Multiple impedance control for object manipulation

the presence of an unknown environment, have been proposed [8]. The Object Impedance Control (OIC), an extension of impedance control, has been developed for multiple robotic arms manipulating a common object [9]. The OIC enforces a designated impedance not of an individual manipulator endpoint, but of the manipulated object itself. A combination of feedforward and feedback controls is employed to make the object behave like a reference impedance. It has been realized that applying the OIC to manipulation of a flexible object may lead to instability [10]. Based on the analysis of a representative system, it was suggested that in order to solve the instability problem, one should either increase the desired mass parameters or filter and lower the frequency content of the estimated contact force. Impedance Control was formulated originally to impose a desired behavior on a single manipulator interacting with its environment. In this paper, a new algorithm called Multiple Impedance Control (MIC) is proposed for the cooperative manipulation of a common object. The general formulation for the MIC algorithm is developed and is shown that under the MIC law all cooperating manipulators, and the manipulated object exhibit the same designated impedance behavior. At the same time, the potentially large object inertia and other forces are taken into account. An estimation procedure for contact force determination is given which results in a good approximation, even during an impact. Using an example, the response of the MIC algorithm is compared to that of the Object Impedance Control (OIC). It is shown that in the presence of flexibility, the MIC algorithm results in an improved performance. The Multiple Impedance Control (MIC) was newly presented and applied to space free-flying multi-arm robotic systems [11]. In this article, the new MIC algorithm is developed for distinct cooperating manipulators, and important issues are detailed. The MIC enforces a reference impedance on both the manipulator end-points, and the manipulated object. Physically speaking, this means that both manipulator end-effectors and the object are controlled to behave like a designated impedance in reaction to any disturbing external force on the object, and hence, an accordant motion of the manipulators and payload is achieved. First, the basic concepts are introduced. Then, the general formulation for the MIC algorithm is presented, and the resulting tracking errors are studied. In addition, an estimation procedure is given for contact force determination. Finally, a simple model of a robotic arm manipulating an object is used to compare the performance of the MIC and OIC algorithms.