## Heterogeneity- and Risk-Aware Algorithms for Task Allocation To Mobile Agents

In this thesis, we investigate and characterize policies for task allocation to teams of agents in settings with heterogeneity and risk. We first consider a scenario consisting of a set of heterogeneous mobile agents located at a base (or depot), and a set of tasks dispersed over a geographic area. The agents are partitioned into different types. The tasks are partitioned into specialized tasks that can only be done by agents of a certain type, and generic tasks that can be done by any agent. The distances between every pair of tasks are specified and satisfy the triangle inequality. Given this scenario, we address the problem of allocating these tasks among the available agents (subject to type compatibility constraints) while minimizing the maximum travel cost for any agent. We first look at the Heterogeneous Agent Cycle Problem (HACP) where agents start at a common base (or depot) and need to tour the set of tasks allocated to them before returning to the base. This problem is NP-hard, and we provide a 5-approximation algorithm. We then consider the Heterogeneous Agent Path Problem (HAPP) where agents can start from arbitrary locations and are not constrained to return to their start location. We consider two approaches to solve HAPP and provide a 15-approximation algorithm for HAPP.

We then look at the effect of risk on path planning by considering a scenario where a mobile agent is required to collect measurements from a geographically dispersed set of sensors and return them to a base. The agent faces a risk of destruction while traversing the environment to reach the sensors and gets the reward for gathering a sensor measurement only if it successfully returns to base. We call this the Single Agent Risk Aware Task Execution (SARATE) problem. We characterize several properties of the optimal policy for the agent. We provide the optimal policy when the risk of destruction is sufficiently high and evaluate several heuristic policies via simulation. We then extend the analysis to multiple heterogeneous agents. We show that the scoring scheme is submodular when the risk is sufficiently high, and the greedy algorithm gives solutions that provide a utility that is guaranteed to be within 50% of the optimal utility.