LAMA is a classical planning system based on heuristic forward search. Its core feature is the use of a pseudo-heuristic derived from landmarks, propositional formulas that must be true in every solution of a planning task. LAMA builds on the Fast Downward planning system, using finite-domain rather than binary state variables and multi-heuristic search. The latter is employed to combine the landmark heuristic with a variant of the well-known FF heuristic. Both heuristics are cost-sensitive, focusing on high-quality solutions in the case where actions have non-uniform cost. A weighted A ∗ search is used with iteratively decreasing weights, so that the planner continues to search for plans of better quality until the search is terminated. LAMA showed best performance among all planners in the sequential satisficing track of the International Planning Competition 2008. In this paper we present the system in detail and investigate which features of LAMA are crucial for its performance. We present individual results for some of the domains used at the competition, demonstrating good and bad cases for the techniques implemented in LAMA. Overall, we find that using landmarks improves performance, whereas the incorporation of action costs into the heuristic estimators proves not to be beneficial. We show that in some domains a search that ignores cost solves far more problems, raising the question of how to deal with action costs more effectively in the future. The iterated weighted A ∗ search greatly improves results, and shows synergy effects with the use of landmarks. 1.

{jtd7, ruml} at cs.unh.edu Anytime search algorithms solve optimisation problems by quickly finding a usually suboptimal solution and then finding improved solutions when given additional time. To deliver a solution quickly, they are typically greedy with respect to the heuristic cost-to-go estimate h. In this paper, we first show that this low-h bias can cause poor performance if the heuristic is inaccurate. Building on this observation, we then present a new anytime approach that restarts the search from the initial state every time a new solution is found. We demonstrate the utility of our method via experiments in PDDL planning as well as other domains. We show that it is particularly useful for hard optimisation problems like planning where heuristics may be quite inaccurate and inadmissible, and where the greedy solution makes early mistakes.

For vehicles navigating initially unknown cluttered environments, current state-of-the-art planning algorithms are able to plan and re-plan dynamicallyfeasible paths efficiently and robustly. It is still a challenge, however, to deal well with the surroundings that are both cluttered and highly dynamic. Planning under these conditions is more difficult for two reasons. First, tracking and predicting the trajectories of moving objects (i.e., cars, humans) is very noisy. Second, the planning process is computationally more expensive because of the increased dimensionality of the statespace, with time as an additional variable. Moreover, re-planning needs to be invoked more often since the trajectories of moving obstacles need to be constantly re-estimated. In this paper, we develop a path planning algorithm that addresses these challenges. First, we choose a representation of dynamic obstacles that efficiently models their predicted trajectories and the uncertainty associated with the predictions. Second, to provide realtime guarantees on the performance of planning with dynamic obstacles, we propose to utilize a novel data structure for planning- a time-bounded lattice- that merges together short-term planning in time with longterm planning without time. We demonstrate the effectiveness of the approach in both simulations with up to 30 dynamic obstacles and on real robots.

Abstract — The Rapidly-exploring Random Tree (RRT) algorithm, based on incremental sampling, efficiently computes motion plans. Although the RRT algorithm quickly produces candidate feasible solutions, it tends to converge to a solution that is far from optimal. Practical applications favor “anytime” algorithms that quickly identify an initial feasible plan, then, given more computation time available during plan execution, improve the plan toward an optimal solution. This paper describes an anytime algorithm based on the RRT ∗ which (like the RRT) finds an initial feasible solution quickly, but (unlike the RRT) almost surely converges to an optimal solution. We present two key extensions to the RRT ∗ , committed trajectories and branch-and-bound tree adaptation, that together enable the algorithm to make more efficient use of computation time online, resulting in an anytime algorithm for real-time implementation. We evaluate the method using a series of Monte Carlo runs in a high-fidelity simulation environment, and compare the operation of the RRT and RRT ∗ methods. We also demonstrate experimental results for an outdoor wheeled robotic vehicle. I.

Anytime variants of Dijkstra’s and A * shortest path algorithms quickly produce a suboptimal solution and then improve it over time. For example, ARA * introduces a weighting value (ε) to rapidly find an initial suboptimal path and then reduces ε to improve path quality over time. In ARA*, ε is based on a linear trajectory with ad-hoc parameters chosen by each user. We propose a new Anytime A * algorithm, Anytime Nonparametric A * (ANA*), that does not require ad-hoc parameters, and adaptively reduces ε to expand the most promising node per iteration, adapting the greediness of the search as path quality improves. We prove that each node expanded by ANA * provides an upper bound on the suboptimality of the current-best solution. We evaluate the performance of ANA * with experiments in the domains of robot motion planning, gridworld planning, and multiple sequence alignment. The results suggest that ANA * is as efficient as ARA * and in most cases: (1) ANA * finds an initial solution faster, (2) ANA * spends less time between solution improvements, (3) ANA * decreases the suboptimality bound of the current-best solution more gradually, and (4) ANA * finds the optimal solution faster. ANA * is freely available from Maxim Likhachev’s Search-based Planning Library (SBPL).

Autonomous robots rely heavily on their ability to plan actions quickly, under massive uncertainty and with a large number of factors that affect execution. Graph searches such as Dijkstra’s search, Breadth-First Search and A * [13] are highly popular means of finding least-cost plans due to their generality, solid theoretical ground and simplicity in the implementation. Unfortunately, these methods can rarely be used to solve complex planning problems on real robotic systems because they don’t provide real-time performance guarantees, are limited to small (i.e., lowdimensional) problems and can not deal with problems that involve uncertainty. My research is driven by developing planning methods that are general, easy-to-use, theoretically well-grounded but at the same time meet the requirements of real robotic systems. In particular, I develop novel graph search algorithms that solve complex and/or large-scale problems in robotics in real-time while maintaining all the positive properties of graph searches. I use these algorithms to build planning modules for real robotic systems that perform challenging tasks. For example, together with my colleagues, I have developed a series of novel versions of A* search that are designed specifically for planning in partially-known and dynamic environments under severe time constraints. For instance, ARA * [7]- an anytime version of A *- finds an initial,

Computing optimal motion plans requires both exploring the configuration space to identify free space regions as well as refining understanding of explored regions in order to optimize the plan. We present the rapidly-exploring roadmap (RRM), a new method for single-query optimal motion planning that allows the user to explicitly consider the trade-off between exploration and refinement. Prior methods have focused solely on exploration or refine prematurely, resulting in wasted computation. RRM initially explores the configuration space like an RRT. Once a path is found, RRM uses a user-specified parameter to weigh whether to explore further or refine the explored space by adding edges to the current roadmap to enable finding higher quality paths in the explored space. We demonstrate the performance of RRM and the trade-off between exploration and refinement using two examples, a point robot moving in a plane and a concentric tube robot capable of following curved trajectories that has the potential to assist physicians in minimally invasive medical procedures.