Multi-Robot Task Allocation and Scheduling with Spatio-Temporal and Energy Constraints

Autonomy in multi-robot systems is bounded by coordination among its agents. Coordination implies simultaneous task decomposition, task allocation, team formation, task scheduling and routing; collectively termed as task planning. In many real-world applications of multi-robot systems such as commercial cleaning, delivery systems, warehousing and inventory management: spatial & temporal constraints, variable execution time, and energy limitations need to be integrated into the planning module. Spatial constraints comprise of the location of the tasks, their reachability, and the structure of the environment; temporal constraints express task completion deadlines. There has been significant research in multi-robot task allocation involving spatio-temporal constraints. However, limited attention has been paid to combine them with team formation and non- instantaneous task execution time. We achieve team formation by including quota constraints which ensure to schedule the number of robots required to perform the task. We introduce and integrate task activation (time) windows with the team effort of multiple robots in performing tasks for a given duration. Additionally, while visiting tasks in space, energy budget affects the robots operation time. We map energy depletion as a function of time to ensure long-term operation by periodically visiting recharging stations. Research on task planning approaches which combines all these conditions is still lacking. In this thesis, we propose two variants of Team Orienteering Problem with task activation windows and limited energy budget to formulate the simultaneous task allocation and scheduling as an optimization problem. A complete mixed integer linear programming (MILP) formulation for both variants is presented in this work, implemented using Gurobi Optimizer and analyzed for scalability. This work compares the different objectives of the formulation like maximizing the number of tasks visited, minimizing the total distance travelled, and/or maximizing the reward, to suit various applications. Finally, analysis of optimal solutions discover trends in task selection based on the travel cost, task completion rewards, robot\u27s energy level, and the time left to task inactivation

Discrete Path Planing Strategies for Coverage and Multi-Robot Rendezvous

This thesis addresses the problem of motion planning for autonomous robots, given a map and an estimate of the robot pose within it. The motion planning problem for a mobile robot can be defined as computing a trajectory in an environment from one pose to another while avoiding obstacles and optimizing some objective such as path length or travel time, subject to constraints like vehicle dynamics limitations. More complex planning problems such as multi-robot planning or complete coverage of an area can also be defined within a similar optimization structure. The computational complexity of path planning presents a considerable challenge for real-time execution with limited resources and various methods of simplifying the problem formulation by discretizing the solution space are grouped under the class of discrete planning methods. The approach suggests representing the environment as a roadmap graph and formulating shortest path problems to compute optimal robot trajectories on it. This thesis presents two main contributions under the framework of discrete planning. The first contribution addresses complete coverage of an unknown environment by a single omnidirectional ground rover. The 2D occupancy grid map of the environment is first converted into a polygonal representation and decomposed into a set of convex sectors. Second, a coverage path is computed through the sectors using a hierarchical inter-sector and intra-sector optimization structure. It should be noted that both convex decomposition and optimal sector ordering are known NP-hard problems, which are solved using a greedy cut approximation algorithm and Travelling Salesman Problem (TSP) heuristics, respectively. The second contribution presents multi-robot path-planning strategies for recharging autonomous robots performing a persistent task. The work considers the case of surveillance missions performed by a team of Unmanned Aerial Vehicles (UAVs). The goal is to plan minimum cost paths for a separate team of dedicated charging robots such that they rendezvous with and recharge all the UAVs as needed. To this end, planar UAV trajectories are discretized into sets of charging locations and a partitioned directed acyclic graph subject to timing constraints is defined over them. Solutions consist of paths through the graph for each of the charging robots. The rendezvous planning problem for a single recharge cycle is formulated as a Mixed Integer Linear Program (MILP), and an algorithmic approach, using a transformation to the TSP, is presented as a scalable heuristic alternative to the MILP. The solution is then extended to longer planning horizons using both a receding horizon and an optimal fixed horizon strategy. Simulation results are presented for both contributions, which demonstrate solution quality and performance of the presented algorithms

Discrete Path Planing Strategies for Coverage and Multi-Robot Rendezvous

This thesis addresses the problem of motion planning for autonomous robots, given a map and an estimate of the robot pose within it. The motion planning problem for a mobile robot can be defined as computing a trajectory in an environment from one pose to another while avoiding obstacles and optimizing some objective such as path length or travel time, subject to constraints like vehicle dynamics limitations. More complex planning problems such as multi-robot planning or complete coverage of an area can also be defined within a similar optimization structure. The computational complexity of path planning presents a considerable challenge for real-time execution with limited resources and various methods of simplifying the problem formulation by discretizing the solution space are grouped under the class of discrete planning methods. The approach suggests representing the environment as a roadmap graph and formulating shortest path problems to compute optimal robot trajectories on it. This thesis presents two main contributions under the framework of discrete planning. The first contribution addresses complete coverage of an unknown environment by a single omnidirectional ground rover. The 2D occupancy grid map of the environment is first converted into a polygonal representation and decomposed into a set of convex sectors. Second, a coverage path is computed through the sectors using a hierarchical inter-sector and intra-sector optimization structure. It should be noted that both convex decomposition and optimal sector ordering are known NP-hard problems, which are solved using a greedy cut approximation algorithm and Travelling Salesman Problem (TSP) heuristics, respectively. The second contribution presents multi-robot path-planning strategies for recharging autonomous robots performing a persistent task. The work considers the case of surveillance missions performed by a team of Unmanned Aerial Vehicles (UAVs). The goal is to plan minimum cost paths for a separate team of dedicated charging robots such that they rendezvous with and recharge all the UAVs as needed. To this end, planar UAV trajectories are discretized into sets of charging locations and a partitioned directed acyclic graph subject to timing constraints is defined over them. Solutions consist of paths through the graph for each of the charging robots. The rendezvous planning problem for a single recharge cycle is formulated as a Mixed Integer Linear Program (MILP), and an algorithmic approach, using a transformation to the TSP, is presented as a scalable heuristic alternative to the MILP. The solution is then extended to longer planning horizons using both a receding horizon and an optimal fixed horizon strategy. Simulation results are presented for both contributions, which demonstrate solution quality and performance of the presented algorithms

Optimal Mission Planning of Autonomous Mobile Agents for Applications in Microgrids, Sensor Networks, and Military Reconnaissance

As technology advances, the use of collaborative autonomous mobile systems for various applications will become evermore prevalent. One interesting application of these multi-agent systems is for autonomous mobile microgrids. These systems will play an increasingly important role in applications such as military special operations for mobile ad-hoc power infrastructures and for intelligence, surveillance, and reconnaissance missions. In performing these operations with these autonomous energy assets, there is a crucial need to optimize their functionality according to their specific application and mission. Challenges arise in determining mission characteristics such as how each resource should operate, when, where, and for how long. This thesis explores solutions in determining optimal mission plans around the applications of autonomous mobile microgrids and resource scheduling with UGVs and UAVs. Optimal network connections, energy asset locations, and cabling trajectories are determined in the mobile microgrid application. The resource scheduling applications investigate the use of a UGV to recharge wireless sensors in a wireless sensor network. Optimal recharging of mobile distributed UAVs performing reconnaissance missions is also explored. With genetic algorithm solution approaches, the results show the proposed methods can provide reasonable a-priori mission plans, considering the applied constraints and objective functions in each application. The contributions of this thesis are: (1) The development and analysis of solution methodologies and mission simulators for a-priori mission plan development and testing, for applications in organizing and scheduling power delivery with mobile energy assets. Applying these methods results in (2) the development and analysis of reasonable a-priori mission plans for autonomous mobile microgrids/assets, in various scenarios. This work could be extended to include a more diverse set of heterogeneous agents and incorporate dynamic loads to provide power to

Coverage & cooperation: Completing complex tasks as quickly as possible using teams of robots

As the robotics industry grows and robots enter our homes and public spaces, they are increasingly expected to work in cooperation with each other. My thesis focuses on multirobot planning, specifically in the context of coverage robots, such as robotic lawnmowers and vacuum cleaners. Two problems unique to multirobot teams are task allocation and search. I present a task allocation algorithm which balances the workload amongst all robots in the team with the objective of minimizing the overall mission time. I also present a search algorithm which robots can use to find lost teammates. It uses a probabilistic belief of a target robot’s position to create a planning tree and then searches by following the best path in the tree. For robust multirobot coverage, I use both the task allocation and search algorithms. First the coverage region is divided into a set of small coverage tasks which minimize the number of turns the robots will need to take. These tasks are then allocated to individual robots. During the mission, robots replan with nearby robots to rebalance the workload and, once a robot has finished its tasks, it searches for teammates to help them finish their tasks faster

Algorithms for Routing Unmanned Vehicles with Motions, Resource, and Communication Constraints

Multiple small autonomous or unmanned aerial and ground vehicles are being used together with stationary sensing devices for a wide variety of data gathering, monitoring and surveillance applications in military, civilian, and agricultural applications, to name a few. Even though there are several advantages due to the small platforms for these vehicles, they pose a variety of challenges. This dissertation aims to address the following challenges to routing multiple small autonomous aerial or ground vehicles: (i) limited communication capabilities of the stationary sensing devices, (ii) dynamics of the vehicles, (iii) varying sensing capabilities of all the vehicles, and (iv) resource constraints in the form of fuel restrictions on each vehicle. The dissertation formulates four different routing problems for multiple unmanned vehicles, one for each of the aforementioned constraints, as mixed-integer linear programs and develops numerically efficient algorithms based on the branch-and-cut paradigm to compute optimal solutions for practically reasonable size of test instances

Hybrid Vehicle-drone Routing Problem For Pick-up And Delivery Services Mathematical Formulation And Solution Methodology

The fast growth of online retail and associated increasing demand for same-day delivery have pushed online retail and delivery companies to develop new paradigms to provide faster, cheaper, and greener delivery services. Considering drones’ recent technological advancements over the past decade, they are increasingly ready to replace conventional truck-based delivery services, especially for the last mile of the trip. Drones have significantly improved in terms of their travel ranges, load-carrying capacity, positioning accuracy, durability, and battery charging rates. Substituting delivery vehicles with drones could result in $50M of annual cost savings for major U.S. service providers. The first objective of this research is to develop a mathematical formulation and efficient solution methodology for the hybrid vehicle-drone routing problem (HVDRP) for pick-up and delivery services. The problem is formulated as a mixed-integer program, which minimizes the vehicle and drone routing cost to serve all customers. The formulation captures the vehicle-drone routing interactions during the drone dispatching and collection processes and accounts for drone operation constraints related to flight range and load carrying capacity limitations. A novel solution methodology is developed which extends the classic Clarke and Wright algorithm to solve the HVDRP. The performance of the developed heuristic is benchmarked against two other heuristics, namely, the vehicle-driven routing heuristic and the drone-driven routing heuristic. Anticipating the potential risk of using drones for delivery services, aviation authorities in the U.S. and abroad have mandated necessary regulatory rules to ensure safe operations. The U.S. Federal Aviation Administration (FAA) is examining the feasibility of drone flights in restricted airspace for product delivery, requiring drones to fly at or below 400-feet and to stay within the pilot’s line of sight (LS). Therefore, a second objective of this research is considered to develop a modeling framework for the integrated vehicle-drone routing problem for pick-up and delivery services considering the regulatory rule requiring all drone flights to stay within the pilot’s line of sight (LS). A mixed integer program (MIP) and an efficient solution methodology were developed for the problem. The solution determines the optimal vehicle and drone routes to serve all customers without violating the LS rule such that the total routing cost of the integrated system is minimized. Two different heuristics are developed to solve the problem, which extends the Clarke and Wright Algorithm to cover the multimodality aspects of the problem and to satisfy the LS rule. The first heuristic implements a comprehensive multimodal cost saving search to construct the most efficient integrated vehicle-drone routes. The second heuristic is a light version of the first heuristic as it adopts a vehicle-driven cost saving search. Several experiments are conducted to examine the performance of the developed methodologies using hypothetical grid networks of different sizes. The capability of the developed model in answering a wide variety of questions related to the planning of the vehicle-drone delivery system is illustrated. In addition, a case study is presented in which the developed methodology is applied to provide pick-up and delivery services in the downtown area of the City of Dallas. The results show that mandating the LS rule could double the overall system operation cost especially in dense urban areas with LS obstructions

Multi-Robot Path Planning for Persistent Monitoring in Stochastic and Adversarial Environments

In this thesis, we study multi-robot path planning problems for persistent monitoring tasks. The goal of such persistent monitoring tasks is to deploy a team of cooperating mobile robots in an environment to continually observe locations of interest in the environment. Robots patrol the environment in order to detect events arriving at the locations of the environment. The events stay at those locations for a certain amount of time before leaving and can only be detected if one of the robots visits the location of an event while the event is there. In order to detect all possible events arriving at a vertex, the maximum time spent by the robots between visits to that vertex should be less than the duration of the events arriving at that vertex. We consider the problem of finding the minimum number of robots to satisfy these revisit time constraints, also called latency constraints. The decision version of this problem is PSPACE-complete. We provide an O(log p) approximation algorithm for this problem where p is the ratio of the maximum and minimum latency constraints. We also present heuristic algorithms to solve the problem and show through simulations that a proposed orienteering-based heuristic algorithm gives better solutions than the approximation algorithm. We additionally provide an algorithm for the problem of minimizing the maximum weighted latency given a fixed number of robots. In case the event stay durations are not fixed but are drawn from a known distribution, we consider the problem of maximizing the expected number of detected events. We motivate randomized patrolling paths for such scenarios and use Markov chains to represent those random patrolling paths. We characterize the expected number of detected events as a function of the Markov chains used for patrolling and show that the objective function is submodular for randomly arriving events. We propose an approximation algorithm for the case where the event durations for all the vertices is a constant. We also propose a centralized and an online distributed algorithm to find the random patrolling policies for the robots. We also consider the case where the events are adversarial and can choose where and when to appear in order to maximize their chances of remaining undetected. The last problem we study in this thesis considers events triggered by a learning adversary. The adversary has a limited time to observe the patrolling policy before it decides when and where events should appear. We study the single robot version of this problem and model this problem as a multi-stage two player game. The adversary observes the patroller’s actions for a finite amount of time to learn the patroller’s strategy and then either chooses a location for the event to appear or reneges based on its confidence in the learned strategy. We characterize the expected payoffs for the players and propose a search algorithm to find a patrolling policy in such scenarios. We illustrate the trade off between hard to learn and hard to attack strategies through simulations