A unified approach for control of redundant mechanical systems under equality and inequality constraints

The equality and inequality constraints on constraint force and/or the actuator force/torque arise in several robotic applications, for which different controllers have been specifically developed. This paper presents a unified approach to control a rather general class of robotic systems with closed loops under a set of linear equality and inequality constraints using the notion of projection operator. The controller does not require the kinematic constraints to be independent, i.e., systems with time-varying topology can be dealt with, while demanding minimum-norm actuation force or torque in the case that the system becomes redundant. The orthogonal decomposition of the generalized force yields the tangential (potent) and normal (impotent) components leads. The tangential component is obtained using projected inverse dynamics control law, while the optimal normal component is found through solving a quadratic programming problem, in which the equality and inequality constraints are derived to be equivalent to the originally specified ones. Finally, a case study is presented to demonstrate how the control technique can be applied to multi-arms manipulation of an object.