Understanding How Odometry Is Calculated In The Diff_Drive Controller

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I assume you are talking about Odometry::updateOpenLoop() vs. Odometry::update() (used in diff_drive_controller.cpp here and here respectively)?

If so, I don't know of any formal documentation, but I find the code reasonably clear if you follow it through. There isn't much change between the math performed in each. The big difference is the information used to perform the odometric estimate.

The Open Loop update uses the commanded linear and angular velocities and the time step to estimate where the robot moved to (assuming perfect response of the vehicle to the control input).

The "closed loop" update uses measured wheel positions to get an improved estimate of the distance the robot actually travelled. If there is more than one wheel per side (e.g. for skid steer robots), then the average position of the wheels on each side is taken to hopefully reduce noise / uncertainty / the effect of slip.

Regardless of whether open or closed loop is used, both methods use the same RungaKutta2 implementation to update the odometric estimate.

Both methods are susceptible to drift over time due to slip and other sources of uncertainty, though certainly using position feedback will result in lower drift than the fully open-loop approach.

If you want to mitigate unbounded drift over time, then you need to incorporate other local/global measurement sources. One of the most popular ways to do this in ROS/ROS2 is with the robot_localization package, which will incorporate IMU and GPS data and other odometry sources (e.g. visual odometry) to improve your robots pose estimate.

As far as modifying the control loop to add additional feedback goes, it really depends on your application. diff_drive_controller is open-loop with respect to whatever hardware interface it is interacting with. It sets the velocity that would be appropriate for the desired body twist. If under the hood you want to modify the velocity controller to behave a certain way or incorporate certain feedback, you can certainly do so. In most applications, however, your goal is to meet a target position (the intermediate velocities are often less important). If so, then I'd recommend using the navigation2 package. As long as you're publishing odometry and, localizing the robot if applicable, nav2 will perform the closed loop position control for you.