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We solve the TSP for moving targets. 

Conventional Multi-Agent Path Finding (MAPF) problems aim to compute an ensemble of collision-free paths for multiple agents from their respective starting locations to pre-allocated destinations. This work considers a generalized version of MAPF called Multi-Agent Combinatorial Path Finding (MCPF) where agents must collectively visit a large number of intermediate target locations along their paths before arriving at destinations. This problem involves not only planning collision-free paths for multiple agents but also assigning targets and specifying the visiting order for each agent (i.e., target sequencing). To solve the problem, we leverage Conflict-Based Search (CBS) for MAPF and propose a novel approach called Conflict-Based Steiner Search (CBSS). CBSS interleaves (1) the collision resolution strategy in CBS to bypass the curse of dimensionality in MAPF and (2) multiple traveling salesman algorithms to handle the combinatorics in target sequencing, to compute optimal or bounded sub-optimal paths for agents while visiting all the targets. We also develop two variants of CBSS that trade off runtime against solution optimality. Our test results verify the advantage of CBSS over the baselines in terms of computing cheaper paths and improving success rates within a runtime limit for up to 20 agents and 50 targets. Finally, we run both Gazebo simulation and physical robot tests to validate that the planned paths are executable. 

Multi-Agent Path Finding (MA-PF) computes a set of collision-free paths for multiple agents from their respective starting locations to destinations. This paper considers a generalization of MA-PF called Multi-Agent Teamwise Cooperative Path Finding (MA-TC-PF), where agents are grouped as multiple teams and each team has its own objective to be minimized. For example, an objective can be the sum or max of individual arrival times of the agents. In general, there is more than one team, and MA-TC-PF is thus a multi-objective planning problem with the goal of finding the entire Paretooptimal front that represents all possible trade-offs among the objectives of the teams. To solve MA-TC-PF, we propose two algorithms TC-CBS and TC-M*, which leverage the existing CBS and M* for conventional MA-PF. We discuss the conditions under which the proposed algorithms are complete and are guaranteed to find the Pareto-optimal front. We present numerical results for several types of MA-TC-PF problems. 

Conventional Multi-Agent Path Finding (MAPF) problems aim to compute an ensemble of collision-free paths for multiple agents from their respective starting locations to pre-allocated destinations. This work considers a generalized version of MAPF called Multi-Agent Combinatorial Path Finding (MCPF) where agents must collectively visit a large number of intermediate target locations along their paths before arriving at destinations. This problem involves not only planning collision-free paths for multiple agents but also assigning targets and specifying the visiting order for each agent (i.e., target sequencing). To solve the problem, we leverage Conflict-Based Search (CBS) for MAPF and propose a novel approach called Conflict-Based Steiner Search (CBSS). CBSS interleaves (1) the collision resolution strategy in CBS to bypass the curse of dimensionality in MAPF and (2) multiple traveling salesman algorithms to handle the combinatorics in target sequencing, to compute optimal or bounded sub-optimal paths for agents while visiting all the targets. We also develop two variants of CBSS that trade off runtime against solution optimality. Our test results verify the advantage of CBSS over the baselines in terms of computing cheaper paths and improving success rates within a runtime limit for up to 20 agents and 50 targets. Finally, we run both Gazebo simulation and physical robot tests to validate that the planned paths are executable 

Abstract—The Resource Constrained Shortest Path Problem (RCSPP) seeks to determine a minimum-cost path between a start and a goal location while ensuring that one or multiple types of resource consumed along the path do not exceed their limits. This problem is often solved on a graph where a path is incrementally built from the start towards the goal during the search. RCSPP is computationally challenging as comparing these partial solution paths is based on multiple criteria (i.e., the accumulated cost and resource along the path), and in general, there does not exist a single path that optimizes all criteria simultaneously. Consequently, the search needs to maintain and explore a large number of partial paths in order to find an optimal solution. While a variety of algorithms have been developed to solve RCSPP, they either have little consideration about efficiently comparing and maintaining the partial paths, which reduces their overall runtime efficiency, or are restricted to handle only one resource constraint as opposed to multiple resource constraints. This paper develops Enhanced Resource Constrained A* (ERCA*), a fast A*-based algorithm that can find an optimal solution while satisfying multiple resource constraints. ERCA* leverages both the recent advances in multi-objective path planning to efficiently compare and maintain partial paths, and techniques from the existing RCSPP literature. Furthermore, ERCA* has a functional parameter to broker a trade-off between solution quality and runtime efficiency. The results show ERCA* often runs several orders of magnitude faster than an existing leading algorithm for RCSPP. 

This work addresses a Multi-Objective Shortest Path Problem (MO-SPP) on a graph where the goal is to find a set of Pareto-optimal solutions from a start node to a destination in the graph. A family of approaches based on MOA* have been developed to solve MO-SPP in the literature. Typically, these approaches maintain a “frontier” set at each node during the search process to keep track of the non-dominated, partial paths to reach that node. This search process becomes computationally expensive when the number of objectives increases as the number of Pareto-optimal solutions becomes large. In this work, we introduce a new method to efficiently maintain these frontiers for multiple objectives by incrementally constructing balanced binary search trees within the MOA* search framework. We first show that our approach correctly finds the Pareto-optimal front, and then provide extensive simulation results for problems with three, four and five objectives to show that our method runs faster than existing techniques by up to an order of magnitude. 

Conventional Multi-Agent Path Finding (MAPF) problems aim to compute an ensemble of collision-free paths for multiple agents from their respective starting locations to pre-allocated destinations. This work considers a generalized version of MAPF called Multi-Agent Combinatorial Path Finding (MCPF) where agents must collectively visit a large number of intermediate target locations along their paths before arriving at destinations. This problem involves not only planning collisionfree paths for multiple agents but also assigning targets and specifying the visiting order for each agent (i.e. multi-target sequencing). To solve the problem, we leverage the well-known Conflict-Based Search (CBS) for MAPF and propose a novel framework called Conflict-Based Steiner Search (CBSS). CBSS interleaves (1) the conflict resolving strategy in CBS to bypass the curse of dimensionality in MAPF and (2) multiple traveling salesman algorithms to handle the combinatorics in multi-target sequencing, to compute optimal or bounded sub-optimal paths for agents while visiting all the targets. Our extensive tests verify the advantage of CBSS over baseline approaches in terms of computing shorter paths and improving success rates within a runtime limit for up to 20 agents and 50 targets. We also evaluate CBSS with several MCPF variants, which demonstrates the generality of our problem formulation and the CBSS framework. 

This work considers a Motion Planning Problem with Dynamic Obstacles (MPDO) in 2D that requires finding a minimum-arrivaltime collision-free trajectory for a point robot between its start and goal locations amid dynamic obstacles moving along known trajectories. Existing methods, such as continuous Dijkstra paradigm, can find an optimal solution by restricting the shape of the obstacles or the motion of the robot, while this work makes no such assumptions. Other methods, such as search-based planners and sampling-based approaches can compute a feasible solution to this problem but do not provide approximation bounds. Since finding the optimum is challenging for MPDO, this paper develops a framework that can provide tight lower bounds to the optimum. These bounds act as proxies for the optimum which can then be used to bound the deviation of a feasible solution from the optimum. To accomplish this, we develop a framework that consists of (i) a bi-level discretization approach that converts the MPDO to a relaxed path planning problem, and (ii) an algorithm that can solve the relaxed problem to obtain lower bounds. We also present numerical results to corroborate the performance of the proposed framework. These results show that the bounds obtained by our approach for some instances are up to twice tighter than a baseline approach showcasing potential advantages of the proposed approach.