Monte-Carlo Tree Search for Multi-Agent Pathfinding: Preliminary Results

In this work we study a well-known and challenging problem of Multi-agent Pathfinding, when a set of agents is confined to a graph, each agent is assigned a unique start and goal vertices and the task is to find a set of collision-free paths (one for each agent) such that each agent reaches its respective goal. We investigate how to utilize Monte-Carlo Tree Search (MCTS) to solve the problem. Although MCTS was shown to demonstrate superior performance in a wide range of problems like playing antagonistic games (e.g. Go, Chess etc.), discovering faster matrix multiplication algorithms etc., its application to the problem at hand was not well studied before. To this end we introduce an original variant of MCTS, tailored to multi-agent pathfinding. The crux of our approach is how the reward, that guides MCTS, is computed. Specifically, we use individual paths to assist the agents with the the goal-reaching behavior, while leaving them freedom to get off the track if it is needed to avoid collisions. We also use a dedicated decomposition technique to reduce the branching factor of the tree search procedure. Empirically we show that the suggested method outperforms the baseline planning algorithm that invokes heuristic search, e.g. A*, at each re-planning step.

TransPath: Learning Heuristics For Grid-Based Pathfinding via Transformers

Heuristic search algorithms, e.g. A*, are the commonly used tools for pathfinding on grids, i.e. graphs of regular structure that are widely employed to represent environments in robotics, video games etc. Instance-independent heuristics for grid graphs, e.g. Manhattan distance, do not take the obstacles into account and, thus, the search led by such heuristics performs poorly in the obstacle-rich environments. To this end, we suggest learning the instance-dependent heuristic proxies that are supposed to notably increase the efficiency of the search. The first heuristic proxy we suggest to learn is the correction factor, i.e. the ratio between the instance independent cost-to-go estimate and the perfect one (computed offline at the training phase). Unlike learning the absolute values of the cost-to-go heuristic function, which was known before, when learning the correction factor the knowledge of the instance-independent heuristic is utilized. The second heuristic proxy is the path probability, which indicates how likely the grid cell is lying on the shortest path. This heuristic can be utilized in the Focal Search framework as the secondary heuristic, allowing us to preserve the guarantees on the bounded sub-optimality of the solution. We learn both suggested heuristics in a supervised fashion with the state-of-the-art neural networks containing attention blocks (transformers). We conduct a thorough empirical evaluation on a comprehensive dataset of planning tasks, showing that the suggested techniques i) reduce the computational effort of the A* up to a factor of $4$x while producing the solutions, which costs exceed the costs of the optimal solutions by less than $0.3$% on average; ii) outperform the competitors, which include the conventional techniques from the heuristic search, i.e. weighted A*, as well as the state-of-the-art learnable planners.

Analysis Of The Anytime MAPF Solvers Based On The Combination Of Conflict-Based Search (CBS) and Focal Search (FS)

Conflict-Based Search (CBS) is a widely used algorithm for solving multi-agent pathfinding (MAPF) problems optimally. The core idea of CBS is to run hierarchical search, when, on the high level the tree of solutions candidates is explored, and on the low-level an individual planning for a specific agent (subject to certain constraints) is carried out. To trade-off optimality for running time different variants of bounded sub-optimal CBS were designed, which alter both high- and low-level search routines of CBS. Moreover, anytime variant of CBS does exist that applies Focal Search (FS) to the high-level of CBS - Anytime BCBS. However, no comprehensive analysis of how well this algorithm performs compared to the naive one, when we simply re-invoke CBS with the decreased sub-optimality bound, was present. This work aims at filling this gap. Moreover, we present and evaluate another anytime version of CBS that uses FS on both levels of CBS. Empirically, we show that its behavior is principally different from the one demonstrated by Anytime BCBS. Finally, we compare both algorithms head-to-head and show that using Focal Search on both levels of CBS can be beneficial in a wide range of setups.

POGEMA: Partially Observable Grid Environment for Multiple Agents

We introduce POGEMA (https://github.com/AIRI-Institute/pogema) a sandbox for challenging partially observable multi-agent pathfinding (PO-MAPF) problems . This is a grid-based environment that was specifically designed to be a flexible, tunable and scalable benchmark. It can be tailored to a variety of PO-MAPF, which can serve as an excellent testing ground for planning and learning methods, and their combination, which will allow us to move towards filling the gap between AI planning and learning.

Towards Time-Optimal Any-Angle Path Planning With Dynamic Obstacles

Path finding is a well-studied problem in AI, which is often framed as graph search. Any-angle path finding is a technique that augments the initial graph with additional edges to build shorter paths to the goal. Indeed, optimal algorithms for any-angle path finding in static environments exist. However, when dynamic obstacles are present and time is the objective to be minimized, these algorithms can no longer guarantee optimality. In this work, we elaborate on why this is the case and what techniques can be used to solve the problem optimally. We present two algorithms, grounded in the same idea, that can obtain provably optimal solutions to the considered problem. One of them is a naive algorithm and the other one is much more involved. We conduct a thorough empirical evaluation showing that, in certain setups, the latter algorithm might be as fast as the previously-known greedy non-optimal solver while providing solutions of better quality. In some (rare) cases, the difference in cost is up to 76%, while on average it is lower than one percent (the same cost difference is typically observed between optimal and greedy any-angle solvers in static environments).

Improving Continuous-time Conflict Based Search

Conflict-Based Search (CBS) is a powerful algorithmic framework for optimally solving classical multi-agent path finding (MAPF) problems, where time is discretized into the time steps. Continuous-time CBS (CCBS) is a recently proposed version of CBS that guarantees optimal solutions without the need to discretize time. However, the scalability of CCBS is limited because it does not include any known improvements of CBS. In this paper, we begin to close this gap and explore how to adapt successful CBS improvements, namely, prioritizing conflicts (PC), disjoint splitting (DS), and high-level heuristics, to the continuous time setting of CCBS. These adaptions are not trivial, and require careful handling of different types of constraints, applying a generalized version of the Safe interval path planning (SIPP) algorithm, and extending the notion of cardinal conflicts. We evaluate the effect of the suggested enhancements by running experiments both on general graphs and $2^k$-neighborhood grids. CCBS with these improvements significantly outperforms vanilla CCBS, solving problems with almost twice as many agents in some cases and pushing the limits of multiagent path finding in continuous-time domains.

Revisiting Bounded-Suboptimal Safe Interval Path Planning

Safe-interval path planning (SIPP) is a powerful algorithm for finding a path in the presence of dynamic obstacles. SIPP returns provably optimal solutions. However, in many practical applications of SIPP such as path planning for robots, one would like to trade-off optimality for shorter planning time. In this paper we explore different ways to build a bounded-suboptimal SIPP and discuss their pros and cons. We compare the different bounded-suboptimal versions of SIPP experimentally. While there is no universal winner, the results provide insights into when each method should be used.

Prioritized Multi-agent Path Finding for Differential Drive Robots

Methods for centralized planning of the collision-free trajectories for a fleet of mobile robots typically solve the discretized version of the problem and rely on numerous simplifying assumptions, e.g. moves of uniform duration, cardinal only translations, equal speed and size of the robots etc., thus the resultant plans can not always be directly executed by the real robotic systems. To mitigate this issue we suggest a set of modifications to the prominent prioritized planner -- AA-SIPP(m) -- aimed at lifting the most restrictive assumptions (syncronized translation only moves, equal size and speed of the robots) and at providing robustness to the solutions. We evaluate the suggested algorithm in simulation and on differential drive robots in typical lab environment (indoor polygon with external video-based navigation system). The results of the evaluation provide a clear evidence that the algorithm scales well to large number of robots (up to hundreds in simulation) and is able to produce solutions that are safely executed by the robots prone to imperfect trajectory following. The video of the experiments can be found at https://youtu.be/Fer_irn4BG0.

Combining Safe Interval Path Planning and Constrained Path Following Control: Preliminary Results

We study the navigation problem for a robot moving amidst static and dynamic obstacles and rely on a hierarchical approach to solve it. First, the reference trajectory is planned by the safe interval path planning algorithm that is capable of handling any-angle translations and rotations. Second, the path following problem is treated as the constrained control problem and the original flatness-based approach is proposed to generate control. We suggest a few enhancements for the path planning algorithm aimed at finding trajectories that are more likely to be followed by a robot without collisions. Results of the conducted experimental evaluation show that the number of successfully solved navigation instances significantly increases when using the suggested techniques.

Multi-Agent Pathfinding (MAPF) with Continuous Time

MAPF is the problem of finding paths for multiple agents such that every agent reaches its goal and the agents do not collide. Most prior work on MAPF were on grid, assumed all actions cost the same, agents do not have a volume, and considered discrete time steps. In this work we propose a MAPF algorithm that do not assume any of these assumptions, is complete, and provides provably optimal solutions. This algorithm is based on a novel combination of SIPP, a continuous time single agent planning algorithms, and CBS, a state of the art multi-agent pathfinding algorithm. We analyze this algorithm, discuss its pros and cons, and evaluate it experimentally on several standard benchmarks.