Decentralized multi-robot allocation of tasks with temporal and precedence constraints

Ernesto Nunes, Mitchell McIntire, Maria Gini
2017 Advanced Robotics  
We present an auction-based method for a team of robots to allocate and execute tasks that have temporal and precedence constraints. Temporal constraints are expressed as time windows, within which a task must be executed. The robots use our priority-based iterated sequential single-item auction algorithm to allocate tasks among themselves and keep track of their individual schedules. A key innovation is in decoupling precedence constraints from temporal constraints and dealing with them
more » ... ely. We demonstrate the performance of the allocation method and show how it can be extended to handle failures and delays during task execution. We leverage the power of simulation as a tool to analyze the robustness of schedules. Data collected during simulations are used to compute well-known indexes that measure the risk of delay and failure in the robots' schedules. We demonstrate the effectiveness of our method in simulation and with real robot experiments. a single robot (SR), and tasks are scheduled over a planning horizon (TA). We defined the class of multi-robot task allocation problems with temporal and ordering constraints as MRTA/TOC [3] , and extended the MRTA taxonomy to include temporal constraints expressed in the form of time windows (TA:TW) and ordering constraints expressed in the form of synchronization and precedence constraints (TA:SP). In this paper we handle both types of temporal constraints. Unlike many other MRTA problems, this problem in its general form, allowing arbitrary precedence constraints and time windows for tasks, has not been thoroughly studied, due in part to its complexity even for approximate solutions. Our main contribution is an auction-based algorithm, TePSSI (Temporal and Precedence constrained Sequential Single-Item auction), which provides a decentralized method of computing a solution for task allocation problems with temporal and precedence constraints. In our approach each robot owns its schedule for the subset of tasks assigned to it. A schedule is represented as a simple temporal network (STN) [4] , which stores the execution times of the tasks. In this paper, we describe the auction algorithm, analyze its complexity, prove its soundness and completeness when only precedence constraints are considered, and demonstrate the algorithm's performance empirically. We also show how to combine the task allocation algorithm with an executive that monitors the execution of the tasks, reallocating tasks via a one-shot greedy auction when needed because of execution delays or failures. The framework herein proposed supports task execution and recovery via a planning-execution-replanning cycle. We present an experimental evaluation of the framework in simulation and through experiments with real robots. In our previous work we designed TeSSI (Temporal Sequential Single-I tem auction) [5] and pIA (Prioritized Iterated Auction) [6], to handle general temporal and precedence constraints independently, and only at planning time. The auction herein proposed is, to the best of our knowledge, the first auction-based algorithm that is designed to handle general precedence and temporal constraints simultaneously, whilst also considering plan execution aspects. Related Work Methods for multi-robot task allocation can be broadly categorized into centralized, decentralized, and hybrid; and depending on the optimality of the solution, exact or heuristic. A recent example of a centralized method uses an efficient mixed-integer linear programming approach for multi-robot scheduling with spatial constraints [7] . Centralized methods can achieve optimal results, but are not suitable for field operations where communication can be limited and unreliable, and faults are common. Hence, we choose a decentralized approach. Distributed Constraint Optimization Problem (DCOP) [8] algorithms provide a viable option for modeling constraint problems in a distributed way. However, solving DCOP exactly is NP-hard and impractical even for unconstrained Multi-Robot Task Allocation (MRTA) problems [9] . Approximate methods such as Max-Sum have been proposed [10, 11 ], yet we are not aware of any DCOP algorithm that handles task allocation with precedence and time window constraints. Auction-based approaches have become popular for their flexibility, decentralized nature, and robustness to failure [12, 13] . Auctions move the burden of computation onto individual robots and are robust to local changes or failures, since the auction can proceed with the remaining robots when some robots malfunction [14] .
doi:10.1080/01691864.2017.1396922 fatcat:nvbk2pv4dve67bsaeywxoynpm4