Generalized Assignment for Multi-Robot Systems via Distributed Branch-And-Price

In this paper, we consider a network of agents that has to self-assign a set of tasks while respecting resource constraints. One possible formulation is the Generalized Assignment Problem, where the goal is to find a maximum payoff while satisfying capability constraints. We propose a purely distributed branch-and-price algorithm to solve this problem in a cooperative fashion. Inspired by classical (centralized) branch-and-price schemes, in the proposed algorithm each agent locally solves small linear programs, generates columns by solving simple knapsack problems, and communicates to its neighbors a fixed number of basic columns. We prove finite-time convergence of the algorithm to an optimal solution of the problem. Then, we apply the proposed scheme to a generalized assignment scenario in which a team of robots has to serve a set of tasks. We implement the proposed algorithm in a ROS testbed and provide experiments for a team of heterogeneous robots solving the assignment problem

A Tutorial on Distributed Optimization for Cooperative Robotics: from Setups and Algorithms to Toolboxes and Research Directions

Several interesting problems in multi-robot systems can be cast in the framework of distributed optimization. Examples include multi-robot task allocation, vehicle routing, target protection and surveillance. While the theoretical analysis of distributed optimization algorithms has received significant attention, its application to cooperative robotics has not been investigated in detail. In this paper, we show how notable scenarios in cooperative robotics can be addressed by suitable distributed optimization setups. Specifically, after a brief introduction on the widely investigated consensus optimization (most suited for data analytics) and on the partition-based setup (matching the graph structure in the optimization), we focus on two distributed settings modeling several scenarios in cooperative robotics, i.e., the so-called constraint-coupled and aggregative optimization frameworks. For each one, we consider use-case applications, and we discuss tailored distributed algorithms with their convergence properties. Then, we revise state-of-the-art toolboxes allowing for the implementation of distributed schemes on real networks of robots without central coordinators. For each use case, we discuss their implementation in these toolboxes and provide simulations and real experiments on networks of heterogeneous robots

A Subgradient Based Algorithm for Distributed Task Assignment for Heterogeneous Mobile Robots

The Task Assignment Problem is a common problem in every environment that includes different units and tasks. In this thesis we consider the problem of dynamic assigning tasks to a set of mobile and heterogeneous robots based on their ability and their costs to accomplish a task. Moreover, the dynamics of the robot and a private cost function to be optimized together with the assignment are also taken into account. We solve the problem through a distributed algorithm based on the subgradient method, which allows to deal with a possibly high number of tasks and robots. A local dynamic optimal control and task assignment problem based on the information exchanged through a communication network are solved. Different types of kinematic vehicles with different motion constraints can be taken into account due to the proposed dynamic approach

Distributed Task Allocation and Task Sequencing for Robots with Motion Constraints

This thesis considers two routing and scheduling problems. The first problem is task allocation and sequencing for multiple robots with differential motion constraints. Each task is defined as visiting a point in a subset of the robot configuration space -- this definition captures a variety of tasks including inspection and servicing, as well as one-in-a-set tasks. Our approach is to transform the problem into a multi-vehicle generalized traveling salesman problem (GTSP). We analyze the GTSP insertion methods presented in literature and we provide bounds on the performance of the three insertion mechanisms. We then develop a combinatorial-auction-based distributed implementation of the allocation and sequencing algorithm. The number of the bids in a combinatorial auction, a crucial factor in the runtime, is shown to be linear in the size of the tasks. Finally, we present extensive benchmarking results to demonstrate the improvement over existing distributed task allocation methods. In the second part of this thesis, we address the problem of computing optimal paths through three consecutive points for the curvature-constrained forward moving Dubins vehicle. Given initial and final configurations of the Dubins vehicle and a midpoint with an unconstrained heading, the objective is to compute the midpoint heading that minimizes the total Dubins path length. We provide a novel geometrical analysis of the optimal path and establish new properties of the optimal Dubins' path through three points. We then show how our method can be used to quickly refine Dubins TSP tours produced using state-of-the-art techniques. We also provide extensive simulation results showing the improvement of the proposed approach in both runtime and solution quality over the conventional method of uniform discretization of the heading at the mid-point, followed by solving the minimum Dubins path for each discrete heading

Decentralized task allocation for dynamic, time-sensitive tasks

Thesis: S.M., Massachusetts Institute of Technology, Department of Mechanical Engineering, 2018.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student-submitted PDF version of thesis.Includes bibliographical references (pages 103-110).In time-sensitive and dynamic missions, autonomous vehicles must respond quickly to new information and objectives. In the case of dynamic task allocation, a team of agents are presented with a new, unknown task that must be allocated with their original allocations. This is exacerbated further in decentralized settings where agents are limited to utilizing local information during the allocation process. This thesis presents a fully decentralized, dynamic task allocation algorithm that extends the Consensus-Based Bundle Algorithm (CBBA) to allow for allocating new tasks. Whereas static CBBA requires a full resetting of previous allocations, CBBA with Partial Replanning (CBBA-PR) enables the agents to only partially reset their allocations to efficiently and quickly allocate a new task. By varying the number of existing tasks that are reset during replan, the team can trade-off convergence speed with amount of coordination. By specifically choosing the lowest bid tasks for resetting, CBBA-PR is shown to converge linearly with the number of tasks reset and the network diameter of the team. In addition, limited replanning methods are presented for scenarios without sufficient replanning time. These include a single reset bidding procedure for agents at capacity, a no-replanning heuristic that can identify scenarios that does not require replanning, and a subteam formation algorithm for reducing the network diameter. Finally, this thesis describes hardware and simulation experiments used to explore the effects of ad-hoc, decentralized communication on consensus algorithms and to validate the performance of CBBA-PR.by Noam Buckman.S.M