Multi-Agent Pathfinding in continuous time (MAPF\(_{R}\)) is the problem of computing collision-free trajectories for multiple agents moving in continuous space and time without discretizing time into time steps and unit-duration actions. Unlike classical MAPF, which assumes uniform, discrete time steps and unit-duration actions, MAPF\(_{R}\) models arbitrary action durations and continuous motion, making it better suited for complex, real-world and multi-agent robotic systems. However, many practical applications also require agents to maintain reliable communication throughout execution, imposing a global connectivity constraint on their movements. The current state of the literature reveals that prior approaches are either constrained to discrete-time models that are unsuitable for complex real-world scenarios, or they completely omit the requirement of maintaining global connectivity. In this paper, we formalize this extended problem as CMAPF\(_{R}\) (MAPF\(_{R}\) with connectivity constraints), where agents must plan continuous-time trajectories that avoid collisions with each other while ensuring that their communication graph remains a single connected component. In response to this challenging variant, we propose a novel planning framework, called Connectivity-Constrained Continuous-Time Conflict-Based Search (C\(^{3}\)BS), that integrates Continuous-Time Conflict-Based Search (CCBS) with dynamic connectivity graph maintenance to generate global network connectivity-preserving trajectories for each agent. Our approach enforces connectivity constraints during path generation, ensuring that all agents remain within both the required communication range and maintain unobstructed line-of-sight throughout their trajectories. We evaluated the method on benchmark multi-agent scenarios with varying map structures, number of agents, communication ranges, connectivity types (including range-only, line-of-sight-only, and combined), and overall task complexity. The experiment results demonstrate that the framework achieves success rates exceeding 90% within feasible execution times even in large-scale multi-agent scenarios, depending on the specific constraint configurations. This means that our approach successfully produces feasible, collision-free, connectivity-preserving trajectories for even a large number of agents in cluttered environments with efficient computational performance. This capability enables robust and coordinated operation in domains requiring continuous communication, including complex and multi-agent systems such as robotic swarms, distributed surveillance networks, and disaster response missions.
