzadeh ◽  
Cody H. Fleming
Keyword(s):  
Path Planning ◽  
Free Path ◽  
Time Complexity ◽  
Optimal Path ◽  
Exact Algorithm ◽  
Planning Problem ◽  
Two Dimensional ◽  
Probabilistic Algorithms ◽  
Road Map ◽  
Path Planning Problem

Abstract A novel, exact algorithm is presented to solve the path planning problem that involves finding the shortest collision-free path from a start to a goal point in a two-dimensional environment containing convex and non-convex obstacles. The proposed algorithm, which is called the shortest possible path (SPP) algorithm, constructs a network of lines connecting the vertices of the obstacles and the locations of the start and goal points which is smaller than the network generated by the visibility graph. Then it finds the shortest path from start to goal point within this network. The SPP algorithm generates a safe, smooth and obstacle-free path that has a desired distance from each obstacle. This algorithm is designed for environments that are populated sparsely with convex and nonconvex polygonal obstacles. It has the capability of eliminating some of the polygons that do not play any role in constructing the optimal path. It is proven that the SPP algorithm can find the optimal path in O(nnr2) time, where n is the number of vertices of all polygons and n ̓ is the number of vertices that are considered in constructing the path network (n ̓ ≤ n). The performance of the algorithm is evaluated relative to three major classes of algorithms: heuristic, probabilistic, and classic. Different benchmark scenarios are used to evaluate the performance of the algorithm relative to the first two classes of algorithms: GAMOPP (genetic algorithm for multi-objective path planning), a representative heuristic algorithm, as well as RRT (rapidly-exploring random tree) and PRM (probabilistic road map), two well-known probabilistic algorithms. Time complexity is known for classic algorithms, so the presented algorithm is compared analytically.

PATH PLANNING FOR TWO COOPERATING ROBOTS

1990 ◽  
Vol 04 (02) ◽  
pp. 269-301 ◽  
Author(s):  
QING XUE ◽  
PHILLIP C.-Y. SHEU
Keyword(s):  
Path Planning ◽  
Free Path ◽  
Initial Position ◽  
Planning Problem ◽  
Path Finding ◽  
Closed Chain ◽  
Discrete Interval ◽  
Cooperating Robots ◽  
Position And Orientation ◽  
Path Planning Problem

We investigate the problem of finding collision-free paths for two planar robots which coordinately carry a rectangular object from an initial position and orientation to a destination position and orientation in a cluttered 2-D environment. The robot arms and the carried object construct a 6-link closed chain. The path planning problem for the 6-link closed chain is solved by using two major algorithms: the collision-free feasible configuration finding algorithm and the collision-free path finding algorithm. The collision-free feasible configuration finding algorithm finds all collision-free feasible configurations (CFFCs) of the 6-link closed chain in each discrete interval of two joint angles. The collision-free path finding algorithm builds a connection graph by CFFCs and the transitions between any two groups of CFFCs at adjacent joint intervals. Then a graph search method is used to find a collision-free path for each joint of the robots.

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