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's energy level, and the time left to task inactivation.

For unmanned vehicles, autonomy means that the vehicle’s route can be planned and executed according to some pre-defined rules in the absence of human intervention. Autonomous vehicles (AVs) have become a common type of vehicle for various kinds of transport, for example autonomous forklifts within a warehouse environment. Volvo Autonomous Solution (VAS) works with autonomous vehicles in different areas. To better understand how different methods can be used for planning of autonomous vehicles, VAS initiated this project. To increase the efficiency of AVs, several problems can be examined. One such problem is the allocation problem, also called Multi-Robot Task Allocation, which aims to find out which vehicle should execute which task to achieve a global goal cooperatively. The AVs used by VAS handle Planning Missions (PMs). A PM is, for example, to move goods from a loading point to an unloading point. So, the problem examined in this study is how to assign PMs to vehicles in the most efficient way. The thesis also includes a collection of publications on the area. The problem is solved by using three methods: Mixed Integer Linear Programming (MILP), a Genetic Algorithm that was originally proposed for task assignment in a warehouse environment (GA – Warehouse), and a Genetic Algorithm that was initially proposed for train scheduling (GA – Train). With the MILP method, the problem has been formulated mathematically and the method guarantees an optimal solution. However, the major drawback of this approach is the large computational time required to retrieve a solution. The GA – Warehouse method has a quite simple allocation process but a more complicated path planning part and is, in its entirety, not as flexible as the other methods. The GA – Train method has a lower computational time and can consider many different aspects. All three methods generate similar solutions for the limited set of simple scenarios in this study, but an optimal solution can only be guaranteed by the MILP method. Regardless of which method is used, there is always a trade-off: a guarantee of the optimal solution at the expense of high computational time or a result where no optimal solution can be guaranteed but can be generated quickly. Which method to use depends on the context, what resources are available, and what requirements are placed on the solution. / <p>Examensarbetet är utfört vid Institutionen för teknik och naturvetenskap (ITN) vid Tekniska fakulteten, Linköpings universitet</p>