Human-robot collaborative applications require scene representations that are kept up-to-date and facilitate safe motions in dynamic scenes. In this letter, we present an interactive distance field mapping and planning (IDMP) framework that handles dynamic objects and collision avoidance through an efficient representation. We define \textit{interactive} mapping and planning as the process of creating and updating the representation of the scene online while simultaneously planning and adapting the robot's actions based on that representation. Given depth sensor data, our framework builds a continuous field that allows to query the distance and gradient to the closest obstacle at any required position in 3D space. The key aspect of this work is an efficient Gaussian Process field that performs incremental updates and implicitly handles dynamic objects with a simple and elegant formulation based on a temporary latent model. In terms of mapping, IDMP is able to fuse point cloud data from single and multiple sensors, query the free space at any spatial resolution, and deal with moving objects without semantics. In terms of planning, IDMP allows seamless integration with gradient-based motion planners facilitating fast re-planning for collision-free navigation. The framework is evaluated on both real and synthetic datasets. A comparison with similar state-of-the-art frameworks shows superior performance when handling dynamic objects and comparable or better performance in the accuracy of the computed distance and gradient field. Finally, we show how the framework can be used for fast motion planning in the presence of moving objects. An accompanying video, code, and datasets are made publicly available https://uts-ri.github.io/IDMPTest.
