How does SLAM handle a changing environment?

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There are many ways to address this challenge for dynamic changes to the environment, for example multi session graph based SLAM. It also depends on what is changing in the environment, is it pedestrians walking by? Or is it furniture moving around?

Take a look at the following paper

Summary of the approach used:

the underlying structure of the map is a graph with nodes and links. The nodes save odometry poses for each location in the map. The nodes also contain visualization information like laser scans, RGB images, depth images and visual words [17] used for loop closure detection. The links store rigid geometrical transformations between nodes. There are two types of links: neighbor and loop closure. Neighbor links are added between the current and the previous nodes with their odometry transformation. Loop closure links are added when a loop closure detection is found between the current node and one from the same or previous maps. Our contribution in this paper involves combining two algorithms, loop closure detection [16] and graph optimization [14], through a memory management process [16] that limits the number of nodes available from the graph for loop closure detection and graph optimization, so that they always satisfy online requirements.

But there are other examples of using machine learning for object detection and remove those objects while updating SLAM, take a look at this paper