Robust Hybrid Control of Constrained Robot Manipulators via Decomposed Equations

Basing on a constraint Jacobian induced orthogonal decomposition of the task space and by requiring the force controller to be orthogonal to the constraint manifold, the dynamics of the constrained robots under hybrid control is decomposed into a set of two equations. One describes the motion of robots moving on the constraint manifold, while the other relates the constraint force with the hybrid controller. This decomposition does not require the solution of the constraint equation in partition form. In this setting, the hybrid control of constrained robots can be essentially reduced to robust stabilization of uncertain nonlinear systems whose uncertainties do not satisfy the matching condition. A continuous version of the sliding-mode controller (from Khalil [12]) is employed to design a position controller. The force controller is designed as a proportional force error feedback of high gain type. The coordination of the position controller and the force controller is shown to achieve ultimately bounded position and force tracking with tunable accuracy. Moreover, an estimate of the domain of attraction is provided for the motion on the constraint manifold. Simulation for a planar two-link robot constraining on an ellipse is given to show the effectiveness of a hybrid controller. In addition, the friction effect, viewed as external disturbance to the system, is also examined through simulations.