This paper presents two approaches to obtain the dynamical equations of
serial manipulators using dual quaternion algebra. The first one is based on
the recursive Newton-Euler formulation and uses twists and wrenches instead of
3D vectors, which simplifies the classic procedure by removing the necessity of
exhaustive geometrical analyses since wrenches and twists are propagated
through high-level algebraic operations. Furthermore, the proposed formulation
works for arbitrary types of joints and does not impose any particular
convention for the propagation of twists. The second approach, based on Gauss's
Principle of Least Constraint (GPLC), takes into account elements of the dual
quaternion algebra and provides a linear relationship between twists
derivatives and joint accelerations, which can be particularly useful in robot
control. Differently from other approaches based on the GPLC, which have
representational singularities or require constraints, our method does not have
those drawbacks. We present a thorough methodology to obtain the computational
cost of both algorithms and compared them with their classic counterparts.
Although our current formulations are more computationally expensive, they are
more general than their counterparts in the state of the art. Simulation
results showed that both methods are as accurate as the classic recursive
Newton-Euler algorithm.Comment: Submitted for publication (currently under review