Applications of a logic of knowledge to motion planning under uncertainty

1997 ◽  
Vol 44 (5) ◽  
pp. 633-668 ◽  
Author(s):  
Ronen I. Brafman ◽  
Jean-Claude Latombe ◽  
Yoram Moses ◽  
Yoav Shoham
Keyword(s):  
Motion Planning ◽  
Planning Under Uncertainty ◽  
Logic Of Knowledge

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.

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