Performance bounds for planning in unknown terrain

Abstract

Planning in nondeterministic domains is typically intractable due to the large number of contingencies. Two techniques for speeding up planning in nondeterministic domains are agent-centered search and assumption-based planning. Both techniques interleave planning in deterministic domains with plan execution. They differ in how they make planning deterministic. To determine how suboptimal their plans are, we study two planning methods for robot navigation in initially unknown terrain that have successfully been used on mobile robots but not been analyzed before. The planning methods differ both in the technique they use to speed up planning and in the robot-navigation task they solve. Greedy Mapping uses agentcentered search to map unknown terrain. Dynamic A* uses assumption-based planning to navigate to a given goal location in unknown terrain. When we formalize abstractions of these planning methods on undirected graphs G = (V, E), they turn out to be similar enough that we are able to analyze their travel distance in a unified way. We discover that neither method is optimal in a worst-case sense, by a factor of Ω(log |V |/ log log |V |). We also derive factor O(|V |) upper bounds to show that these methods are not very badly sub-optimal in this sense. These results provide a first step towards explaining the good empirical results that have been reported about Greedy Mapping and Dynamic A* in the experimental literature. More generally, they show how to use tools from graph theory to analyze the plan quality of practical planning methods for nondeterministic domains.

Applying Case-Based Learning to Improve the Efficiency in the Web Service Compositions

“…The new current state S is calculated as: result (a next , S o , 0); modification of the current state S takes place considering that the execution of a next shall have the expected effects, that is, assuming there are no external factors (δ = 0). This model of operation is called assumption-based planning [6]: actions are deemed determinists (δ = 0); to simplify the real problem, and an alternative action is recalculated when the real effect of the actions does not coincide with the expected effect (δ ≠ 0). In case one of the actions fails during its execution, the executor informs the planner this failed event so that the planner may perform a new calculation for an alternative action while the executor waits, and after a respective time, it may ask the planner for the corresponding action.…”

“…A valid P plan (valid_plan (P, I, G, {δ i })), is that which is successful when executed on an initial state I, reaching a G target state. (6) Sequence {δ i } equals {δ 0, δ 1, …., δ n } and defines a succession of unforeseen situations that have taken place during the execution of the plan. This sequence makes that the execution of the same plan to resolve the same problem does not always render the same result.…”

An On-Line Approach for Planning in Time-Limited Situations

“…However, working concurrently with the execution, implies the planner must make assumptions about the outcomes of action executions. Following the assumption-based planning approach [12], we have considered all actions as deterministic, replanning when an executed action has an unexpected outcome.…”

Scrubbing During Learning In Real-time Heuristic Search

“…This well-studied problem has led to numerous algorithms (Korf, 1990;Furcy & Koenig, 2000;Shimbo & Ishida, 2003;Hernández & Meseguer, 2005;Bulitko & Lee, 2006;Hernández & Baier, 2012) and various theoretical analysis (Ishida & Korf, 1991;Koenig & Simmons, 1993;Koenig, Tovey, & Smirnov, 2003;Bulitko & Lee, 2006;Bulitko & Bulitko, 2009;Sturtevant, Bulitko, & Björnsson, 2010).…”