Algorithms for calculating the forward and inverse dynamics of a kinematic tree.
Trees (and chains) of kinematic equations are used in robotics, computer games, and animation. In robotics {\it forward kinematics} refers to the use of kinematic equations to compute the position of an end-effector, such as a jointed robotic arm, from specified values for the joint parameters.
https://en.wikipedia.org/wiki/Forward_kinematics
The reverse calculation, that computes the joint parameters that achieve a specified arm position, is known as {\it inverse kinematics}.
https://en.wikipedia.org/wiki/Inverse_kinematics
BDynamics is an implementation of:
i) the articulated-body algorithm (ABA) and
ii) the recursive Newton-Euler algorithm (RNEA),
presented in:
"Rigid Body Dynamics Algorithms" (RBDA), R. Featherstone, Springer, 2008 (see https://royfeatherstone.org).
ABA is an example of a propagation algorithm, and it is the fastest known algorithm
for calculating the forward dynamics of a kinematic tree with a computational complexity of
RNEA calculate the inverse dynamics of a kinematic tree.
It is the simplest, most efficient known algorithm for trees, and also has a computational
complexity of
The implementations presented here, are intended for use in computer games, and are based on those in the RBDL library (see https://github.com/rbdl/rbdl). We intentionally use similar variable names and the same object structure and hierarchy. Some variables have been moved to their appropriate classes and accessor methods have been added throughout. This improves encapsulation and readability.
RBDL employs the Eigen3 linear algebra library. Eigen3 supports all matrix sizes, from small fixed-size matrices to arbitrarily large dense matrices, and even sparse matrices. This code does not depend on Eigen3, and instead relies on the lighter-weight GLM library for simple 3D-linear algebra types and operations (see https://github.com/g-truc/glm). As the GLM library does not support 6D vectors and matricies, the code for RBDL custom joint types is not implemented.
This code depends on the 3D GLM types and functions: glm::dvec3, glm::dmat3, glm::dquat, glm::cross(v1, v2), glm::dot(v1, v2), glm::length(v1), glm::inverse(m1), glm::toMat3(q).
It should be relatively straightforward to convert back to Eigen3 (although see the note on Eigen3 and GLM differences), or replace GLM with some other simple linear algebra library.