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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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Real-time Safe Interval Path Planning
Navigation among dynamic obstacles is a fundamental task in robotics that has been modeled in various ways. In Safe Interval Path Planning, location is discretized to a grid, time is continuous, future trajectories of obstacles are assumed known, and planning takes place offline. In this work, we define the Real-time Safe Interval Path Planning problem setting, in which the agent plans online and must issue its next action within a strict time bound. Unlike in classical real-time heuristic search, the cost-to-go in Real-time Safe Interval Path Planning is a function of time rather than a scalar. We present several algorithms for this setting and prove that they learn admissible heuristics. Empirical evaluation shows that the new methods perform better than classical approaches under a variety of conditions.
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- Award ID(s):
- 2008594
- PAR ID:
- 10546013
- Publisher / Repository:
- AAAI Press
- Date Published:
- Journal Name:
- Proceedings of the International Symposium on Combinatorial Search
- Volume:
- 17
- ISSN:
- 2832-9171
- Page Range / eLocation ID:
- 161 to 169
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1609/socs.v17i1.31554
