Cooperative operation of multiple manipulators has been increasingly used in industrial automation, outer space and hazardous terrestrial applications. Moreover, the requirement for increased speeds of operation and light-weight design of robot m anipulators has made structural flexibility a dominant factor in the design and control of cooperating manipulator systems.

When multiple manipulators act cooperatively on an object, a closed-loop chain structure is formed. Redundant actuation is one of the inherent characteristics of such systems. Determining actuator torques necessary to achieve a prescribed object motion is known as the inverse dynamics process. Due to the presence of the redundant actuators, inverse dynamics torques for cooperating m anipulator systems admit an infinite number of solutions.

Consideration of flexibility in the links of manipulators, particularly relevant in space applications, not only complicates the dynamics modeling of the system, but also introduces instability in the inverse dynamics solution. In this study, a dynamics model is derived for a flexiblc-link cooperating manipulator system and the inverse dynamics procedure for such a system is investigated. In particular, the latter is divided into two subproblems — the force distribution problem and the inverse flynamics problem for serial flexible-link manipulators. The approach chosen to the force distribution problem is to formulate it as a linearly constrained local optimization problem. Several objectives particularly relevant to flexible-link cooperating manipulators are proposed. These include minimum strain energy, minimum weighted norm of elastic accelerations and optimal load sharing schemes. The result ing algorithms are shown to be effective in reducing the vibration of the system and stabilizing the inverse dvnamics solution.

A stability analysis of the internal dynamics of the inverse dynamics system is also performed by using linearization. Agreement in the behavior of the inverse dynamics system is dem onstrated between directly solving the nonlinear dynamics equations with optimal force distribution and calculating the eigenvalues of the plant matrix of the linearized system. .A stability approach to the force distribution problem is then proposed which ensures stable behavior of the internal dynamics system under the condition that the number of elastic coordinates of the system is less than or equal to the total number of redundant actuators.