Drake Concepts

Drake's core library has 3 big parts:

I. Dynamical Systems Modeling

Dynamical Systems Modeling requires to represent a dynamical system and simulate based on real world physics.


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 system. A system block can be a diagram or a leafsystem. leafsystem is the minimum build block and a diagram is composed of multiple leafsystem or diagram.

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


Drake uses diagram to represent systems that internally have several connected systems that function as a whole. diagram itself is a system and can be nested. Root diagram contains all the sub-systems and sub-diagrams.

Systems can be connected through their input/output ports. Connected systems could also be formed into a diagram.


context is data of system states and parameters cached in a separate place. Each diagram and each system has its own context. The context and the diagram are the only two information a simulator needs for simulation. Given the context, all methods called on a system should be completely deterministic and repeatable (ref. Underactuated Robotics textbook).

Drake has method diagram->CreateDefaultContext() which creates the context with default value for all the subsystems. Things such as the initial state and the initial time can directly be set using context before simulation starts.

A context could have continuous state, discrete state and abstract variable. Based on the variable type, the simulator would update the context data by either numerically integrate the continuous derivative or update the state by state space dynamics.


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 problem in robotics, especially areas like motion planning and control.

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

III. Multibody Kinematics and Dynamics

Multibody means multiple rigid bodies connected in a tree structure. For robotics systems, root diagram has a unique leafsystem called MultibodyPlant. MultibodyPlant internally uses rigid body tree algorithms to compute the robot kinematics dynamics jacobian, etc.

MultibodyPlant is a system. So it has input/output port that could be connect to other systems like controllers and visualizer.

Tools that Drake uses

1. Eigen

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


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 bridge between system ports, so all the communication between systems are transported using LCM, and thus can be inspected by LCM spy tool.

3. Tinyxml2

A handy tool to parse XML file, enables Drake to parse URDF and SDF, thus create MultibodyPlant for simulation.

4. The Visualization Toolkit (VTK)

Drake uses VTK as geometry rendering tool. The Drake visualizer communicate with the simulation through LCM.