Distributed mobile robotics (DMR) involves teams of networked robots navigating in a physical space to achieve tasks in a coordinated fashion. A major challenge in DMR is to program the ensemble of robots with formal guarantees and high assurance of correct operation. To this end, we introduce Drona, a framework for building reliable DMR applications. This paper makes three central contributions: (1) We present a novel and provably correct decentralized asynchronous motion planner that can perform on-the-fly collision-free planning for dynamically generated tasks. Moreover, the motion planner is the first to take into account the fact that distributed robots may have clocks that are only synchronized up to a tolerance, i.e., they are almost synchronous; (2) We formalize the DMR system as a mixed-synchronous system, and present a sound abstraction-based verification approach for DMR systems, and (3) Drona provides a state-machine based language for safe event-driven programming of a DMR system and the code generated by the compiler can be executed on platforms such as the robot operating system (ROS). To demonstrate the efficacy of Drona, we build and verify a priority mail delivery system. Using our abstraction-based verification approach we were able to find, within a few minutes, bugs which could not be found by performing random simulation for several hours. Our verified decentralized motion-planner scales efficiently for large number of robots (upto 128 robots) and workspace sizes (upto a 256×256 grid).