This thesis proposes a novel and efficient method (Method of Evolving Junctions)
for solving optimal control problems with path constraints, and whose optimal
paths are separable. A path is separable if it is the concatenation of finite
number of subarcs that are optimal and either entirely constraint active or
entirely constraint inactive. In the case when the subarcs can be computed
efficiently, the search for the optimal path boils down to determining the
junctions that connect those subarcs. In this way, the original infinite
dimensional problem of finding the entire path is converted into a finite
dimensional problem of determine the optimal junctions. The finite dimensional
optimization problem is then solved by a recently developed global optimization
strategy, intermittent diffusion. The idea is to add perturbations (noise) to
the gradient flow intermittently, which essentially converts the ODE's (gradient
descent) into a SDE's problem. It can be shown that the probability of finding
the globally optimal path can be arbitrarily close to one. Comparing to existing
methods, the method of evolving junctions is fundamentally faster and able to
find the globally optimal path as well as a series of locally optimal paths.
The efficiency of the algorithm will be demonstrated by solving path planning
problems, more specifically, finding the optimal path in cluttered environments
with static or dynamic obstacles.
| Identifer | oai:union.ndltd.org:GATECH/oai:smartech.gatech.edu:1853/53428 |
| Date | 08 June 2015 |
| Creators | Lu, Jun |
| Contributors | Zhou, Haomin |
| Publisher | Georgia Institute of Technology |
| Source Sets | Georgia Tech Electronic Thesis and Dissertation Archive |
| Language | en_US |
| Detected Language | English |
| Type | Dissertation |
| Format | application/pdf |
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