Synthesizing a positive definite spatial stiffness matrix with a hybrid connection of simple compliances

Achieving adequate force control is an important problem in the application of robotics technology to manufacturing tasks. This is particularly true for assembly tasks that require constrained interaction between a robotic manipulator and a work-part. One approach to this problem is the use of passive compliance. This can be accomplished by realizing a given spatial stiffness or compliance matrix with a connection of simple compliances. Isotropic spatial stiffness matrices can be realized with a parallel connection of simple springs. Similarly, a serial connection of simple compliances can realize an isotropic compliance matrix. However, the family of isotropic stiffness and compliance matrices constitute a very small subset of the family of all stable stiffness/compliance matrices. In this article, we propose a method to realize any positive definite spatial stiffness/compliance matrix using a hybrid connection of simple compliances