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Planning under time pressure arises in many situations. Real-time heuristic search, in which an agent must compute its next action within a prespecified time bound, has proven to be a useful model of real-time planning. However, it is laborious to prove the completeness of new real-time search algorithms. In this paper, we provide a general proof of the completeness of a standard real-time heuristic search algorithm in any problem domain that obeys the axioms of a cost algebra. The proof includes additional detail on how h values change as the algorithm learns. This foundation clarifies the dependence of the proof on domain and algorithm properties and will ease future applications of real-time planning. 

Agents operating in the real world must cope with the fact that time passes while they plan. In some cases, such as under tight deadlines, the only way for such an agent to achieve its goal is to execute an action before a complete plan has been found. This problem is called Concurrent Planning and Execution (CoPE). Previous work on CoPE relied on a value function that assumes search will finish before actions are executed, causing the agent to be overly pessimistic in many situations.In this paper, we define a new value function that takes into account the agent's ability to dispatch actions incrementally. This allows us to devise a much simpler algorithm for concurrent planning and execution. An experimental evaluation on problems with time pressure shows that the new method significantly outperforms the previous state-of-the-art. 

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. 

Finding optimal solutions to state-space search problems often takes too long, even when using A* with a heuristic function. Instead, practitioners often use a tunable approach, such as weighted A*, that allows them to adjust a trade-off between search time and solution cost until the search is sufficiently fast for the intended application. In this paper, we study algorithms for this problem setting, which we call `tunable suboptimal search'. We introduce a simple baseline, called Speed*, that uses distance-to-go information to speed up search. Experimental results on standard search benchmarks suggest that 1) bounded-suboptimal searches suffer overhead due to enforcing a suboptimality bound, 2) beam searches can perform well, but fare poorly in domains with dead-ends, and 3) Speed* provides robust overall performance. 

Train routing is sensitive to delays that occur in the network. When a train is delayed, it is imperative that a new plan be found quickly, or else other trains may need to be stopped to ensure safety, potentially causing cascading delays. In this paper, we consider this class of multi-agent planning problems, which we call Multi-Agent Execution Delay Replanning. We show that these can be solved by reducing the problem to an any-start-time safe interval planning problem. When an agent has an any-start-time plan, it can react to a delay by simply looking up the precomputed plan for the delayed start time. We identify crucial real-world problem characteristics like the agent's speed, size, and safety envelope, and extend the any-start-time planning to account for them. Experimental results on real-world train networks show that any-start-time plans are compact and can be computed in reasonable time while enabling agents to instantly recover a safe plan. 

Anytime heuristic search algorithms try to find a (potentially suboptimal) solution as quickly as possible and then work to find better and better solutions until an optimal solution is obtained or time is exhausted. The most widely-known anytime search algorithms are based on best-first search. In this paper, we propose a new algorithm, rectangle search, that is instead based on beam search, a variant of breadth-first search. It repeatedly explores alternatives at all depth levels and is thus best-suited to problems featuring deep local minima. Experiments using a variety of popular search benchmarks suggest that rectangle search is competitive with fixed-width beam search and often performs better than the previous best anytime search algorithms. 

Metareasoning can be a helpful technique for controlling search in situations where computation time is an important resource, such as real-time planning and search, algorithm portfolios, and concurrent planning and execution. Metareasoning often involves an estimate of the remaining search time of a running algorithm, and several ways to compute such estimates have been presented in the literature. In this paper, we argue that many applications actually require a full estimated probability distribution over the remaining time, rather than just a point estimate of expected search time. We study several methods for estimating such distributions, including some novel adaptations of existing schemes.To properly evaluate the estimates, we introduce `put-up or shut-up games', which probe the distributional estimates without requiring infeasible computation.Our experimental evaluation reveals that estimates that are more accurate in expected value do not necessarily deliver better distributions, yielding worse scores in the game. 

Standard temporal planning assumes that planning takes place offline, and then execution starts at time 0. Recently, situated temporal planning was introduced, where planning starts at time 0, and execution occurs after planning terminates. Situated temporal planning reflects a more realistic scenario where time passes during planning. However, in situated temporal planning a complete plan must be generated before any action is executed. In some problems with time pressure, timing is too tight to complete planning before the first action must be executed. For example, an autonomous car that has a truck backing towards it should probably move out of the way now, and plan how to get to its destination later. In this paper, we propose a new problem setting: concurrent planning and execution, in which actions can be dispatched (executed) before planning terminates. Unlike previous work on planning and execution, we must handle wall clock deadlines that affect action applicability and goal achievement (as in situated planning) while also supporting dispatching actions before a complete plan has been found. We extend previous work on metareasoning for situated temporal planning to develop an algorithm for this new setting. Our empirical evaluation shows that when there is strong time pressure, our approach outperforms situated temporal planning.