# Drake Concepts

Drake's core library has 3 big parts:

### I. Dynamical Systems Modeling

Drake provides tools to model the physics of a dynamic system, which can be used for analysis and simulation.

#### System

Drake's system modeling works like Matlab Simulink. Drake constructs complex systems from blocks called `system`

. `system`

has input/output ports that could be connected with other systems. **A ****system**** block can be a ****diagram**** or a ****leafsystem****. **`leafsystem`

is the minimum build block, and a `diagram`

is composed of multiple `leafsystems`

or `diagrams`

.

`leafsystem`

functions as basic components in robotics systems, such as signals, sensors, controllers, planners, etc.

#### Diagram

Drake uses `diagram`

to represent compound `systems`

. `diagram`

internally contain several connected subsystems. `diagram`

itself is a `system`

and can be nested. The root diagram contains all the subsystems and subdiagrams.

The main function in Drake usually starts from a blank root `diagram`

. `systems`

are added to the root`diagram`

and connected through their input/output ports.

#### Context

`context`

contains the data of system states and parameters cached in a separate place. Each `diagram`

and `system`

has its own `context`

. The `context`

and the `diagram`

are the only information a `simulator`

requires to simulate. Given the `context`

, all methods called on a `system`

should be completely deterministic and repeatable (Ref. Underactuated Robotics textbook).

Drake has a method `diagram->CreateDefaultContext()`

to create the context with default values for all the subsystems. Values in the context, such as the initial state and the initial time, can be independently set before the simulation begins.

A context can have continuous state, discrete state, and abstract variable. Based on the variable type, the simulator would update the context data by either numerically integrating the continuous derivative or updating the states using state-space dynamics.

#### Simulation

Drake is a simulation software. The Drake `simulator`

takes in the system `diagram`

together with its `context`

to simulate by updating parameters such as integral continuous state derivatives, compute discrete state updates, allocates the various outputs of a `system`

, etc.

### II. Mathematical Programs Solving

Drake incorporates famous and useful optimization tools, for example, Gurobi, SNOPT, IPOPT, SCS, MOSEK. These tools help to solve mathematical problems in robotics, such as motion planning and control.

To use Mathematical Programming, there is a very good starting point written in python. The same idea applies to C++.

### III. Multibody Kinematics and Dynamics

Multibody means multiple rigid bodies connected in an articulated structure. The root `diagram`

that contains a unique `leafsystem`

named`MultibodyPlant`

is considered as a robotic system. `MultibodyPlant`

internally uses rigid body tree algorithms to compute the robot's kinematics, dynamics, jacobian, etc.

`MultibodyPlant`

is a `system`

. So it has input/output ports that could be connected to other systems like controllers and visualizers.

## Tools that Drake uses

### 1. Eigen

Eigen is a C++ library with linear algebra operations and algorithms.

#### AutoDiff

A convenient technique to compute Derivative. Computing Integral is trivial and computing Derivative is non-trivial. AutoDiff is a good solution that Eigen provides to solve the derivative.

### 2. Lightweight Communications and Marshalling (LCM)

LCM is a multi-process communication tool. LCM is everywhere in Drake. It serves as the bridge between system ports, so all the communications between systems are transported using LCM, which can be inspected by LCM spy tool.

pageVisualize data in LCM### 3. Tinyxml2

A handy tool that parses XML files, enables Drake to parse URDF and SDF, thus creating `MultibodyPlant`

for simulation.

### 4. The Visualization Toolkit (VTK)

Drake uses VTK as a geometry rendering tool. The Drake visualizer communicates with the simulator through LCM.

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