Target Assignment in Robotic Networks: Distance Optimality Guarantees and Hierarchical Strategies

We study the problem of multi-robot target assignment to minimize the total distance traveled by the robots until they all reach an equal number of static targets. In the first half of the paper, we present a necessary and sufficient condition under which true distance optimality can be achieved for robots with limited communication and target-sensing ranges. Moreover, we provide an explicit, non-asymptotic formula for computing the number of robots needed to achieve distance optimality in terms of the robots' communication and target-sensing ranges with arbitrary guaranteed probabilities. The same bounds are also shown to be asymptotically tight. In the second half of the paper, we present suboptimal strategies for use when the number of robots cannot be chosen freely. Assuming first that all targets are known to all robots, we employ a hierarchical communication model in which robots communicate only with other robots in the same partitioned region. This hierarchical communication model leads to constant approximations of true distance-optimal solutions under mild assumptions. We then revisit the limited communication and sensing models. By combining simple rendezvous-based strategies with a hierarchical communication model, we obtain decentralized hierarchical strategies that achieve constant approximation ratios with respect to true distance optimality. Results of simulation show that the approximation ratio is as low as 1.4

An integrated multi-population genetic algorithm for multi-vehicle task assignment in a drift field

This paper investigates the task assignment problem for a team of autonomous aerial/marine vehicles driven by constant thrust and maneuvering in a planar lateral drift field. The aim is to minimize the total traveling time in order to guide the vehicles to deliver a number of customized sensors to a set of target points with different sensor demands in the drift field. To solve the problem, we consider together navigation strategies and target assignment algorithms; the former minimizes the traveling time between two given locations in the drift field and the latter allocates a sequence of target locations to each vehicle. We first consider the effect of the weight of the carried sensors on the speed of each vehicle, and construct a sufficient condition to guarantee that the whole operation environment is reachable for the vehicles. Then from optimal control principles, time-optimal path planning is carried out to navigate each vehicle from an initial position to its given target location. Most importantly, to assign the targets to the vehicles, we combine the virtual coding strategy, multiple offspring method, intermarriage crossover strategy, and the tabu search mechanism to obtain a co-evolutionary multi-population genetic algorithm, short-named CMGA. Simulations on sensor delivery scenarios in both fixed and time-varying drift fields are shown to highlight the satisfying performances of the proposed approach against popular greedy algorithms

Distributed multi-vehicle task assignment in a time-invariant drift field with obstacles

This study investigates the task assignment problem where a fleet of dispersed vehicles needs to visit multiple target locations in a time-invariant drift field with obstacles while trying to minimise the vehicles' total travel time. The vehicles have different capabilities, and each kind of vehicles can visit a certain type of the target locations; each target location might require to be visited more than once by different kinds of vehicles. The task assignment problem has been proven to be NP-hard. A path planning algorithm is first designed to minimise the time for a vehicle to travel between two given locations through the drift field while avoiding any obstacle. The path planning algorithm provides the travel cost matrix for the target assignment, and generates routes once the target locations are assigned to the vehicles. Then, a distributed algorithm is proposed to assign the target locations to the vehicles using only local communication. The algorithm guarantees that all the visiting demands of every target will be satisfied within a total travel time that is at worst twice of the optimal when the travel cost matrix is symmetric. Numerical simulations show that the algorithm can lead to solutions close to the optimal

Efficient Routing for Precedence-Constrained Package Delivery for Heterogeneous Vehicles

This paper studies the precedence-constrained task assignment problem for a team of heterogeneous vehicles to deliver packages to a set of dispersed customers subject to precedence constraints that specify which customers need to be visited before which other customers. A truck and a micro drone with complementary capabilities are employed where the truck is restricted to travel in a street network and the micro drone, restricted by its loading capacity and operation range, can fly from the truck to perform the last-mile package deliveries. The objective is to minimize the time to serve all the customers respecting every precedence constraint. The problem is shown to be NP-hard, and a lower bound on the optimal time to serve all the customers is constructed by using tools from graph theory. Then, integrating with a topological sorting technique, several heuristic task assignment algorithms are proposed to solve the task assignment problem. Numerical simulations show the superior performances of the proposed algorithms compared with popular genetic algorithms. Note to Practitioners - This paper presents several task assignment algorithms for the precedence-constrained package delivery for the team of a truck and a micro drone. The truck can carry the drone moving in a street network, while the drone completes the last-mile package deliveries. The practical contributions of this paper are fourfold. First, the precedence constraints on the ordering of the customers to be served are considered, which enables complex logistic scheduling for customers prioritized according to their urgency or importance. Second, the package delivery optimization problem is shown to be NP-hard, which clearly shows the need for creative approximation algorithms to solve the problem. Third, the constructed lower bound on the optimal time to serve all the customers helps to clarify for practitioners the limiting performance of a feasible solution. Fourth, the proposed task assignment algorithms are efficient and can be adapted for real scenarios

Distributed and Adaptive Algorithms for Vehicle Routing in a Stochastic and Dynamic Environment

In this paper we present distributed and adaptive algorithms for motion coordination of a group of m autonomous vehicles. The vehicles operate in a convex environment with bounded velocity and must service demands whose time of arrival, location and on-site service are stochastic; the objective is to minimize the expected system time (wait plus service) of the demands. The general problem is known as the m-vehicle Dynamic Traveling Repairman Problem (m-DTRP). The best previously known control algorithms rely on centralized a-priori task assignment and are not robust against changes in the environment, e.g. changes in load conditions; therefore, they are of limited applicability in scenarios involving ad-hoc networks of autonomous vehicles operating in a time-varying environment. First, we present a new class of policies for the 1-DTRP problem that: (i) are provably optimal both in light- and heavy-load condition, and (ii) are adaptive, in particular, they are robust against changes in load conditions. Second, we show that partitioning policies, whereby the environment is partitioned among the vehicles and each vehicle follows a certain set of rules in its own region, are optimal in heavy-load conditions. Finally, by combining the new class of algorithms for the 1-DTRP with suitable partitioning policies, we design distributed algorithms for the m-DTRP problem that (i) are spatially distributed, scalable to large networks, and adaptive to network changes, (ii) are within a constant-factor of optimal in heavy-load conditions and stabilize the system in any load condition. Simulation results are presented and discussed.Comment: Paper to be submitted to IEEE Transactions on Automatic Contro

Clustering-based algorithms for multi-vehicle task assignment in a time-invariant drift field

This paper studies the multi-vehicle task assignment problem where several dispersed vehicles need to visit a set of target locations in a time-invariant drift field while trying to minimize the total travel time. Using optimal control theory, we first design a path planning algorithm to minimize the time for each vehicle to travel between two given locations in the drift field. The path planning algorithm provides the cost matrix for the target assignment, and generates routes once the target locations are assigned to a vehicle. Then, we propose several clustering strategies to assign the targets, and we use two metrics to determine the visiting sequence of the targets clustered to each vehicle. Mainly used to specify the minimum time for a vehicle to travel between any two target locations, the cost matrix is obtained using the path planning algorithm, and is in general asymmetric due to time-invariant currents of the drift field. We show that one of the clustering strategies can obtain a min-cost arborescence of the asymmetric target vehicle graph where the weight of a directed edge between two vertices is the minimum travel time from one vertex to the other respecting the orientation. Using tools from graph theory, a lower bound on the optimal solution is found, which can be used to measure the proximity of a solution from the optimal. Furthermore, by integrating the target clustering strategies with the target visiting metrics, we obtain several task assignment algorithms. Among them, two algorithms guarantee that all the target locations will be visited within a computable maximal travel time, which is at most twice of the optimal when the cost matrix is symmetric. Finally, numerical simulations show that the algorithms can quickly lead to a solution that is close to the optimal

Dynamic Vehicle Routing for Robotic Systems

Recent years have witnessed great advancements in the science and technology of autonomy, robotics, and networking. This paper surveys recent concepts and algorithms for dynamic vehicle routing (DVR), that is, for the automatic planning of optimal multivehicle routes to perform tasks that are generated over time by an exogenous process. We consider a rich variety of scenarios relevant for robotic applications. We begin by reviewing the basic DVR problem: demands for service arrive at random locations at random times and a vehicle travels to provide on-site service while minimizing the expected wait time of the demands. Next, we treat different multivehicle scenarios based on different models for demands (e.g., demands with different priority levels and impatient demands), vehicles (e.g., motion constraints, communication, and sensing capabilities), and tasks. The performance criterion used in these scenarios is either the expected wait time of the demands or the fraction of demands serviced successfully. In each specific DVR scenario, we adopt a rigorous technical approach that relies upon methods from queueing theory, combinatorial optimization, and stochastic geometry. First, we establish fundamental limits on the achievable performance, including limits on stability and quality of service. Second, we design algorithms, and provide provable guarantees on their performance with respect to the fundamental limits.United States. Air Force Office of Scientific Research (Award FA 8650-07-2-3744)United States. Army Research Office. Multidisciplinary University Research Initiative (Award W911NF-05-1-0219)National Science Foundation (U.S.) (Award ECCS-0705451)National Science Foundation (U.S.) (Award CMMI-0705453)United States. Army Research Office (Award W911NF-11-1-0092

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