Flexible Solution of the Inverse Kinematic Task for Cooperating Robots of Different Structures

In this paper a system of cooperating robots manipulating a rigid object is considered. The robots are constructed of redundant open kinematics chains containing prismatic and rotary joints, and may have different, general structures. For solving the inverse kinematic task of such structures generally only differential approaches are applicable that may cope with problems in the unavoidable kinematic singularities. In the present approach the “master” robot can rigidly grip the workpiece and moves it accordingly. The cooperating ones (the “slaves”) can grip the same workpiece with grippers provided with“elastic adapters” that can be deformed if they execute their motion nearby their kinematic singularities where the tracking precision of the construction is limited. A general differential solution is provided for the inverse kinematic task that is based on the Moore-Penrose pseudoinverse with a tracking errordependent damping factor. Simulation results are presented for two cooperating 8 Degree of Freedom robot arms to exemplify the simplicity of the suggested method.