Dynamic modelling and adaptive control of robotic hand with singular mass matrix

This paper addresses stable grasping and precise manipulation of objects with unknown parameters under continuous contact, proposing a dynamic modelling and adaptive control framework for soft-fingertip robotic hands. To resolve the singularity of the system inertia matrix caused by compliant contact, the Extended Rosenberg Embedding Method is adopted. This approach systematically decomposes the mass matrix into nonsingular lower-dimensional block matrices, thereby circumventing the strict requirement of a full-rank global matrix. Simultaneously, joint angle limits are embedded as equality constraints via a diffeomorphic transformation to ensure feasible actuator solutions. In controller design, a compensation term combining an improved Extreme Learning Machine network with an adaptive weight-update law is designed to counteract the influence of system parametric uncertainties on stability. This compensation term, together with a feedforward term derived from the dynamic model and servo constraints and a feedback term based on tracking errors, collectively form a composite control law. Theoretical analysis demonstrates that under this control law, the tracking error for object manipulation is uniformly ultimately bounded. Numerical simulations further verify the effectiveness of the framework: in the presence of uncertain object parameters, the tracking error achieves asymptotic convergence within finite time.