Virtual kinematic chains to solve the underwater vehicle-manipulator systems redundancy

A new kinetostatic model for humanoid robots using screw theory

“…The kinetostatic model for HRs proposed in this study is based on screw theory, Assur's virtual chains, Davies' method, and graph theory, whose main concepts and techniques have already been discussed in refs. [31,33,34,35].…”

“…Our proposal is that through the use of virtual chains, HRs can always be kinematically modeled as a parallel mechanism whose differential kinematics can be systematically solved with the application of Davies' method. Therefore, the objective of using Davies' method to solve differential kinematic models is to determine a suitableq p that makes N s square and invertible in the following equation [40,33,34]:…”

“…Therefore, to solve the differential kinematics of HRs through Davies' method, j k − cλ = 30 primary joints velocities, the form and the vectorq p ∈ R 30 are needed. Since one of the purposes of using virtual chains is to control the motion of "actual" chains, the vector of primary magnitudesq p is composed of the virtual chains' joints velocities [33,34]. As in Eq.…”

“…In order to assemble the network of unit actions matrix N , two more matrices have to be built: the unit action cutset matrix D ∈ R λ×C and the fundamental cutset matrix Q A ∈ R K×C [40,33,34]. In order to assemble the matrix D , the vector of the wrenches' magnitudes Ψ = Ψ T S Ψ T…”

“…Based on these grounds, the main objective of this work is to present the kinetostatic modelbased on screw theory [30,31] and its tools, such as Davies' method and Assur's virtual chains [32,31,33,34,35] -for HRs, which, as a new paradigm for modeling these robots, solve the issues and propose advancement based on other modeling techniques that have already been discussed. The kinetostatic model is a combination of both kinematic and static models.…”