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https://github.com/locusrobotics/fuse

The fuse stack provides a general architecture for performing sensor fusion live on a robot. Some possible applications include state estimation, localization, mapping, and calibration.
https://github.com/locusrobotics/fuse

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The fuse stack provides a general architecture for performing sensor fusion live on a robot. Some possible applications include state estimation, localization, mapping, and calibration.

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# fuse



The fuse stack provides a general architecture for performing sensor fusion live on a robot. Some possible applications

include state estimation, localization, mapping, and calibration.



## Overview



fuse is a ROS framework for performing sensor fusion using nonlinear least squares optimization techniques. In

particular, fuse provides:



* a plugin-based system for modeling sensor measurements

* a similar plugin-based system for motion models

* a plugin-based system for publishing optimized state values

* an extensible state variable definition

* a "contract" on how an optimizer will interact with the above components

* and some common implementations to get everyone started



(unpresented) ROSCon 2018 Lightning Talk [slides](doc/fuse_lightning_talk.pdf)



Data flows through the system approximately like this:



* A sensor model receives raw sensor data. The sensor model generates a constraint and sends it to the optimizer.

* The optimizer receives the new sensor constraint. A request is sent to each configured motion model to generate

  a constraint between the previous state and the new state involved in the sensor constraint.

* The motion model receives the request and generates the required constraints to connect the new state to the

  previously generated motion model chain. The motion model constraints are sent to the optimizer.

* The optimizer adds the new sensor model and motion model constraints and variables to the graph and

  computes the optimal values for each state variable.

* The optimal state values are sent to each configured publisher (as well as the sensor models and motion models).

* The publishers receive the optimized state values and publish any derived quantities on ROS topics.

* Repeat



It is important to note that much of this flow happens asynchronously in practice. Sensors are expected to operate

independently from each other, so each sensor will be sending constraints to the optimizer at its own frequency. The

optimizer will cache the constraints and process them in small batches on some schedule. The publishers may

require considerable processing time, introducing a delay between the completion of the optimization cycle and the

publishing of data to the ROS topic.



![fuse sequence diagram](doc/fuse_sequence_diagram.png)



## Example



Let's consider a simple robotics example to illustrate this. Assume we have a typical indoor differential-drive robot.

This robot has wheel encoders and a horizontal laser.



The first thing we must do is define our state variables. At a minimum, we want the robot pose at each timestamp.

We model the pose using a 2D position and an orientation. Each 2D pose _at a specific time_ gets a unique variable

name. For ease of notation, let's call the pose variables `X1`, `X2`, `X3`, etc. (In reality, each variable gets

a UUID, but those are much harder to write down.) Each 2D pose is instantiated as a `example_robot::Pose2D` which is

derived from the `fuse_core::Variable` base class. (`fuse` ships with several basic variables, such as 2D and 3D

versions of position, orientation, and velocity variables, but you can derive your own variable types as you need them.)



Next we need to decide how to model our sensors. We can model the wheel encoders as providing an incremental

pose measurement. Given a starting pose, `X1`, and a wheel encoder delta, `z`, we predict the pose `X2'` using some

measurement function `f`.



`X2' = f(X1, z)`



The error term for our constraint is the difference between the predicted pose `X2'` and the actual pose `X2`



`error = X2'^-1 * X2`



where `X2'^-1` is the inverse of the pose `X2'`



We derive a `fuse_core::Constraint` that implements that error function. Similarly, we perform scan-to-scan matching

using out laser data and create an incremental pose constraint between consecutive scans.



In the simplest example, the sensors are synchronized, i.e. the laser and the wheel encoders are sampled at the same

time. This is enough to construct our first `fuse` system. Below is the constraint graph generated from this first

system. The large circles represent state variables at a given time, while the small squares represent measurements.

The graph connectivity indicates which variables are involved in what measurements.



![fuse graph](doc/fuse_graph_1.png)



The two sensor models are configured as plugins to an optimizer implementation. The optimizer performs the required

computation to generate the optimal state variable values based on the provided sensor constraints. We will never be

able to exactly satisfy both the wheel encoder constraints and the laserscan constraints. Instead we minimize the error

of all the constraints using nonlinear least squares optimization.



![fuse optimizer](doc/fuse_optimizer_1.png)



While our `fuse` system is optimizing constraints from two different sensors, it is not yet publishing any data back

out to ROS. In order to publish data to ROS, we derive a `fuse_core::Publisher` class and add it to the

optimizer. Derived publishers have access to the optimized values of all state variables. The specific publisher

implementation determines what type of messages are published and at what frequency. For our example system,

we would like visualize the current pose of the robot in RViz, so we create a `fuse` publisher that finds the most

recent pose and converts it into a `geometry_msgs::PoseStamped` message, then publishes the message to a topic.



![fuse optimizer](doc/fuse_optimizer_2.png)



We finally have something that is starting to be useful.



### Adaptation #1: Asynchronous sensors



Typically the laser measurements and the wheel encoder measurements are not synchronized. The encoder measurements are

sampled faster than the laser, and are sampled at different times using a different clock. If we do not do anything

different in this situation, the constraint graph becomes disconnected.



![fuse graph](doc/fuse_graph_2.png)



This is where motion models come into play. A motion model differs from a sensor model in that constraints can be

generated between any two requested timestamps. Motion model constraints are generated upon request, not due to their

own internal clock. We use the motion model to connect the states introduced by the other sensor measurements. We

derive a class from the `fuse_core::MotionModel` base class and implement a differential drive kinematic

constraint for our robot.



![fuse optimizer](doc/fuse_optimizer_3.png)



The motion models are also configured as plugins to the optimizer. The optimizer requests motion models constraints

from the configured plugins whenever new states are created by the sensor models.



![fuse graph](doc/fuse_graph_3.png)



### Adaptation #2: Full path publishing



Nothing about the `fuse` framework limits you to having a single publisher. What if you want to visualize the entire

robot trajectory, instead of just the most recent pose? Well, we can create a new derived `fuse_core::Publisher` class

that publishes all of the robot poses using a `nav_msgs::Path` message.



![fuse optimizer](doc/fuse_optimizer_4.png)



### Adaptation #3: Changing kinematics



In your spare time, you also build [autonomous power wheels racers](http://www.powerracingseries.org/). But race cars

don't use differential drive; you need a different motion model. Easy enough. We simply derive a new

`fuse_core::MotionModel` class that implements an Ackermann steering model. Everything else can be reused.



![fuse optimizer](doc/fuse_optimizer_5.png)



![fuse graph](doc/fuse_graph_4.png)



### Adaptation #4: Online calibration



Over time you notice that the accuracy of the odometry measurements is decreasing. After some investigation you realize

that the soft rubber racing tires are wearing, decreasing the diameter of the wheels over time. It sure would be nice

if the odometry system could compensate for that automatically. To do that, we derive a new variable type from

`fuse_core::Variable` that holds a single scalar value representing a wheel diameter at a specific point in time. For

ease of notation, we refer to this new variable as `D1, D2, ...`, etc. We also need to derive a new wheel encoder sensor

model from the `fuse_core::SensorModel` base class. This new sensor model involves the previous pose and next pose as

before, but it also involves the previous wheel diameter. Finally, we need a `fuse_core::MotionModel` that describes

how the wheel diameter is expected to change over time. Maybe some sort of exponential decay? And for good measure, we

derive a new publisher plugin from `fuse_core::Publisher` that publishes the current wheel diameter. This allows us to

plot how the wheel diameter changes over the length of the race.



![fuse optimizer](doc/fuse_optimizer_6.png)



![fuse graph](doc/fuse_graph_5.png)



Now our system estimates the wheel diameters at each time step as well as the robot's pose.



## The Math



Internally `fuse` uses Google's [Ceres Solver](http://ceres-solver.org) to perform the nonlinear least squares

optimization, which produces the optimal state variable values. I direct any interested parties to the Ceres Solver

["Non-linear Least Squares"](http://ceres-solver.org/nnls_tutorial.html) tutorial for an excellent primer on the core

concepts and involved math.



## Summary



The purpose of `fuse` is to provide a framework for performing sensor fusion tasks, allowing common components to be

reused between systems, while also allowing components to be customized for different use cases. The goal is to allow

end users to concentrate on modeling the robot, sensor, system, etc. and spend less time wiring the different

sensor models together into runable code. And since all of the models are implemented as plugins, separate plugin

libraries can be shared or kept private at the discretion of their authors.



## API Concepts



* [Variables](doc/Variables.md)

* [Constraints](doc/Constraints.md)

* Sensor Models -- coming soon

* Motion Models -- coming soon

* Publishers -- coming soon

* Optimizers -- coming soon