Nanobot Algorithms for Treatment of Diffuse Cancer

Motile nanosized particles, or "nanobots", promise more effective and less toxic targeted drug delivery because of their unique scale and precision. We consider the case in which the cancer is "diffuse", dispersed such that there are multiple distinct cancer sites. We investigate the problem of a swarm of nanobots locating these sites and treating them by dropping drug payloads at the sites. To improve the success of the treatment, the drug payloads must be allocated between sites according to their "demands"; this requires extra nanobot coordination. We present a mathematical model of the behavior of the nanobot agents and of their colloidal environment. This includes a movement model for agents based upon experimental findings from actual nanoparticles in which bots noisily ascend and descend chemical gradients. We present three algorithms: The first algorithm, called KM, is the most representative of reality, with agents simply following naturally existing chemical signals that surround each cancer site. The second algorithm, KMA, includes an additional chemical payload which amplifies the existing natural signals. The third algorithm, KMAR, includes another additional chemical payload which counteracts the other signals, instead inducing negative chemotaxis in agents such that they are repelled from sites that are already sufficiently treated. We present simulation results for all algorithms across different types of cancer arrangements. For KM, we show that the treatment is generally successful unless the natural chemical signals are weak, in which case the treatment progresses too slowly. For KMA, we demonstrate a significant improvement in treatment speed but a drop in eventual success, except for concentrated cancer patterns. For KMAR, our results show great performance across all types of cancer patterns, demonstrating robustness and adaptability.

Swarm Algorithms for Dynamic Task Allocation in Unknown Environments

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.

A Comparison of New Swarm Task Allocation Algorithms in Unknown Environments with Varying Task Density

Task allocation is an important problem for robot swarms to solve, allowing agents to reduce task completion time by performing tasks in a distributed fashion. Existing task allocation algorithms often assume prior knowledge of task location and demand or fail to consider the effects of the geometric distribution of tasks on the completion time and communication cost of the algorithms. In this paper, we examine an environment where agents must explore and discover tasks with positive demand and successfully assign themselves to complete all such tasks. We propose two new task allocation algorithms for initially unknown environments -- one based on N-site selection and the other on virtual pheromones. We analyze each algorithm separately and also evaluate the effectiveness of the two algorithms in dense vs. sparse task distributions. Compared to the Levy walk, which has been theorized to be optimal for foraging, our virtual pheromone inspired algorithm is much faster in sparse to medium task densities but is communication and agent intensive. Our site selection inspired algorithm also outperforms Levy walk in sparse task densities and is a less resource-intensive option than our virtual pheromone algorithm for this case. Because the performance of both algorithms relative to random walk is dependent on task density, our results shed light on how task density is important in choosing a task allocation algorithm in initially unknown environments.