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 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.

Avoidance of obstacles with unknown trajectories: locally optimal paths and path complexity, Part II

Robotica ◽  
1993 ◽  
Vol 11 (5) ◽  
pp. 403-412 ◽  
Author(s):  
James Gil de Lamadrid ◽  
Jill Zimmermanf
Keyword(s):  
Path Planning ◽  
Maximum Velocity ◽  
Local Information ◽  
Planning Problem ◽  
Two Dimensional ◽  
Robot Trajectory ◽  
Optimal Paths ◽  
Sensor Information ◽  
Minimum Velocity ◽  
Path Planning Problem

SUMMARYContinuing the work presented in part I, ‡ we consider the problem of moving a point robot through a two dimensional workspace containing polygonal obstacles moving on unknown trajectories. We propose to use sensor information to predict the trajectories of the obstacles, and interleave path planning and execution. We define a locally minimum velocity path as an optimal robot trajectory, given only local information about obstacle trajectories. We show that the complexity of a path planning problem can be characterized by how frequently the robot must change directions to approximate the locally minimum velocity path. Our results apply to both robots with and without maximum velocity limits.

scholarly journals Proposed Smooth-STC Algorithm for Enhanced Coverage Path Planning Performance in Mobile Robot Applications

Robotics ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 44 ◽  
Author(s):  
Hai Van Pham ◽  
Philip Moore ◽  
Dinh Xuan Truong
Keyword(s):  
Path Planning ◽  
Optimal Path ◽  
Forest Monitoring ◽  
Planning Problem ◽  
Operational Environment ◽  
Uncertain Environments ◽  
Coverage Path Planning ◽  
Agricultural Robots ◽  
Cleaning Robots ◽  
Path Planning Problem

Robotic path planning is a field of research which is gaining traction given the broad domains of interest to which path planning is an important systemic requirement. The aim of path planning is to optimise the efficacy of robotic movement in a defined operational environment. For example, robots have been employed in many domains including: Cleaning robots (such as vacuum cleaners), automated paint spraying robots, window cleaning robots, forest monitoring robots, and agricultural robots (often driven using satellite and geostationary positional satellite data). Additionally, mobile robotic systems have been utilised in disaster areas and locations hazardous to humans (such as war zones in mine clearance). The coverage path planning problem describes an approach which is designed to determine the path that traverses all points in a defined operational environment while avoiding static and dynamic (moving) obstacles. In this paper we present our proposed Smooth-STC model, the aim of the model being to identify an optimal path, avoid all obstacles, prevent (or at least minimise) backtracking, and maximise the coverage in any defined operational environment. The experimental results in a simulation show that, in uncertain environments, our proposed smooth STC method achieves an almost absolute coverage rate and demonstrates improvement when measured against alternative conventional algorithms.

Path planning of a mobile robot using genetic heuristics

Robotica ◽  
1998 ◽  
Vol 16 (5) ◽  
pp. 575-588 ◽  
Author(s):  
Andreas C. Nearchou
Keyword(s):  
Genetic Algorithm ◽  
Path Planning ◽  
Mobile Robot ◽  
Optimal Path ◽  
Hill Climbing ◽  
Planning Problem ◽  
Well Performance ◽  
Simulation Results ◽  
Task Oriented ◽  
Path Planning Problem

A genetic algorithm for the path planning problem of a mobile robot which is moving and picking up loads on its way is presented. Assuming a findpath problem in a graph, the proposed algorithm determines a near-optimal path solution using a bit-string encoding of selected graph vertices. Several simulation results of specific task-oriented variants of the basic path planning problem using the proposed genetic algorithm are provided. The results obtained are compared with ones yielded by hill-climbing and simulated annealing techniques, showing a higher or at least equally well performance for the genetic algorithm.

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.

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.

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.

Avoidance of obstacles with unknown trajectories: locally optimal paths and path complexity, Part I

Robotica ◽  
1993 ◽  
Vol 11 (4) ◽  
pp. 299-308 ◽  
Author(s):  
James Gil de Lamadrid ◽  
Jill Zimmerman†
Keyword(s):  
Path Planning ◽  
Local Information ◽  
Planning Problem ◽  
Two Dimensional ◽  
Basic Algorithm ◽  
Robot Trajectory ◽  
Optimal Paths ◽  
Sensor Information ◽  
Minimum Velocity ◽  
Path Planning Problem

SUMMARYWe consider the problem of moving a point robot through a two dimensional workspace containing polygonal obstacles moving on unknown trajectories. We propose to use sensor information to predict the trajectories of the obstacles, and interleave path planning and execution. In this paper, we present preliminary work in which we propose our basic algorithm and define a locally minimum velocity path as an optimal robot trajectory, given only local information about obstacle trajectories. In the sequel (part II) to this paper we will show that the complexity of a path planning problem can be characterized by how frequently the robot must change directions to approximate the locally minimum velocity path.

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