Manipulator transition to and from contact tasks: a discontinuous control approach

The stability and control of robotic manipulators during the execution of tasks that require the manipulator to make a transition from noncontact motion to contact motion, or vice versa, are investigated. A dynamic model of the manipulator during noncontact and contact motion is developed. This model includes the effect of the inevitable collision that occurs between the manipulator end effector and the work environment during the transition from noncontact to contact motion. The work environment that the manipulator comes into contact with is modeled as a very still surface. The dynamic model of the robot during this transition is transformed through a nonlinear coordinate transformation into a new set of generalized coordinates in which the form of the dynamics is greatly simplified. A discontinuous control is proposed for the robotic manipulator system. It is shown that with this discontinuous control applied to the system, the closed-loop system can be treated as a generalized dynamical system. Using the theory associated with generalized dynamical systems, it is possible to extend Lyapunov stability analysis to systems with discontinuous controls. The system dynamics is written as a contingent equation to which a set valued control function is applied. Within this mathematical framework, the uniform asymptotic stability in the larger of the closed-loop systems is proved. The controller has several desirable properties, including the ability to return to contact motion if the manipulator end effector inadvertently leaves the surface due to some external disturbance acting on the system