Multi-robot Coverage and Redeployment Algorithms

In this thesis, we focus on two classes of multi-robot task allocation and deployment problems motivated by applications in ride-sourcing transportation networks and service robots: 1) coverage control with multiple robots, and 2) robots servicing tasks arriving sequentially over time. The first problem considers the deployment of multiple robots to cover a domain. The multi-robot problem consists of multiple robots with sensors on-board observing the spatially distributed events in an environment. The objective is to maximize the sensing quality of the events via optimally distributing the robots in the environment. This problem has been studied extensively in the literature and several algorithms have been proposed for different variants of this problem. However, there has been a lack of theoretical results on the quality of the solutions provided by these algorithms. In this thesis, we provide a new distributed multi-robot coverage algorithm with theoretical guarantees on the solution quality, run-time complexity, and communication complexity. The theoretical bound on the solution quality holds for on-board sensors where the sensing quality of the sensors is a sub-additive function of the distance to the event location in convex and non-convex environments. A natural extension of the multi-robot coverage control problem is considered in this thesis where each robot is equipped with a set of different sensors and observes different event types in the environment. Servicing a task in this problem corresponds to sensing an event occurring at a particular location and does not involve visiting the task location. Each event type has a different distribution over the domain. The robots are heterogeneous in that each robot is capable of sensing a subset of the event types. The objective is to deploy the robots into the domain to maximize the total coverage of the multiple event types. We propose a new formulation for the heterogeneous coverage problem. We provide a simple distributed algorithm to maximize the coverage. Then, we extend the result to the case where the event distribution is unknown before the deployment and provide a distributed algorithm and prove the convergence of the approach to a locally optimal solution. The third problem considers the deployment of a set of autonomous robots to efficiently service tasks that arrive sequentially in an environment over time. Each task is serviced when a robot visits the corresponding task location. Robots can then redeploy while waiting for the next task to arrive. The objective is to redeploy the robots taking into account the next N task arrivals. We seek to minimize a linear combination of the expected cost to service tasks and the redeployment cost between task arrivals. In the single robot case, we propose a one-stage greedy algorithm and prove its optimality. For multiple robots, the problem is NP-hard, and we propose two constant-factor approximation algorithms, one for the problem with a horizon of two task arrivals and the other for the infinite horizon when the redeployment cost is weighted more heavily than the service cost. Finally, we extend the second problem to scenarios where the robots are self-interested service units maximizing their payoff. The payoff of a robot is a linear combination of its relocation cost and its expected revenue from servicing the tasks in its vicinity. In this extension, the global objective is either to minimize the expected time or minimize the maximum time to respond to the tasks. We introduce two indirect control methods to relocate the self-interested service units: 1) an information sharing method, and 2) a method that incentivizes relocation with payments. We prove NP-hardness of finding the optimal controls and provide algorithms to find the near-optimal control. We quantify the performance of the proposed algorithms with analytical upper-bounds and real-world data from ride-sourcing applications

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

Distributed Multi-Robot Coverage Control of Non-Convex Environments With Guarantees

© 2023 IEEE Yengejeh, A. S., Asghar, A. B., & Smith, S. L. (2023). Distributed multirobot coverage control of nonconvex environments with guarantees. IEEE Transactions on Control of Network Systems, 10(2), 796–808. https://doi.org/10.1109/tcns.2022.3210328In this article, we revisit the problem of distributed coverage with a fleet of robots in convex and nonconvex environments. In the majority of approaches for this problem, the environment is partitioned, each robot is assigned to a partition and each robot moves toward a location that improves the service quality in its partition. These approaches converge to a locally optimal solution; however, there is no guarantee on the quality of the locally optimal solution with respect to the globally optimal solution. We propose distributed algorithms for the coverage problem in convex continuous, nonconvex continuous, and metric graphs. We consider subadditive sensing functions, which capture scenarios where the service quality of a location is proportional to the distance between the robot and the location. For these sensing functions, we provide the first constant factor approximation algorithms for the distributed coverage problem. We also characterize the time and communication complexity of the proposed algorithm and show that the robots converge to a near-optimal solution in polynomial time. The approximation factor guarantees on the solution quality requires twice the conventional communication range; however, the extensive simulation results show that the proposed algorithm provides a close to optimal solution with the conventional communication range as well, and outperforms several existing algorithms in convex, nonconvex continuous environments and metric graphs.Research partially supported by the Natural Sciences and Engineering Research Council of Canada (NSERC