Toward a Natural Language Interface for Transferring Grasping Skills to Robots

Abstract

In Sections III-VI, admittance selection conditions for four typical two-PC states each in single-point contact were presented. The strategies and procedures can be used for any combination of two single-contact PCs. In general, for each PC, translational variables δ ij are chosen based on the PC's type. Using translational variables δ ij and orientational variables (u, θ), the contact wrenches w i and errormeasure vector d are obtained and the interaction of the wrenches from the two PCs is addressed in the calculation of their magnitudes. Then, by (5), the error-reduction function is expressed in terms of (δ ij , u, θ). The function obtained is a polynomial in (δ ij , sin θ) with coefficients being functions of u and the admittance A. Based on the nature of the contact and the properties of the error-reduction function, selection conditions for the admittance are obtained.Sections III-VI present results for four of the six combinations of two single-point contact PCs. The remaining two combinations are similar. Note that both the wrench associated with {e − e} contact (34) and the wrench associated with {{v − f } contact (22) contain only the linear term in sin θ.The admittance selection conditions are obtained by geometric and force analysis of each contact state. Redundant coordinates δ ij are used to describe the translational variation. These coordinates are treated as independent variables in a large range (without considering the constraints due to contact). Thus, the conditions obtained are conservative. To make the conditions less conservative, the range of configuration variables considered can be decomposed into a number of nonoverlapping subranges, each addressed with equivalent conditions.In this paper, a single admittance control law (1) is considered for each contact state. The sufficient conditions obtained impose conditions on the admittance to ensure error reducing motion for the entire contact state. Due to uncertainty in identifying which contact state actually occurs, a single admittance control law (1) could be used for all contact cases, if the conditions for all contact states were satisfied simultaneously.In practice, the selection of an appropriate admittance A can be formulated as a search routine to find an admittance matrix A subject to the appropriate conditions. For instance, an optimization procedure can be used to find an admittance matrix for which sufficient conditions such as those described in the paper are used as "constraints." An example illustrating the application of error-reduction conditions to obtain a desired admittance was presented in [5] for a planar case. This procedure applies to the spatial cases as well.In summary, we have presented conditions for admittance selection of a polyhedral rigid body for force-guided assembly in cases having two point contact PCs. We have shown that, for these cases, the admittance control law can be selected based on its behavior at a finite number of configurations. If the error-reduction conditions are satisfied at these configur...

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