Multi-agent Path Planning and Network Flow

This paper connects multi-agent path planning on graphs (roadmaps) to network flow problems, showing that the former can be reduced to the latter, therefore enabling the application of combinatorial network flow algorithms, as well as general linear program techniques, to multi-agent path planning problems on graphs. Exploiting this connection, we show that when the goals are permutation invariant, the problem always has a feasible solution path set with a longest finish time of no more than $n + V - 1$ steps, in which $n$ is the number of agents and $V$ is the number of vertices of the underlying graph. We then give a complete algorithm that finds such a solution in $O(nVE)$ time, with $E$ being the number of edges of the graph. Taking a further step, we study time and distance optimality of the feasible solutions, show that they have a pairwise Pareto optimal structure, and again provide efficient algorithms for optimizing two of these practical objectives.Comment: Corrected an inaccuracy on time optimal solution for average arrival tim

Downwash-Aware Trajectory Planning for Large Quadrotor Teams

We describe a method for formation-change trajectory planning for large quadrotor teams in obstacle-rich environments. Our method decomposes the planning problem into two stages: a discrete planner operating on a graph representation of the workspace, and a continuous refinement that converts the non-smooth graph plan into a set of C^k-continuous trajectories, locally optimizing an integral-squared-derivative cost. We account for the downwash effect, allowing safe flight in dense formations. We demonstrate the computational efficiency in simulation with up to 200 robots and the physical plausibility with an experiment with 32 nano-quadrotors. Our approach can compute safe and smooth trajectories for hundreds of quadrotors in dense environments with obstacles in a few minutes.Comment: 8 page

Motion Planning for Unlabeled Discs with Optimality Guarantees

We study the problem of path planning for unlabeled (indistinguishable) unit-disc robots in a planar environment cluttered with polygonal obstacles. We introduce an algorithm which minimizes the total path length, i.e., the sum of lengths of the individual paths. Our algorithm is guaranteed to find a solution if one exists, or report that none exists otherwise. It runs in time $\tilde{O}(m^4+m^2n^2)$, where $m$ is the number of robots and $n$ is the total complexity of the workspace. Moreover, the total length of the returned solution is at most $\text{OPT}+4m$, where OPT is the optimal solution cost. To the best of our knowledge this is the first algorithm for the problem that has such guarantees. The algorithm has been implemented in an exact manner and we present experimental results that attest to its efficiency

coordinated selection and timing of multiple trajectories of discretely mobile robots

Abstract The paper addresses the multi-agent path planning (MPP) of mobile agents with multiple goals taking into consideration the kinematic constraints of each agent. The "Swing and Dock" (SaD) robotic system being discussed uses discrete locomotion, where agents swing around fixed pins and dock with their mounting legs to realize displacement from one point to another. The system was developed as a subsystem for mobile robotic fixture (SwarmItFix). Previous work dealt with MPP for SaD agents using the concept of extended temporal graph with Integer Linear Programming (ILP) based formulations. The approach discretized time into unit steps, whereas in reality, the agents are constrained by velocity limits. Hence, a real-time schedule is required to accurately plan the agent movement in a working scenario. We utilize the concept of simple temporal network and extend our ILP formulations to model the velocity kinematic constraints. The mathematical formulations are implemented and tested using a GUROBI solver. Computational results display the effectiveness of the approach

Scalable Robotic Intra-Logistics with Answer Set Programming

Over time, Answer Set Programming (ASP) has gained traction as a versatile logic programming semantics with performant processing systems, used by a growing number of significant applications in academia and industry. However, this development is threatened by a lack of commonly accepted design patterns and techniques for ASP to address dynamic application on a real-world scale. To this end, we identified robotic intra-logistics as representative scenario, a major domain of interest in the context of the fourth industrial revolution. For this setting, we aim to provide a scalable and efficient ASP-based solutions by (1) stipulating a standardized test and benchmark framework; (2) leveraging existing ASP techniques through new design patterns; and (3) extending ASP with new functionalities. In this paper we will expand on the subject matter as well as detail our current progress and future plans