The contact problem in Lagrangian systems with redundant frictional bilateral and unilateral constraints and singular mass matrix. The all-sticking contacts problem

Modeling, analysis and control of robot–object nonsmooth underactuated Lagrangian systems: A tutorial overview and perspectives

“…Adding Coulomb's friction (or an extension of it) to the contact problem makes it more complex [92,93,6].…”

“…These two equalities (in general, non-holonomic constraints) are used in manipulation system to transform the dynamics [16,23,21]. Using (8), the CP is constructed as follows [93]:…”

Algorithm for calculating the problem of unilateral frictional contact with an increscent external load parameter

“…These problems are stated in the form of variational inequalities [21][22][23][24], and the following numerical methods were used to solve them: Lagrange multipliers [25][26][27], penalty functions [28; 29] and their combinations [30][31][32]. And other methods using contact finite elements [32][33]; quadratic programming approach [34][35][36]; finite element methods (Spigot-algorithms) [37][38][39]; and other [40][41][42][43][44][45][46].…”