Determination of Contact Forces for Two Manipulators Mutually Lifting a Rigid Object Using A Technique of Dynamic Load Distribution

Cooperative Robot Manipulators Dynamical Modeling and Control: An Overview

“…where the grasp matrix, J o , is defined in Equation ( 9) and F is defined in Equation (3). The above equality represents the basis for most of the analysis performed so far [58,66,104,116,[129][130][131][132][133][134]. If the desired object wrench, F o , is given, for example, by specifying the payload trajectory and computing F o through inverse dynamics, there are infinite solution for F given F o [116,129].…”

“…In [29], the value of is calculated based on optimizing the energy consumption by the joints, i.e., the cost function is equal to T T T , and the external and internal wrenches are determined. In [130], Unseren introduced the practice of setting the value of as = MF, with M being a matrix whose determination is required. Equation ( 21) is expressed as F = ΦF o + Ψ .…”

Cooperative Manipulation

“…In order to confer robustness to the grasp and/or optimize the manipulators' efforts, optimization methods for load sharing were proposed, e.g., in Uchiyama and Yamashita (1991). In Unseren (1994) a reduced order model of the whole manipulators/object system taking into account the kinematic constraints is derived in the joint space and adopted for load sharing and control purposes. Another successful approach is the so-called augmented object model (Khatib 1988), where the cooperative system is modeled as an augmented object in the operational space to pave the way for control strategies that are dynamically consistent with the operational space formulation.…”