Automatic generation of dynamics for modular robots with hybrid geometry

Manual derivation of the dynamic model of a modular robot is almost impossible because it may have very different geometries and DOFs through module reconfiguration. This paper presents an algorithm to automatically generate the closed-form equation of motion of a modular robot from a kinematic graph based representation of the assembly configuration. We consider modular robots with the more general branching geometry. The formulation of the dynamic model is started with recursive Newton-Euler algorithm. The generalized velocity, acceleration, and forces are expressed in terms of linear operations on se(3), the Lie algebra of the Euclidean group SE(3). Based on the equivalence relationship between the recursive formulation and the closed-form Lagrangian formulation, we use the accessibility matrix of the kinematic graph to assist the construction of the closed-form equation of motion of a modular robot. Applications of the closed-form dynamic model of a branching robot are in robot design, calibration, and motion optimization