Computer simulation of controlled motion of dual fingers with soft tips grasping and manipulating an object

In the previous paper, the dynamics of a set of dual multi-joint fingers with soft, deformable tips grasping and manipulating a rigid object were formulated by a system of nonlinear differential equations of Euler-Lagrange's formalism. Although geometric constraints of tight area contacts have been pointed out, they were neglected purposely in motion equations of the system in order to avoid increasing complication arising in design of control laws and in the analysis of the stability of the dynamics. On the basis of passivity, sensory feedback control schemes for stably grasping an object by a set of dual soft-tip fingers and regulating the object's posture have been explored and a proof for asymptotic convergences of controlled variables has been presented by theoretical analysis without showing any simulation result. In this paper, first, we carry out a numerical simulation based on the thorough dynamics of the overall system and, secondly, find the important role of constraint forces arising from tight area contacts between soft finger-tips and the object. The paper shows that ignorance of these constraints does not yield any faithful motion of the system even in an approximate sense, although the terms do not induce any work and are irrelevant to the passivity. In fact, in simulation, it causes increased instabilities of state variables and it should be concluded that they cannot be neglected in the dynamics. Thirdly, motions of the object-fingers system under geometric constraints of tight area contacts have been expressed by a set of mixed nonlinear differential and algebraic equations. Then, the overall system dynamics for simulation in which the constraint conditions are taken into account are developed by using the idea of a constraints stabilization method. Computer simulation results have confirmed the effectiveness of the proposed control laws. In particular, it is verified that the constraint forces appearing in the directions tangential to the object surfaces converge to zero quickly as stable grasping is realized. Finally, a stick graph of simulated motion is presented to illustrate a process of grasping and manipulating a rigid object by soft fingers.