Dual relationship in dextrous sliding manipulation under force and position controls

In this paper, we investigate dextrous sliding manipulation, under both force and position controls using soft fingers. We study the motion trajectory of sliding manipulation under force control as well as the force/moment trajectory on the limit surface under position control. It is found that the characteristic pitch, λ (defined as the ratio between the maximum moment and the maximum friction force of a soft finger) and ξ (the ratio between characteristic dimension and the characteristic pitch) characterize sliding manipulation. The rate of change of grasping parameters, such as the velocity of a grasped object, can be represented by the dimensionless geometric parameter, ξ, and the partial geometric velocity, ∂Ξ/∂t. In addition, a dual relationship for the parameters of the manipulation is deduced. The dual relationship is a consequence of the force control (trajectory prediction) and position control (trajectory planning) as applied in sliding manipulation. The results are presented with both analytical results and simulation using Λ and Ξ. The results of numerical simulation were found to match well with the theoretical analysis using a differential relationship.