Pathfinding in Games

Commercial games can be an excellent testbed to artificial intelligence (AI) research, being a middle ground between synthetic, highly abstracted academic benchmarks, and more intricate problems from real life. Among the many AI techniques and problems relevant to games, such as learning, planning, and natural language processing, pathfinding stands out as one of the most common applications of AI research to games. In this document we survey recent work in pathfinding in games. Then we identify some challenges and potential directions for future work. This chapter summarizes the discussions held in the pathfinding workgroup

Engineering LaCAM∗^\ast: Towards Real-Time, Large-Scale, and Near-Optimal Multi-Agent Pathfinding

This paper addresses the challenges of real-time, large-scale, and near-optimal multi-agent pathfinding (MAPF) through enhancements to the recently proposed LaCAM* algorithm. LaCAM* is a scalable search-based algorithm that guarantees the eventual finding of optimal solutions for cumulative transition costs. While it has demonstrated remarkable planning success rates, surpassing various state-of-the-art MAPF methods, its initial solution quality is far from optimal, and its convergence speed to the optimum is slow. To overcome these limitations, this paper introduces several improvement techniques, partly drawing inspiration from other MAPF methods. We provide empirical evidence that the fusion of these techniques significantly improves the solution quality of LaCAM*, thus further pushing the boundaries of MAPF algorithms.Comment: 20 page

Reducing Redundant Work in Jump Point Search

JPS (Jump Point Search) is a state-of-the-art optimal algorithm for online grid-based pathfinding. Widely used in games and other navigation scenarios, JPS nevertheless can exhibit pathological behaviours which are not well studied: (i) it may repeatedly scan the same area of the map to find successors; (ii) it may generate and expand suboptimal search nodes. In this work, we examine the source of these pathological behaviours, show how they can occur in practice, and propose a purely online approach, called Constrained JPS (CJPS), to tackle them efficiently. Experimental results show that CJPS has low overheads and is often faster than JPS in dynamically changing grid environments: by up to 7x in large game maps and up to 14x in pathological scenarios

GPU Accelerated Multi-agent Path Planning Based on Grid Space Decomposition

In this work, we describe a simple and powerful method to implement real-time multi-agent path-finding on Graphics Processor Units (GPUs). The technique aims to find potential paths for many thousands of agents, using the A* algorithm and an input grid map partitioned into blocks. We propose an implementation for the GPU that uses a search space decomposition approach to break down the forward search A* algorithm into parallel independently forward sub-searches. We show that this approach fits well with the programming model of GPUs, enabling planning for many thousands of agents in parallel in real-time applications such as computer games and robotics. The paper describes this implementation using the Compute Unified Device Architecture programming environment, and demonstrates its advantages in GPU performance compared to GPU implementation of Real-Time Adaptive A*

Search for sources of gamma radiation

Práce se zabývá aplikací metaheuristického algoritmu GLNS v praktické úloze - hledání zdrojů gama záření. Přesná pozice zdroje záření může být určena robotem nesoucím detektor, pokud projede v jeho blízkém okolí po trajektorii odpovídající kruhovému oblouku. V obecném případě je zdrojů radiace více a každý z nich může být detekován průjezdem mnoha různými oblouky, což umožňuje po vhodné diskretizaci formulaci úlohy jako zobecněného problému obchodního cestujícího. Je dáno m množin (zdrojů radiace) a n vrcholů (kruhových oblouků), rozdělených do m množin. Cílem je najít takovou sekvenci vrcholů, aby výsledná trajektorie byla co nejkratší. Za tímto účelem byl modifikován a implementován algoritmus GLNS, který je založen na heuristickém adaptivním prohledáváním širokého okolí aktuálního řešení problému. Plánovač je rozšířen o možnost plánování s kubickými křivkami jakožto hranami, které navíc dodržují definovanou maximální křivost. Zároveň je představen postup, jak pro účely plánování odhadovat jejich délku, namísto časově náročnější přesné kalkulace. Dále je do algoritmu přidána intenzifikační metoda zvaná DenseOpt, která lokálně optimalizuje výslednou trajektorii získanou diskrétním plánovačem, čehož je docíleno prohledáváním spojitého prostoru přípustných vrcholů v blízkém okolí vrcholů diskrétního řešení.This thesis documents the application of a metaheuristic algorithm GLNS on practical task - search for sources of gamma radiation. An individual source of radiation can be precisely located by a robot carrying a detector if it passes nearby through a trajectory segment, represented by a circular arc. As there can be more than one potential source of radiation and there are many valid arcs for each of them, the trajectory planning task can be after discretization formulated as Generalized Traveling Salesman Problem with m sets (sources) and n vertices (arcs), partitioned into these m sets. The goal is to find a tour, that visits each set exactly once and has a minimum length. For this purpose, an adaptive large neighborhood search algorithm GLNS is modified and implemented. Additionally, the planner is adapted to plan with cubic curves with predefined minimal curvature as edges, and a procedure for fast estimation of their weights is presented. Moreover, we propose a new intensification procedure called DenseOpt, which serves to improve the quality of the solution obtained from the discrete planner by performing a local search in the continuous space

Motion Primitives and Planning for Robots with Closed Chain Systems and Changing Topologies

When operating in human environments, a robot should use predictable motions that allow humans to trust and anticipate its behavior. Heuristic search-based planning offers predictable motions and guarantees on completeness and sub-optimality of solutions. While search-based planning on motion primitive-based (lattice-based) graphs has been used extensively in navigation, application to high-dimensional state-spaces has, until recently, been thought impractical. This dissertation presents methods we have developed for applying these graphs to mobile manipulation, specifically for systems which contain closed chains. The formation of closed chains in tasks that involve contacts with the environment may reduce the number of available degrees-of-freedom but adds complexity in terms of constraints in the high-dimensional state-space. We exploit the dimensionality reduction inherent in closed kinematic chains to get efficient search-based planning. Our planner handles changing topologies (switching between open and closed-chains) in a single plan, including what transitions to include and when to include them. Thus, we can leverage existing results for search-based planning for open chains, combining open and closed chain manipulation planning into one framework. Proofs regarding the framework are introduced for the application to graph-search and its theoretical guarantees of optimality. The dimensionality-reduction is done in a manner that enables finding optimal solutions to low-dimensional problems which map to correspondingly optimal full-dimensional solutions. We apply this framework to planning for opening and navigating through non-spring and spring-loaded doors using a Willow Garage PR2. The framework motivates our approaches to the Atlas humanoid robot from Boston Dynamics for both stationary manipulation and quasi-static walking, as a closed chain is formed when both feet are on the ground

Autonomous Exploration over Continuous Domains

Motion planning is an essential aspect of robot autonomy, and as such it has been studied for decades, producing a wide range of planning methodologies. Path planners are generally categorised as either trajectory optimisers or sampling-based planners. The latter is the predominant planning paradigm as it can resolve a path efficiently while explicitly reasoning about path safety. Yet, with a limited budget, the resulting paths are far from optimal. In contrast, state-of-the-art trajectory optimisers explicitly trade-off between path safety and efficiency to produce locally optimal paths. However, these planners cannot incorporate updates from a partially observed model such as an occupancy map and fail in planning around information gaps caused by incomplete sensor coverage. Autonomous exploration adds another twist to path planning. The objective of exploration is to safely and efficiently traverse through an unknown environment in order to map it. The desired output of such a process is a sequence of paths that efficiently and safely minimise the uncertainty of the map. However, optimising over the entire space of trajectories is computationally intractable. Therefore, most exploration algorithms relax the general formulation by optimising a simpler one, for example finding the single next best view, resulting in suboptimal performance. This thesis investigates methodologies for optimal and safe exploration over continuous paths. Contrary to existing exploration algorithms that break exploration into independent sub-problems of finding goal points and planning safe paths to these points, our holistic approach simultaneously optimises the coupled problems of where and how to explore. Thus, offering a shift in paradigm from next best view to next best path. With exploration defined as an optimisation problem over continuous paths, this thesis explores two different optimisation paradigms; Bayesian and functional