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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:

(unpresented) ROSCon 2018 Lightning Talk slides

Data flows through the system approximately like this:

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

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

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

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

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

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

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

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

Adaptation #3: Changing kinematics

In your spare time, you also build autonomous power wheels racers. 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

fuse graph

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

fuse graph

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 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" 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