Abstract: Based on the early result that the nonlinear friction cone constraints are transformed into positive definiteness of certain symmetric matrices, further cast the friction cone constraints into linear matrix inequalities (LMIs) and formulate the force closure problem as an LMI feasibility problem. The latter was extensively studied in optimization and control community and highly efficient algorithms with polynomial time complexity are now available for its solution. Then, with the observation that the linear constraint matrix of friction cone is sparse and constant, and only the linear constraint matrix of grasp map is dependent on the contact coordinates of the object, extend the grasping force optimization algorithm to realize the real – time grasping force optimization for multifingered manipulation with rolling contact. Finally, give the experiment results to verify the proposed algorithms on the multifingered hand platform.

Key words: Force closure, Force optimization, Linear matrix inequalities, Multifingered manipulation, Robots