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For 1,2): Odom is the robots odometry, its motion estimate. How the tf tree should look like is described in the Coordinate Frames document. The odometry is the transformation /odom -> /base_link and should be provided by the robot driver.

gmapping will provide the /map -> /odom part, if it is running.

For 3): I would assume the turtlebot driver provides odometry, but I never used it. Some turtlebot user/developer can give this information.