The objectives of this research are:​ i) to model the grasp between the fingers of a dexterous mechanical hand with soft finger-tips and an object;​ ii) to devise a control law such that the actual linear impedance model of each grasping finger is matched with the desired impedance;​ iii) to develop a control law such that the contact wrenches between each grasping finger and the object are maintained during a task and the presence of uncertainties.

Using the causality principle, each grasping finger is modelled as a system consisting of a mass, a spring and a damper in each direction of the end-point reference coordinate frame. In this model, the spring and damper are connected in parallel between the mass model of the finger and the palm of the hand. Similarly, the soft finger-tip is modelled as a spring and damper system connected in parallel between the mass model of the finger and the grasped object. The model of the finger, with its mass, spring and damper parameters given, is referred to as the targeted impedance.

In general, the actual linear model of each grasping finger is different from the model specified by a targeted impedance. In order for each finger to have the impedance model specified by the targeted impedance, the concept of impedance matching and a method of implementation are proposed. Implementation of the impedance matching concept is based on the linear dynamic decoupling approach. It is shown that when the exact model parameters of the finger are known, the implementation of this method results in the actual impedance model of the finger to be replaced with the targeted impedance.

When fingers of a dexterous mechanical hand are grasping an object, they must exert wrenches equal to the desired grasping wrenches. Furthermore they must maintain these wrenches during the task and presence of uncertainties. Using the matched impedance model of the finger and the model of the soft finger-tip, a grasping wrench control architecture is developed. This architecture is obtained based on the input/output relationships of the impedance/admittance of these models. It is shown that in the presence of uncertainties in the actual parameters of the finger and the presence of disturbance wrench, the grasping wrench controller would not have the desired performance. Based on the theory of the servomechanism problem, the feedforward control impedance/admittance blocks of the general control architecture are modified such that the controller exhibits robustness. The modified architecture has the property that the error between the actual and desired grasping wrenches approaches zero asymptotically. This asymptotic regulation occurs even when there are uncertainties in the parameters of the actual finger, and where there is a constant disturbance wrench. The performance of the robust controller is demonstrated through simulation and shown experimentally using a 2DOF planar finger with soft finger-tip making contact with a rigid wall. Also, based on the robustness theory, a robust grasping wrench controller is proposed for tooling tasks. In this controller, a model of the exogenous disturbance wrench which arises from the interaction of the tool with the environment is included in the control architecture.