Hardness of Motion Planning with Obstacle Uncertainty in Two Dimensions

2021 ◽  
pp. 027836492199278
Author(s):  
Luke Shimanuki ◽  
Brian Axelrod
Keyword(s):  
Motion Planning ◽  
Free Path ◽  
Configuration Space ◽  
Exact Algorithm ◽  
Two Dimensions ◽  
Planning Under Uncertainty ◽  
Constant Number ◽  
3D Motion ◽  
Practical Algorithms ◽  
Case Planning

We consider the problem of motion planning in the presence of uncertain obstacles, modeled as polytopes with Gaussian-distributed faces (PGDFs). A number of practical algorithms exist for motion planning in the presence of known obstacles by constructing a graph in configuration space, then efficiently searching the graph to find a collision-free path. We show that such an exact algorithm is unlikely to be practical in the domain with uncertain obstacles. In particular, we show that safe 2D motion planning among PGDF obstacles is [Formula: see text]-hard with respect to the number of obstacles, and remains [Formula: see text]-hard after being restricted to a graph. Our reduction is based on a path encoding of MAXQHORNSAT and uses the risk of collision with an obstacle to encode variable assignments and literal satisfactions. This implies that, unlike in the known case, planning under uncertainty is hard, even when given a graph containing the solution. We further show by reduction from [Formula: see text]-SAT that both safe 3D motion planning among PGDF obstacles and the related minimum constraint removal problem remain [Formula: see text]-hard even when restricted to cases where each obstacle overlaps with at most a constant number of other obstacles.

scholarly journals A Fast Algorithm for Planning Collision-Free Paths With Rotations

1998 ◽  
Vol 120 (1) ◽  
pp. 52-57 ◽  
Author(s):  
S.-F. Chen ◽  
J. H. Oliver ◽  
D. Fernandez-Baca
Keyword(s):  
Motion Planning ◽  
Free Path ◽  
Configuration Space ◽  
Fast Algorithm ◽  
Experimental Results ◽  
Optimal Motion ◽  
Running Time ◽  
Practical Algorithm

Motion planning is a major problem in robotics. The objective is to plan a collision-free path for a robot moving through a workspace populated with obstacles. In this paper, we present a fast and practical algorithm for moving a convex polygonal robot among a set of polygonal obstacles with translations and rotations. The running time is O(c((n + k)N + n log n)), where c is a parameter controlling the precision of the results, n is the total number of obstacle vertices, k is the number of intersections of configuration space obstacles, and N is the number of obstacles, decomposed into convex objects. This work builds upon the slabbing method proposed by Ahrikencheikh et al. [2], which finds an optimal motion for a point among a set of nonoverlapping obstacles. Here, we extend the slabbing method to the motion planning of a convex polygonal robot with translations and rotations, which also allows overlapping configuration space obstacles. This algorithm has been fully implemented and the experimental results show that it is more robust and faster than other approaches.

scholarly journals A Fast Algorithm for Planning Collision-Free Paths With Rotations

1997 ◽  
Author(s):  
Shiang-Fong Chen ◽  
James H. Oliver ◽  
David Fernandez-Baca
Keyword(s):  
Motion Planning ◽  
Free Path ◽  
Configuration Space ◽  
Fast Algorithm ◽  
Experimental Results ◽  
Optimal Motion ◽  
Running Time ◽  
Practical Algorithm

Abstract Motion planning is a major problem in robotics. The objective is to plan a collision-free path for a robot moving through a workspace populated with obstacles. In this paper, we present a fast and practical algorithm for moving a convex polygonal robot among a set of polygonal obstacles with translations and rotations. The running time is O(c((n + k)N + nlogn)), where c is a parameter controlling the precision of the results, n is the total number of obstacle vertices, k is the number of intersections of configuration space obstacles, and N is the number of obstacles, decomposed into convex objects. This work builds upon the slabbing method proposed by Ahrikencheikh et al. (1994), which finds an optimal motion for a point among a set of non-overlapping obstacles. Here, we extend the slabbing method to the motion planning of a convex polygonal robot with translations and rotations, which also allows overlapping configuration space obstacles. This algorithm has been fully implemented and the experimental results show that it is more robust and faster than other approaches.

ADD-RRV for motion planning in complex environments

Robotica ◽  
2021 ◽  
pp. 1-18
Author(s):  
Peng Cai ◽  
Xiaokui Yue ◽  
Hongwen Zhang
Keyword(s):  
Principal Component Analysis ◽  
Motion Planning ◽  
Configuration Space ◽  
Principal Component ◽  
Component Analysis ◽  
Planning Method ◽  
Complex Environments ◽  
Local Configuration ◽  
Narrow Passage

Abstract In this paper, we present a novel sampling-based motion planning method in various complex environments, especially with narrow passages. We use online the results of the planner in the ADD-RRT framework to identify the types of the local configuration space based on the principal component analysis (PCA). The identification result is then used to accelerate the expansion similar to RRV around obstacles and through narrow passages. We also propose a modified bridge test to identify the entrance of a narrow passage and boost samples inside it. We have compared our method with known motion planners in several scenarios through simulations. Our method shows the best performance across all the tested planners in the tested scenarios.

Instruction Generation for Assembly Operations Performed by Humans

2012 ◽  
Author(s):  
Krishnanand Kaipa ◽  
Carlos Morato ◽  
Boxuan Zhao ◽  
Satyandra K. Gupta
Keyword(s):  
Motion Planning ◽  
Free Path ◽  
Generation System ◽  
Complex Assembly ◽  
Learning Time ◽  
Design Changes ◽  
Multimodal Information ◽  
Information Text ◽  
Assembly Operations

This paper presents the design of an instruction generation system that can be used to automatically generate instructions for complex assembly operations performed by humans on factory shop floors. Multimodal information—text, graphical annotations, and 3D animations—is used to create easy-to-follow instructions. This thereby reduces learning time and eliminates the possibility of assembly errors. An automated motion planning subsystem computes a collision-free path for each part from its initial posture in a crowded scene onto its final posture in the current subassembly. Visualization of this computed motion results in generation of 3D animations. The system also consists of an automated part identification module that enables the human to identify, and pick, the correct part from a set of similar looking parts. The system’s ability to automatically translate assembly plans into instructions enables a significant reduction in the time taken to generate instructions and update them in response to design changes.

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.

scholarly journals Automated 3D-motion planning for ramps and stairs in intra-logistics material flow simulations

2010 ◽  
Author(s):  
Matthias Fischer ◽  
Hendrik Renken ◽  
Christoph Laroque ◽  
Guido Schaumann ◽  
Wilhelm Dangelmaier
Keyword(s):  
Motion Planning ◽  
Material Flow ◽  
3D Motion ◽  
Flow Simulations
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