The reset disambiguation policy for navigating stochastic obstacle fields

Abstract

Abstract:The problem we consider is a stochastic shortest path problem in the presence of a dynamic learning capability. Specifically, a spatial arrangement of possible obstacles needs to be traversed as swiftly as possible, and the status of the obstacles may be disambiguated (at a cost) en route. No efficiently computable optimal policy is known, and many similar problems have been proven intractable. In this article, we adapt a policy which is optimal for a related problem and prove that this policy is indeed also optimal for a restricted class of instances of our problem. Otherwise, this policy is generally suboptimal but, nonetheless, it is both effective and efficiently computable. Examples/simulations are provided in a mine countermeasures application. Of central use is the Tangent Arc Graph, a polynomially sized topological superimposition of exponentially many visibility graphs. © 2011 Wiley Periodicals, Inc. Naval Research Logistics 58: 389-399, 2011 Keywords: mine countermeasures; probabilistic path planning; random disambiguation path; tangent arc graph; markov decision process THE DISAMBIGUATION PROBLEMA disambiguation problem instance is a tuple (s, t, A, ρ, c), where s and t are points in R 2 , A is a finite set of open discs in R 2 , ρ is a function A → (0, 1], and c is a function A → R ≥0 . An agent wants to traverse from s to t through R 2 , along a continuous curve which is as short as possible in the sense of arclength. However, the discs of A are potential obstacles; for each A ∈ A, the probability that A is an obstacle is ρ(A), independently from the other discs in A. If ρ(A) < 1 then we say A is ambiguous and if ρ(A) = 1 then A is definitely an obstacle. The traversing agent cannot enter discs which are obstacles or ambiguous but, if and when the agent is located at the boundary ∂A for any A ∈ A, the agent has the option to disambiguate the disc A at a cost c(A) added to the traversal arclength, and the agent will learn whether or not A is actually an obstacle. The status of a disc will never change; if A is revealed to be an obstacle then the traversing agent may never enter A, and if A is not an obstacle then A may be entered anytime thereafter. The central issue is how to direct the agent's traversal to optimally utilize this disambiguation capability; that is, to find a policy for the agent which minimizes the expected length of the agent's s, t traversal.Correspondence to: C.E. Priebe (cep@jhu.edu) An example of a disambiguation problem instance is shown in Fig. 1; suppose the values of ρ(A i ), for i = 1, 2, 3, 4, 5 are 0.6, 0.4, 0.9, 0.8, 0.7, and suppose c(A i ) = 1.1 for all i. One particular traversal policy is illustrated in Fig. 1; from s the agent proceeds to the red bullet labeled 1, at which point A 1 is disambiguated. If A 1 is traversable then the agent is to continue till the red bullet labeled 2, at which point A 2 is disambiguated. Then the agent is to proceed to t through A 2 or clockwise around A 2 , according as A 2 is traversable or not. If A 1 was not traversa...

Penalty-Based Algorithms for the Stochastic Obstacle Scene Problem

“…Thus, a clear advantage of RDA over SRA is the lack of a finetuning parameter that results in significant computational savings. Aksakalli et al (2011) illustrates, via computational experiments, that performance of RDA is comparable to that of SRA, whereas the run time of SRA is about 60 times greater than that of RDA. Thus, it can be argued that F RD is a "better" penalty function compared to F SR .…”

“…The reset disambiguation algorithm (RDA) introduced in Aksakalli et al (2011) for the continuous SOSP is provably optimal for a particular variant of the problem, called the reset variant. It is also optimal for a restricted class of instances for the original SOSP.…”

“…The specific application domain we consider is maritime minefield navigation, which has received considerable attention from scientific and engineering communities recently (Witherspoon et al 1995, Muhandiramge 2008. A particular instance we consider is a United States Navy minefield data set (called the COBRA data) that first appeared in Witherspoon et al (1995) and was later referred to in Priebe et al (1997Priebe et al ( , 2005, Fishkind et al (2007), Ye and Priebe (2010), Ye et al (2011), andAksakalli et al (2011). The COBRA data is illustrated in Figure 5 and tabulated in Table 2.…”

“…Thus, exponentially many such possibilities need to be incorporated when constructing the state space. The reader is referred to Aksakalli et al (2011) and the references therein for a review of the literature that includes the history and development of the problems that fall under the SOSP and CTP umbrella.…”

“…Regarding suboptimal algorithms for continuous SOSP, of particular interest are the simulated risk disambiguation algorithm (SRA) of Fishkind et al (2007) and the reset disambiguation algorithm (RDA) 371 of Aksakalli et al (2011). The idea behind SRA is to temporarily pretend, i.e., simulate, that the ambiguous obstacles are riskily traversable for the sole purpose of deciding where to disambiguate next.…”