Motion planning of the underactuated manipulators with friction in constrained state space

This paper addresses the constrained motion planning problem for passive joint manipulators with friction. Constraints are imposed on a system state space vector. The dynamics of underactuated manipulators are described by a control-affine system with a drift term. In order to solve the constrained motion planning problem the imbalanced Jacobian algorithm derived from an endogenous configuration space approach is used. The state space constraints are included into the system representation of the manipulator dynamics. The extended system is subject to regularisation because of the Jacobian singularities, then the unconstrained motion planning problem is solved for the regularised system. The solution of the motion planning problem for this system is equivalent to the solution of the constrained motion planning problem for an original system. Performance of the imbalanced Jacobian algorithm has been demonstrated with series of simulation for the two kinds of manipulators with and without friction.