Swarm Algorithms for Dynamic Task Allocation in Unknown Environments

TL;DR

Dynamic task allocation in unknown environments is addressed by modeling swarms on a discrete grid with dynamically appearing tasks, and proposing three distributed algorithms: PROP, Division of Labor (DL), and Hybrid. PROP propagates task information to guide low-cost propagators and follower agents toward high-demand tasks, while DL and Hybrid combine propagation with Lévy random walks to mitigate clumping at higher task rates. Through simulations comparing against Lévy RW across varying task arrival rates, the study shows that PROP outperforms RW at low rates, while DL and Hybrid outperform RW and PROP at moderate rates, and RW can dominate at high rates. These results offer practical guidance on tuning propagation radius, the PROP proportion, and RW-switch timings to optimize efficiency in unknown, dynamic environments.

Abstract

Robot swarms, systems of many robots that operate in a distributed fashion, have many applications in areas such as search-and-rescue, natural disaster response, and self-assembly. Several of these applications can be abstracted to the general problem of task allocation in an environment, in which robots must assign themselves to and complete tasks. While several algorithms for task allocation have been proposed, most of them assume either prior knowledge of task locations or a static set of tasks. Operating under a discrete general model where tasks dynamically appear in unknown locations, we present three new swarm algorithms for task allocation. We demonstrate that when tasks appear slowly, our variant of a distributed algorithm based on propagating task information completes tasks more efficiently than a Levy random walk algorithm, which is a strategy used by many organisms in nature to efficiently search an environment. We also propose a division of labor algorithm where some agents are using our algorithm based on propagating task information while the remaining agents are using the Levy random walk algorithm. Finally, we introduce a hybrid algorithm where each agent dynamically switches between using propagated task information and following a Levy random walk. We show that our division of labor and hybrid algorithms can perform better than both our algorithm based on propagated task information and the Levy walk algorithm, especially at low and medium task rates. When tasks appear fast, we observe the Levy random walk strategy performs as well or better when compared to these novel approaches. Our work demonstrates the relative performance of these algorithms on a variety of task rates and also provide insight into optimizing our algorithms based on environment parameters.

Figures (10)

• Figure 1: A simulated example of the propagator mechanism. Green squares represent followers, and yellow square represent tasks (with the number being the residual demand of the task). Blue squares are locations where the propagator agents received task information (with darker blue indicating that the task information was more recently obtained). In this example, the propagators have influence radius $I_p = 1$ and the maximum distance that task information can propagate is $d_p = 8$.
• Figure 2: States of follower behavior. The follower starts in state A, and can move to state C if a task is seen within its influence radius. Otherwise, if the agent sees task information from a propagator it goes to state B. After state D, there is probability $P_{\text{stay at task}}$ of staying in state D at the same task.
• Figure 3: The effect of the rate of tasks appearing (parameterized by $\lambda$) on the average time to complete an individual task per unit demand for RW, PROP, DL (with $P_{\text{PROP}} = 0.6$), and Hybrid (with $t_{\text{RW}}=50$). We chose to highlight these specific DL and hybrid algorithms since they were overall the best performing DL and hybrid algorithms, respectively, that we tested on this range of task rates).
• Figure 4: The effect of the rate of tasks appearing (parameterized by $\lambda$) on average unsatisfied task demand for RW, PROP, DL (with $P_{\text{PROP}} =0.6$), and Hybrid (with $t_{\text{RW}}=50$).
• Figure 5: The effect of the proportion of agents running the PROP algorithm in our DL algorithm on the average time to complete an individual task per unit demand (for three distinct task rates).