Robust Hybrid Control of Constrained Robot Manipulators via Decomposed Equations

• Authors: Jing-Sin Liu;Shyh-Leh Chen
• Venue: Journal of Intelligent and Robotic Systems
• Year: 1998

Basing on a constraint Jacobian induced orthogonal decomposition of thetask space and by requiring the force controller to be orthogonal to theconstraint manifold, the dynamics of the constrained robots under hybridcontrol is decomposed into a set of two equations. One describes the motionof robots moving on the constraint manifold, while the other relates theconstraint force with the hybrid controller. This decomposition does notrequire the solution of the constraint equation in partition form. In thissetting, the hybrid control of constrained robots can be essentially reducedto robust stabilization of uncertain nonlinear systems whose uncertaintiesdo not satisfy the matching condition. A continuous version of thesliding-mode controller (from Khalil [12]) is employed to design a positioncontroller. The force controller is designed as a proportional force errorfeedback of high gain type. The coordination of the position controller andthe force controller is shown to achieve ultimately bounded position andforce tracking with tunable accuracy. Moreover, an estimate of the domain ofattraction is provided for the motion on the constraint manifold. Simulationfor a planar two-link robot constraining on an ellipse is given to show theeffectiveness of a hybrid controller. In addition, the friction effect,viewed as external disturbance to the system, is also examined throughsimulations.