Many systems, such as mobile robots, need to be controlled in real time. Real-time heuristic search is a popular on-line planning paradigm that supports concurrent planning and execution. However,existing methods do not incorporate a notion of safety and we show that they can perform poorly in domains that contain dead-end states from which a goal cannot be reached. We introduce new real-time heuristic search methods that can guarantee safety if the domain obeys certain properties. We test these new methods on two different simulated domains that contain dead ends, one that obeys the properties and one that does not. We find that empirically the new methods provide good performance. We hope this work encourages further efforts to widen the applicability of real-time planning.

Time-Bounded A* is a real-time, single-agent, deterministic search algorithm that expands states of a graph in the same order as A* does, but that unlike A* interleaves search and action execution. Known to outperform state-of-the-art real-time search algorithms based on Korf's Learning Real-Time A* (LRTA*) in some benchmarks, it has not been studied in detail and is sometimes not considered as a ``true'' real-time search algorithm since it fails in non-reversible problems even it the goal is still reachable from the current state. In this paper we propose and study Time-Bounded Best-First Search (TB(BFS)) a straightforward generalization of the time-bounded approach to any best-first search algorithm. Furthermore, we propose Restarting Time-Bounded Weighted A* (TB_R(WA*)), an algorithm that deals more adequately with non-reversible search graphs, eliminating ``backtracking moves'' and incorporating search restarts and heuristic learning. In non-reversible problems we prove that TB(BFS) terminates and we deduce cost bounds for the solutions returned by Time-Bounded Weighted A* (TB(WA*)), an instance of TB(BFS). Furthermore, we prove TB_R(WA*), under reasonable conditions, terminates. We evaluate TB(WA) in both grid pathfinding and the 15-puzzle. In addition, we evaluate TB_R(WA*) on the racetrack problem. We compare our algorithms to LSS-LRTWA*, a variant of LRTA* that can exploit lookahead search and a weighted heuristic. A general observation is that the performance of both TB(WA*) and TB_R(WA*) improves as the weight parameter is increased. In addition, our time-bounded algorithms almost always outperform LSS-LRTWA* by a significant margin.

Many applications, ranging from video games to dynamic robotics, require solving single-agent, deterministic search problems in partially known environments under very tight time constraints. Real-Time Heuristic Search (RTHS) algorithms are specifically designed for those applications. As a subroutine, most of them invoke a standard, but bounded, search algorithm that searches for the goal. In this paper we present FRIT, a simple approach for single-agent deterministic search problems under tight constraints and partially known environments that unlike traditional RTHS does not search for the goal but rather searches for a path that connects the current state with a so-called ideal tree T . When the agent observes that an arc in the tree cannot be traversed in the actual environment, it removes such an arc from T and then carries out a reconnection search whose objective is to find a path between the current state and any node in T . The reconnection search is done using an algorithm that is passed as a parameter to FRIT. If such a parameter is an RTHS algorithm, then the resulting algorithm can be an RTHS algorithm. We show, in addition, that FRIT may be fed with a (bounded) complete blind-search algorithm. We evaluate our approach over grid pathfinding benchmarks including game maps and mazes. Our results show that FRIT, used with RTAA*, a standard RTHS algorithm, outperforms RTAA* significantly; by one order of magnitude under tight time constraints. In addition, FRIT(daRTAA*) substantially outperforms daRTAA*, a state-of-the-art RTHS algorithm, usually obtaining solutions 50% cheaper on average when performing the same search effort. Finally, FRIT(BFS), i.e., FRIT using breadth-first-search, obtains best-quality solutions when time is limited compared to Adaptive A* and Repeated A*. Finally we show that Bug2, a pathfinding-specific navigation algorithm, outperforms FRIT(BFS) when planning time is extremely limited, but when given more time, the situation reverses.

Heuristics used for solving hard real-time search problems have regions with depressions. Such regions are bounded areas of the search space in which the heuristic function is exceedingly low compared to the actual cost to reach a solution. Real-time search algorithms easily become trapped in those regions since the heuristic values of states in them may need to be updated multiple times, which results in costly solutions. State-of-the-art real-time search algorithms like LSS-LRTA*, LRTA*(k), etc., improve LRTA*'s mechanism to update the heuristic, resulting in improved performance. Those algorithms, however, do not guide search towards avoiding or escaping depressed regions. This paper presents depression avoidance, a simple real-time search principle to guide search towards avoiding states that have been marked as part of a heuristic depression. We apply the principle to LSS-LRTA* producing aLSS-LRTA*, a new real-time search algorithm whose search is guided towards exiting regions with heuristic depressions. We show our algorithm outperforms LSS-LRTA* in standard real-time benchmarks. In addition we prove aLSS-LRTA* has most of the good theoretical properties of LSS-LRTA*.

For problems such as pathfinding in video games and robotics, a search algorithm must be real-time (return the next move within a fixed time bound) and dynamic (accommodate edge costs that can increase and decrease before the goal is reached). Existing real-time search algorithms, such as LSS-LRTA*, can handle edge cost increases but do not handle edge cost decreases. Existing dynamic search algorithms, such as D* Lite, are not real-time. We show how these two families of algorithms can be combined using bidirectional search, producing Real-Time D* (RTD*), the first real-time search algorithm designed for dynamic worlds. Our empirical evaluation shows that, for dynamic grid pathfinding, RTD* results in significantly shorter trajectories than either LSS-LRTA* or naive real-time adaptations of D* Lite because of its ability to opportunistically exploit shortcuts.

Real-time heuristic search algorithms are used for planning by agents in situations where a constant-bounded amount of deliberation time is required for each action regardless of the problem size.  Such algorithms interleave their planning and execution to ensure real-time response. Furthermore, to guarantee completeness, they typically store improved heuristic estimates for previously expanded states.  Although subsequent planning steps can benefit from updated heuristic estimates, many of the same states are expanded over and over again.   Here we propose a variant of the A* algorithm, Time-Bounded A* (TBA*), that guarantees real-time response. In the domain of path-finding on video-game maps TBA* expands an order of magnitude fewer states than traditional real-time search algorithms, while finding paths of comparable quality. It reaches the same level of performance as recent state-of-the-art real-time search algorithms but, unlike these, requires neither state-space abstractions nor pre-computed pattern databases.