TransformsGraph

A C++ directed-acyclic graph data structure to hold transforms between reference frames.

This is similar to the tf2 ROS package, but this package is ROS agnostic and is less complex.

Contents

• Requirements
• Usage
  • Required types
  • Maximum number of frames
  • Using enum for Frame
• Transforms storage
  • Mermaid graphs
• Installation
• FAQ

Requirements

The library runs on C++11 and doesn't require external dependencies. However, some of the examples require additional dependencies:

• Eigen 3.3 (optional)
• Sophus, version 1.22.10 (optional)

Usage

Some high-level documentation is provided in this section. Refer to transforms_graph.h for further documentation.

Required types

The TransformsGraph requires two template parameters:

1. Transform type. This is the type that stores the transforms themselves (i.e., poses). This type should have the following defined:
   • A default constructor that sets the transform to the identity transform.
   • A valid Multiplication operator * operator (i.e., T1 = T2 * T2).
   • A valid Transform inverse() const method (i.e., T1.inverse() * T1 should return an identity transform). Alternatively, a function Transform inverse(Transform) can be injected/passed to the TransformsGraph upon construction.
   • An output stream operator << (i.e., std::cout << T).
2. Frame type (default set to char). This is the type that keeps track of the frames. The type should have the following defined:
   • Greater-than comparison operator > (i.e., frame_i > frame_j).
   • An output stream operator << (i.e., std::cout << T).
3. Inv function object (defaults to Transform::inverse). The function object is passed in the constructor.

The classes from Sophus (e.g., Sophus::SE2d) and Eigen (e.g., Eigen::Affine2d) already satisfy the Transform requirements, except for the output stream operator << requirement.

Refer to the examples folder for examples of the Transform and Frame types.

Maximum number of frames

The TransformsGraph requires the maximum number of frames expected to be in the object. The default is set to 100.

Using enum for Frame

The Frame type can take many built-in types without the need for any modification (e.g., char, int, size_t). However, using enum or enum class is a good idea since the user would get compile-time errors when trying to add or retrieve transforms or frames with "unknown" or undefined frames.

Here's an example of using the enum class for Frame:

enum class Frame { MAP, ODOM, BASE_LINK, CAMERA, FRONT_LIDAR };
std::ostream& operator<<(std::ostream& os, const Frame& frame) {
  return os << static_cast<int>(frame);
}

int main() {
  tg::TransformsGraph<Pose, Frame> transforms;
  transforms.InsertTransform(Frame::MAP, Frame::ODOM, Pose({1, 2}, 0.0));
  transforms.InsertTransform(Frame::BASE_LINK, Frame::CAMERA, Pose({0.5, 0.0}, 0.0));
  transforms.InsertTransform(Frame::BASE_LINK, Frame::FRONT_LIDAR, Pose({2, 1}, M_PI_4));
}

Transforms storage

The transforms are stored in the transform graph in a specific way to ensure uniqueness. Specifically, the transform is stored as T_a_b, where a is smaller than b.

This has a minor side effect that the transform could be stored in a way that's different than what the user provided. For example, if the user does

tg::TransformsGraph<Transform> transforms;
transforms.InsertTransform('b', 'a', Transform(M_PI_4, {0, 0}));

Then, since 'b' > 'a', then the transform is inverted and is stored as T_a_b = Transform(M_PI_4, {0, 0}).inverse(). When the user asks for the transform T_b_a, then the transform is computed using T_b_a = T_a_b.inverse() and is returned to the user.

From the user side, everything looks normal, but there are some side effects to this design decision, and some possible remedies:

• Expensive inverse operation: if the user provides the transform T_b_a and keeps asking for T_b_a, then T_a_b.inverse() gets called in the background. This can be worrisome if the inverse() method is expensive.
• Possibly confusing graph visualization: The user may store T_b_a, which will be stored as T_a_b, and thus visualized as T_a_b when using the mermaid graphs. This may lead to some confusions.

Mermaid graphs

The library is equipped with a function that outputs Mermaid graphs that can be visualized online or in Markdown files by inserting them in a code block with mermaid language identifier.

Note that the graph visualizes the stored graph, which may be slightly different from how the user constructed the graph. Check the Transforms storage for additional details on this.

Taking the output from the Sophus example example

transforms.InsertTransform(Frame::A, Frame::B, Transform(M_PI_4, {0, 0}));
transforms.InsertTransform(Frame::A, Frame::C, Transform(M_PI_2, {0, 0}));
transforms.InsertTransform(Frame::B, Frame::D, Transform(0, {1, 2}));
transforms.InsertTransform(Frame::E, Frame::F, Transform(-M_PI_4, {3, 4}));
std::cout << transforms.GetMermaidGraph() << std::endl;

and wrapping it in a Markdown code block with mermaid language identifier, results in the following flowchart.

graph TD
  F
  E
  E --> F
  D
  C
  B
  B --> D
  A
  A --> C
  A --> B

By default, the edges will not be shown. However, the edges (i.e., the transforms) can be shown by passing true to GetMermaidGraph. The output would look like the following.

graph TD
  F
  E
  E --> | x: 3, y: 4, theta: -0.785398 | F
  D
  C
  B
  B --> | x: 1, y: 2, theta: 0 | D
  A
  A --> | x: 0, y: 0, theta: 1.5708 | C
  A --> | x: 0, y: 0, theta: 0.785398 | B

Furthermore, the GetMermaidGraph function takes a unary function that takes a frame and returns a string. This function can be used to override the frame names in the graph. For example,

std::unordered_map<Frame, std::string> frame_names = {{Frame::MAP, "Map"},
                                                        {Frame::ODOM, "Odom"},
                                                        {Frame::BASE_LINK, "Baselink"},
                                                        {Frame::CAMERA, "Camera"},
                                                        {Frame::FRONT_LIDAR, "Front_lidar"}};
const auto get_frame_names = [&frame_names](Frame frame) { return frame_names[frame]; };
std::cout << transforms.GetMermaidGraph(get_frame_names) << std::endl;

results in

graph TD
  Rear_lidar
  Front_lidar
  Front_lidar --> Rear_lidar
  Camera
  Baselink
  Odom
  Odom --> Camera
  Map
  Map --> Baselink
  Map --> Odom

The transforms can be visualized for this option as well by passing true as the second argument to GetMermaidGraph.

Installation

This is a header-only library. It can be used by directly including the include/transforms_graph/transforms_graph.h into your folder, or it can be installed on your system by running the following from the root of this repo.

cmake -S . --build build
cmake --build build
sudo cmake --install build

FAQ

• Why use a graph instead of a tree or a forest?
  • If the user decides to add a transform between the leaves of two disconnected trees, then one of the trees would need to be inverted to keep the data structure a tree. However, keeping the data structure as a graph avoids this hassle.
• Why using a directed acyclic graph (DAG)?
  • Getting transforms between two non-adjacent frames requires chaining multiple transforms. Thus, if the data structure allows for cycles, then suddenly there are multiple ways to get a transform. That is, the system is overdetermined. To avoid having such data structure, a directed acyclic graph will do the trick, since it avoids having redundant paths.
• What are the differences with the tf2 ROS package, and when should you use one over the other?
  • Compared to tf2, this package is ROS and Catkin agnostic
  • The TransformsGraph is a simple data structure and it doesn't do any processing on the frame such as interpolation, extrapolation, etc.
  • The TransformsGraph is time-invariant, and doesn't natively hold timestamps. The user can choose to include timestamps in the passed Transform object, but it's up to the user to manage the timestamps.