A method of constrained mobility mapping includes receiving from at least one sensor of a robot at least one original set of sensor data and a current set of sensor data. Here, each of the at least one original set of sensor data and the current set of sensor data corresponds to an environment about the robot. The method further includes generating a voxel map including a plurality of voxels based on the at least one original set of sensor data. The plurality of voxels includes at least one ground voxel and at least one obstacle voxel. The method also includes generating a spherical depth map based on the current set of sensor data and determining that a change has occurred to an obstacle represented by the voxel map based on a comparison between the voxel map and the spherical depth map. The method additional includes updating the voxel map to reflect the change to the obstacle.