In many robotics applications, multiple robots are working in a shared workspace to complete a set of tasks as fast as possible. Such settings can be treated as multi-modal multi-robot multi-goal path planning problems, where each robot has to reach a set of goals. Existing approaches to this type of problem solve this using prioritization or assume synchronous task completion, and are thus neither optimal nor complete. We formalize this problem as a single centralized path planning problem and present planners that are probabilistically complete and asymptotically optimal. The planners plan in the composite space of all robots and are modifications of standard sampling-based planners with the required changes to work in our multi-modal, multi-robot, multi-goal setting. We validate the planners on a diverse range of problems including scenarios with various robots, planning horizons, and collaborative tasks such as handovers, and compare the planners against a suboptimal prioritized planner. Videos and code for the planners and the benchmark is available at https://vhartmann.com/mrmg-planning/.

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