This paper discusses the problem of stable grasping and object manipulation by a pair of robot fingers when fingertips are covered with soft compressible material and fingers are allowed to incline their last link against the object surface. The area contact between the fingertips and the rigid object surface leads to nonholonomic constraints even for the planar case; however, the variational principle can be applied and the equation of motion is derived as a set of nonlinear differential equations with extra terms of Langrange multipliers incorporating the constraints. The proposed feedback controller is a linear combination of simple feedback control signals each designed for realizing grasp stabilization, regulation of object rotation and regulation of object position respectively. The controller is shown to achieve asymptotic convergence to the desired state at a stable grasping configuration. Simulation results are presented confirming the theoretical findings.
