Incremental Phi*: Incremental Any-Angle Path Planning on Grids

We study path planning on grids with blocked and unblocked cells. Any-angle path-planning algorithms find short paths fast because they propagate information along grid edges without constraining the resulting paths to grid edges. Incremental path-planning algorithms solve a series of similar path-planning problems faster than repeated single-shot searches because they reuse information from the previous search to speed up the next one. In this paper, we combine these ideas by making the any-angle path-planning algorithm Basic Theta* incremental. This is non-trivial because Basic Theta* does not fit the standard assumption that the parent of a vertex in the search tree must also be its neighbor. We present Incremental Phi* and show experimentally that it can speed up Basic Theta* by about one order of magnitude for path planning with the freespace assumption

Trajectory Planning on Grids: Considering Speed Limit Constraints

Trajectory (path) planning is a well known and thoroughly studied field of automated planning. It is usually used in computer games, robotics or autonomous agent simulations. Grids are often used for regular discretization of continuous space. Many methods exist for trajectory (path) planning on grids, we address the well known A* algorithm and the state-of-the-art Theta* algorithm. Theta* algorithm, as opposed to A*, provides ‘any-angle‘ paths that look more realistic. In this paper, we provide an extension of both these algorithms to enable support for speed limit constraints.We experimentally evaluate and thoroughly discuss how the extensions affect the planning process showing reasonability and justification of our approach

A Novel Online Any-Angle Path Planning Algorithm

Any-angle path planning algorithms are a popular topic of research in the fields of robotics and video games with a key focus in finding true shortest paths. Most online grid-constrained path-planning algorithms find suboptimal solutions that present as unrealistic paths, a shortcoming which the any-angle class of algorithms attempt to address. While they do provide improvements in finding shorter paths, it generally comes in the form of a trade-off, by sacrificing runtime performance. The lack of a robust solution, that does not compromise on any of the desirable properties – online, reduced search-space, low runtime, short paths – of an any-angle path-planning algorithm, is a prime motivator for the current research. A novel any-angle algorithm for 2-dimensional uniform-cost octile grids is introduced that operates purely online and reduces the search-space and runtime without sacrificing path-length. The methodology presents an atypical any-angle path-planning algorithm which employs a best first search that races individual paths towards a target with a free-space assumption. The paths exhibit bug-like properties in that they either move towards a target or wall-follow, but are allowed to terminate early. Wall following determines points on the boundary that are candidate heading changes in the path. At each step, the path is analysed and pruned in order to maintain its tautness at all times. Together with a purely heuristic cost based on the assumption of free-space between heading changes, the algorithm drives the search towards expanding the most promising path first. Once a path has reached the goal, it checks the free-space assumption between its heading changes and updates its cost accordingly. The shortest-path is determined when the cost estimate of any remaining paths is longer than the solution path. The proposed algorithm is shown experimentally to be competitive on a number of performance metrics with state-of-the-art any-angle algorithms. It also presents desirable properties that allow it to have a reduced search space and make it suitable for providing multiple solutions

Pengujian Performa Algoritma Lazy Theta* untuk Pencarian Jalur Terpendek berdasarkan Fungsi Heuristik Euclidean dan Manhattan

Pathfinding merupakan studi Artificial Intelligence (AI) untuk mencari jalur terpendek antar dua titik. Algoritma any-angle path planning merupakan algoritma pathfinding yang dirancang untuk menghasilkan jalur yang mendekati true shortest path tanpa terikat dengan hubungan ketetanggaan antar grid karena menggunakan pengecekan line of sight. Lazy Theta* merupakan algoritma any-angle path planning yang berbasis grid dan menggunakan lazy evaluation yang mengurangi kebutuhan pengecekan line of sight. Lazy Theta* masih memiliki ruang untuk ditelusuri, salah satunya melalui fungsi heuristik. Ruang lingkup penelitian adalah fungsi heuristik Euclidean dan Manhattan, dan representasi peta yang digunakan adalah rectangular grid dengan luas 100 × 100 grids. Skenario pengujian performa algoritma dilakukan sebanyak 12 skenario yang terdiri dari 12 posisi pengujian yang masing-masing memiliki 8 peta pengujian. Parameter pengujian algoritma adalah completeness, path count, runtime, path length, dan searched nodes. Berdasarkan penelitian ini, algoritma Lazy Theta* dengan fungsi heuristik Euclidean mampu menghasilkan jalur yang lebih pendek dan natural dibandingkan dengan jalur yang dihasilkan dengan fungsi heuristik Manhattan¸ yaitu 8.90% lebih sedikit pada path count dan 3.24% lebih pendek pada path length. Sedangkan dengan fungsi heuristik Manhattan, runtime-nya yang lebih cepat sebesar 23.30% dan nodes searched nya 26.37% lebih sedikit dari fungsi heuristik Euclidean

Any-Angle Pathfinding for Multiple Agents Based on SIPP Algorithm

The problem of finding conflict-free trajectories for multiple agents of identical circular shape, operating in shared 2D workspace, is addressed in the paper and decoupled, e.g., prioritized, approach is used to solve this problem. Agents' workspace is tessellated into the square grid on which any-angle moves are allowed, e.g. each agent can move into an arbitrary direction as long as this move follows the straight line segment whose endpoints are tied to the distinct grid elements. A novel any-angle planner based on Safe Interval Path Planning (SIPP) algorithm is proposed to find trajectories for an agent moving amidst dynamic obstacles (other agents) on a grid. This algorithm is then used as part of a prioritized multi-agent planner AA-SIPP(m). On the theoretical, side we show that AA-SIPP(m) is complete under well-defined conditions. On the experimental side, in simulation tests with up to 200 agents involved, we show that our planner finds much better solutions in terms of cost (up to 20%) compared to the planners relying on cardinal moves only.Comment: Final version as submitted to ICAPS-2017 (main track); 8 pages; 4 figures; 1 algorithm; 2 table

The 2k neighborhoods for grid path planning

Indexación: Scopus.Grid path planning is an important problem in AI. Its understanding has been key for the development of autonomous navigation systems. An interesting and rather surprising fact about the vast literature on this problem is that only a few neighborhoods have been used when evaluating these algorithms. Indeed, only the 4- and 8-neighborhoods are usually considered, and rarely the 16-neighborhood. This paper describes three contributions that enable the construction of effective grid path planners for extended 2k-neighborhoods; that is, neighborhoods that admit 2k neighbors per state, where k is a parameter. First, we provide a simple recursive definition of the 2k-neighborhood in terms of the 2k− 1-neighborhood. Second, we derive distance functions, for any k ≥ 2, which allow us to propose admissible heuristics that are perfect for obstacle-free grids, which generalize the well-known Manhattan and Octile distances. Third, we define the notion of canonical path for the 2k-neighborhood; this allows us to incorporate our neighborhoods into two versions of A*, namely Canonical A* and Jump Point Search (JPS), whose performance, we show, scales well when increasing k. Our empirical evaluation shows that, when increasing k, the cost of the solution found improves substantially. Used with the 2k-neighborhood, Canonical A* and JPS, in many configurations, are also superior to the any-angle path planner Theta∗ both in terms of solution quality and runtime. Our planner is competitive with one implementation of the any-angle path planner, ANYA in some configurations. Our main practical conclusion is that standard, well-understood grid path planning technology may provide an effective approach to any-angle grid path planning.https://jair.org/index.php/jair/article/view/1138