Grids with blocked and unblocked cells are often used to represent continuous 2D and 3D environments in robotics and video games. The shortest paths formed by the edges of 8-neighbor 2D grids can be up to ≈ 8% longer than the shortest paths in the continuous environment. Theta* typically finds much shorter paths than that by propagating information along graph edges (to achieve short runtimes) without constraining paths to be formed by graph edges (to find short “any-angle” paths). We show in this paper that the shortest paths formed by the edges of 26-neighbor 3D grids can be ≈ 13% longer than the shortest paths in the continuous environment, which highlights the need for smart path planning algorithms in 3D. Theta* can be applied to 3D grids in a straight-forward manner, but it performs a line-of-sight check for each unexpanded visible neighbor of each expanded vertex and thus it performs many more line-of-sight checks per expanded vertex on a 26-neighbor 3D grid than on an 8-neighbor 2D grid. We therefore introduce Lazy Theta*, a variant of Theta* which uses lazy evaluation to perform only one line-of-sight check per expanded vertex (but with slightly more expanded vertices). We show experimentally that Lazy Theta* finds paths faster than Theta* on 26-neighbor 3D grids, with one order of magnitude fewer line-of-sight checks and without an increase in path length.

Goal-directed path planning is one of the basic and widely studied problems in the field of mobile robotics. Homotopy classes of trajectories, arising due to the presence of obstacles, are defined as sets of trajectories that can be transformed into each other by gradual bending and stretching without colliding with obstacles. The problem of finding least-cost paths restricted to a specific homotopy class or finding least-cost paths that do not belong to certain homotopy classes arises frequently in such applications as predicting paths for dynamic entities and computing heuristics for path planning with dynamic constraints. In the present work, we develop a compact way of representing homotopy classes and propose an efficient method of graph search-based optimal path planning with constraints on homotopy classes. The method is based on representing the environment of the robot as a complex plane and making use of the Cauchy Integral Theorem. We prove optimality of the method and show its efficiency experimentally.

We consider the stochastic variant of the Canadian Traveler's Problem, a path planning problem where adverse weather can cause some roads to be untraversable. The agent does not initially know which roads can be used. However, it knows a probability distribution for the weather, and it can observe the status of roads incident to its location. The objective is to find a policy with low expected travel cost. We introduce and compare several algorithms for the stochastic CTP. Unlike the optimistic approach most commonly considered in the literature, the new approaches we propose take uncertainty into account explicitly. We show that this property enables them to generate policies of much higher quality than the optimistic one, both theoretically and experimentally.

In this paper we propose a new algorithm for solving general two-player turn-taking games that performs symbolic search utilizing binary decision diagrams (BDDs). It consists of two stages: First, it determines all breadth-first search (BFS) layers using forward search and omitting duplicate detection, next, the solving process operates in backward direction only within these BFS layers thereby partitioning all BDDs according to the layers the states reside in. We provide experimental results for selected games and compare to a previous approach. This comparison shows that in most cases the new algorithm outperforms the existing one in terms of runtime and used memory so that it can solve games that could not be solved before with a general approach.

Motivated by the recent hardware evolution towards multi-core machines, we investigate parallel planning techniques in a shared-memory environment. We consider, more specifically, parallel versions of a best-first search algorithm that run K threads, each expanding the next best node from the open list. We show that the proposed technique has a number of advantages. First, it is (reasonably) simple: we show how the algorithm can be obtained from a sequential version mostly by adding parallel annotations. Second, we conduct an extensive empirical study that shows that this approach is quite effective.  It is also dynamic in the sense that the number of nodes expanded in parallel is adapted during the search. Overall we show that the approach is promising for parallel domain-independent, suboptimal planning.

Because an agent's resources dictate what actions it can possibly take, it should plan which resources it holds over time carefully, considering its inherent limitations (such as power or payload restrictions), the competing needs of other agents for the same resources, and the stochastic nature of the environment. Such agents can, in general, achieve more of their objectives if they can use -- and even create -- opportunities to change which resources they hold at various times. Driven by resource constraints, the agents could break their overall missions into an optimal series of phases, optimally reconfiguring their resources at each phase, and optimally using their assigned resources in each phase, given their knowledge of the stochastic environment. In this paper, we formally define and analyze this constrained, sequential optimization problem in both the single-agent and multi-agent contexts. We present a family of mixed integer linear programming (MILP) formulations of this problem that can optimally create phases(when phases are not predefined) accounting for costs and limitations in phase creation. Because our formulations simultaneously also find the optimal allocations of resources at each phase and the optimal policies for using the allocated resources at each phase, they exploit structure across these coupled problems. This allows them to find solutions significantly faster (orders of magnitude faster in larger problems) than alternative solution techniques, as we demonstrate empirically.

Autonomous planetary vehicles, also known as rovers, are small autonomous vehicles equipped with a variety of sensors used to perform exploration and experiments on a planet's surface. Rovers work in a partially unknown environment, with narrow energy/time/movement constraints and, typically, small computational resources that limit the complexity of on-line planning and scheduling, thus they represent a great challenge in the field of autonomous vehicles. Indeed, formal models for such vehicles usually involve hybrid systems with nonlinear dynamics, which are difficult to handle by most of the current planning algorithms and tools. Therefore, when offline planning of the vehicle activities is required, for example for rovers that operate without a continuous Earth supervision, such planning is often performed on simplified models that are not completely realistic. In this paper we show how the UPMurphi model checking based planning tool can be used to generate resource-optimal plans to control the engine of an autonomous planetary vehicle, working directly on its hybrid model and taking into account several safety constraints, thus achieving very accurate results.

Plan recognition is the problem of inferring the goals and plans of an agent after observing its behavior. Recently, it has been shown that this problem can be solved efficiently, without the need of a plan library, using slightly modified planning algorithms. In this work, we extend this approach to the more general problem of probabilistic plan recognition where a probability distribution over the set of goals is sought under the assumptions that actions have deterministic effects and both agent and observer have complete information about the initial state. We show that this problem can be solved efficiently using classical planners provided that the probability of a partially observed execution given a goal is defined in terms of the cost difference of achieving the goal under two conditions: complying with the observations, and not complying with them. This cost, and hence the posterior goal probabilities, are computed by means of two calls to a classical planner that no longer has to be modified in any way. A number of examples is considered to illustrate the quality, flexibility, and scalability of the approach.

A common problem faced by expanding companies is the lack of skilled and experienced domain experts, especially planners and controllers. This can seriously slow down or impede growth. This paper describes how we worked with one of the largest travel agencies in Hong Kong to alleviate this problem by using AI to support decision-making and problem-solving so that their planners/controllers can be more productive in sustaining business growth while providing quality service. This paper describes a Web-based mission critical Fleet Management System (FMS) that supports the scheduling and management of a fleet of luxury limousines. Clientele is mainly business travelers. The use of AI allowed our client to increase their business volume and expand fleet size with the same team of planners/controllers while maintaining service quality. This paper also describes our experience in building modern AI systems leveraging on Web 2.0 open-source tools and libraries. Although we used a proven AI model and search algorithm, we believe our innovation is in striking the right balance and combination of AI with modern Web 2.0 techniques to achieve low-risk implementation and deployment success as well as concrete and measurable business benefits.

Goal-directed path planning is one of the basic and widely studied problems in the field of mobile robotics. Homotopy classes of trajectories, arising due to the presence of obstacles, are defined as sets of trajectories that can be transformed into each other by gradual bending and stretching without colliding with obstacles. The problem of finding least-cost paths restricted to a specific homotopy class or finding least-cost paths that do not belong to certain homotopy classes arises frequently in such applications as predicting paths for dynamic entities and computing heuristics for path planning with dynamic constraints. In the present work, we develop a compact way of representing homotopy classes and propose an efficient method of graph search-based optimal path planning with constraints on homotopy classes. The method is based on representing the environment of the robot as a complex plane and making use of the Cauchy Integral Theorem. We prove optimality of the method and show its efficiency experimentally.