# Three-Dimensional Multi-Agent Foraging Strategy Based on Local Interaction
## 7 Conclusions  
In this article, we have proposed a 3D multi-agent foraging strategy composed of puck search and collection. The proposed 3D multi-agent foraging strategy is summarized as follows. In the search process, agents move one by one to expand the network until the 3D cluttered workspace is fully covered. When the bounded workspace is entirely covered by deployed agents, every puck is detected by an agent's local sensors. Next, we generate a path from the base to every puck. All agents along a path to a puck are set as guiding agents. Algorithm 4 then runs to let all agents except for guiding agents rendezvous at the base. Thereafter, every carrier agent at the base is assigned to a puck and travels along the path to its designated puck in order to collect the puck. When a carrier agent reaches its assigned puck, the carrier agent can carry its assigned puck to the base by iteratively visiting guiding agents. When all pucks have been carried to the base, Algorithm 5 runs to make all agents rendezvous at the base while maintaining network connectivity.  
Figure 16: Considering the scenario in Figure 13, this figure describes the positions of guiding agents after the complete 3D network is built. A puck is marked by a red diamond. The base is marked by a green circle. The path from the base to an agent in _AgentsWithPucks_ is depicted by blue line segments. The guiding agents are plotted by small circles along the blue line segments.  
Figure 15: Considering the scenario in Figure 13, this figure plots the MATLAB simulation results of Algorithm 4. The paths taken by agents other than guiding agents to gather at the base are marked by circles with distinct colors.  
In our paper, agents are deployed such that the sensing spheres (spheres with radius \(r^{cs}\) centered at an agent) of all agents cover the entire workspace. In this article, we prove that every puck in the 3D cluttered bounded workspace is detected in finite time. To the best of our knowledge, this article is novel in letting multiple agents perform foraging and puck gathering while satisfying network connectivity requirements in a cluttered unknown 3D workspace. In our future work, we will perform experiments utilizing real robots in order to more rigorously prove the proposed 3D foraging strategy.  
Notably, each carrier agent is assigned to a puck and moves along the path to its designated puck in order to carry the puck. In practice, each puck may have distinct weights and distinct sizes. The maximum weight that can be carried by a carrier agent is limited. In addition, the path length from the base to each puck may be different. Considering these various aspects, it is possible to optimize the assignment of each carrier agent such that carrier agents can carry all of the pucks to the base within a minimum time interval. In the future, we intend to solve this optimal assignment problem.  
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (Grant Number: 2022R1A2C1091682). This research was supported by the faculty research fund of Sejong university in 2023.  
Not applicable.  
Data Availability Statement: Data are available upon reasonable request.  
The authors declare no conflict of interest.