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RBDL is a C++ library that contains some essential and efficient rigid body dynamics algorithms such as the Articulated Body Algorithm (ABA) for forward dynamics, Recursive Newton-Euler Algorithm (RNEA) for inverse dynamics, the Composite Rigid Body Algorithm (CRBA) for the efficient computation of the joint space inertia matrix and is also able…



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RBDL - Rigid Body Dynamics Library Copyright (c) 2011-2020 Martin Felis


RBDL is a highly efficient C++ library that contains some essential rigid body dynamics algorithms such as the Articulated Body Algorithm (ABA) for forward dynamics, Recursive Newton-Euler Algorithm (RNEA) for inverse dynamics and the Composite Rigid Body Algorithm (CRBA) for the efficient computation of the joint space inertia matrix. It further contains code for Jacobians, forward and inverse kinematics, handling of external constraints such as contacts and collisions, and closed-loop models.

The code is developed by Martin Felis at the research group Optimization in Robotics and Biomechanics (ORB) of the Interdisciplinary Center for Scientific Computing (IWR) at Heidelberg University. The code tightly follows the notation used in Roy Featherstone''s book "Rigid Body Dynamics Algorithm".

Recent Changes

  • 02 May 2018: New version 2.6.0:
    • Added support for closed-loop models by replacing Contacts API by a new Constraints API. Loop constraints can be stabilized using Baumgarte stabilization. Special thanks to Davide Corradi for this contribution!
    • New constraint type CustomConstraint: a versatile interface to define more general types of constraints (e.g. time dependent), contributed by Matthew J. Millard.
    • New joint type JointTypeHelical that can be used for screwing motions (translations and simultaneous rotations), contributed by Stuart Anderson.
    • Added support to specify external forces on bodies on constrained forward dynamics and NonlinearEffects() (contributed by Matthew J. Millard)
    • Changed Quaternion multiplication behaviour for a more standard convention: multiplying q1 (1,0,0,0) with q2 (0,1,0,0) results now in (0,0,1,0) instead of the previous (0,0,-1,0).
    • Removed Model::SetFloatingBaseBody(). Use JointTypeFloatingBase instead.
    • LuaModel: extended specification to support ConstraintSets.
  • 28 April 2016: New version 2.5.0:
    • Added an experimental Cython based Python wrapper of RBDL. The API is very close to the C++ API. For a brief glimpse of the API see the file python/
    • Matthew Millard added CustomJoints which allow to create different joint types completely by user code. They are implemented as proxy joints for which their behaviour is specified using virtual functions.
    • Added CalcMInvTimesTau() that evaluates multiplication of the inverse of the joint space inertia matrix with a vector in O(n) time.
    • Added JointTypeFloatingBase which uses TX,TY,TZ and a spherical joint for the floating base joint.
    • Loading of floating base URDF models must now be specified as a third parameter to URDFReadFromFile() and URDFReadFromString()
    • Added the URDF code from Bullet3 which gets used when ROS is not found. Otherwise use the URDF libraries found via Catkin.
    • Added CalcPointVelocity6D, CalcPointAcceleration6D, and CalcPointJacobian6D that compute both linear and angular quantities
    • Removed Model::SetFloatingBase (body). Use a 6-DoF joint or JointTypeFloatingBase instead.
    • Fixed building issues when building DLL with MSVC++.
  • 20 April 2016: New version 2.4.1:
    • This is a bugfix release that maintains binary compatibility and only fixes erroneous behaviour.
    • critical: fixed termination criterion for InverseKinematics. The termination criterion would be evaluated too early and thus report convergence too early. This was reported independently by Kevin Stein, Yun Fei, and Davide Corradi. Thanks for the reports!
    • critical: fixed CompositeRigidBodyAlgorithm when using spherical joints (thanks to Sébastien Barthélémy for reporting!)
  • 23 February 2015: New version 2.4.0:
    • Added sparse range-space method ForwardDynamicsContactsRangeSpaceSparse() and ComputeContactImpulsesRangeSpaceSparse()
    • Added null-space method ForwardDynamicsContactsNullSpace() and ComputeContactImpulsesNullSpace()
    • Renamed ForwardDynamicsContactsLagrangian() to ForwardDynamicsContactsDirect() and ComputeContactImpulsesLagrangian() to ComputeContactImpulsesDirect()
    • Renamed ForwardDynamicsContacts() to ForwardDynamicsContactsKokkevis()
    • Removed/Fixed CalcAngularMomentum(). The function produced wrong values. The functionality has been integrated into CalcCenterOfMass().
    • CalcPointJacobian() does not clear the argument of the result anymore. Caller has to ensure that the matrix was set to zero before using this function.
    • Added optional workspace parameters for ForwardDynamicsLagrangian() to optionally reduce memory allocations
    • Added JointTypeTranslationXYZ, JointTypeEulerXYZ, and JointTypeEulerYXZ which are equivalent to the emulated multidof joints but faster.
    • Added optional parameter to CalcCenterOfMass to compute angular momentum.
    • Added CalcBodySpatialJacobian()
    • Added CalcContactJacobian()
    • Added NonlinearEffects()
    • Added solving of linear systems using standard Householder QR
    • LuaModel: Added LuaModelReadFromLuaState()
    • URDFReader: Fixed various issues and using faster joints for floating base models
    • Various performance improvements

For a complete history see doc/api_changes.txt.


The documentation is contained in the code and can be extracted with the tool doxygen.

To create the documentation simply run

doxygen Doxyfile

which will generate the documentation in the subdirectory ./doc/html. The main page will then be located in ./doc/html/index.html.

An online version of the generated documentation can be found at

Getting RBDL

The latest stable code can be obtained from the master branch at

Building and Installation

The RBDL is built using CMake ( To compile the library in a separate directory in Release mode use:

mkdir build
cd build/
cmake -D CMAKE_BUILD_TYPE=Release ../

For optimal performance it is highly recommended to install the Eigen3 linear algebra library from RBDL also comes with a simple, albeit much slower math library (SimpleMath) that can be used by enabling RBDL_USE_SIMPLE_MATH, i.e.:


VCPKG package manager (for Windows, Linux and Mac)

Install vcpkg by making a local clone from its GitHub repo Then run the vcpkg-bootstrapper script to set it up. For detailed installation instructions, see Install vcpkg. To integrate vcpkg with your Visual Studio or Visual Studio Code development environment, see Integrate vcpkg. Then, to use vcpkg to install or update a library, see Manage libraries with vcpkg. For more information about vcpkg commands, see vcpkg command-line reference.

👀 RBDL is available in VCPKG since 2020-11 release

Python Bindings

RBDL can also build an experimental python wrapper that works with python 3 and python 2. To do this enable the the RBDL_BUILD_PYTHON_WRAPPER cmake options. This will build the wrapper for python 3, if you want to use python 2 instead you will also have to enable the RBDL_USE_PYTHON_2 cmake option. The result of this is an extra python directory in the build directory. From within which you can install it using This is done automically when using make install


An overview of the theoretical and implementation details has been published in [](Felis, M.L. Auton Robot (2017) 41: 495). To cite RBDL in your academic research you can use the following BibTeX entry:

  author="Felis, Martin L.",
  title="RBDL: an efficient rigid-body dynamics library using recursive algorithms",
  journal="Autonomous Robots",


The library is published under the very permissive zlib free software license which should allow you to use the software wherever you need.

This is the full license text (zlib license):

RBDL - Rigid Body Dynamics Library
Copyright (c) 2011-2020 Martin Felis <>

This software is provided 'as-is', without any express or implied
warranty. In no event will the authors be held liable for any damages
arising from the use of this software.

Permission is granted to anyone to use this software for any purpose,
including commercial applications, and to alter it and redistribute it
freely, subject to the following restrictions:

   1. The origin of this software must not be misrepresented; you must not
   claim that you wrote the original software. If you use this software
   in a product, an acknowledgment in the product documentation would be
   appreciated but is not required.

   2. Altered source versions must be plainly marked as such, and must not
   be misrepresented as being the original software.

   3. This notice may not be removed or altered from any source


Work on this library was originally funded by the Heidelberg Graduate School of Mathematical and Computational Methods for the Sciences (HGS), and the European FP7 projects ECHORD (grant number 231143) and Koroibot (grant number 611909).


RBDL is a C++ library that contains some essential and efficient rigid body dynamics algorithms such as the Articulated Body Algorithm (ABA) for forward dynamics, Recursive Newton-Euler Algorithm (RNEA) for inverse dynamics, the Composite Rigid Body Algorithm (CRBA) for the efficient computation of the joint space inertia matrix and is also able…








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