Control of Robotic Manipulators During General Task Execution: A Discontinuous Control Approach

In this article, a control methodology is proposed that ad dresses the problem of control of robotic manipulators during a general class of task that requires the manipulator to make a transition from (I) noncontact motion to contact motion and (2) contact motion to noncontact motion. Specifically, the problem of control of a general n-degree-of-freedom rigid-link robotic manipulator during a general class of tasks, as described ear lier, is treated. It is assumed that during the contact phase of the assumed task, frictionless point contact is made with fixed objects in the manipulator work environment, which is modeled as a linear mechanical impedance. Furthermore, it is assumed that exact knowledge of the manipulator and work environment kinematic and dynamic parameters is available. The following closed-loop behavior is achieved with the pro posed control law: (1) the closed-loop system exhibits global asymptotic stability; (2) asymptotic trajectory tracking of gen eralized force and position inputs is achieved; and significantly, (3) on inadvertent loss of contact by the manipulator, contact is reestablished, and generalized forces and positions are again asymptotically achieved. This closed-loop behavior is achieved in the presence of collisions between the manipulator and ob jects in the manipulator work environment; such collisions may include multiple impacts as a result of bouncing on initial contact. A general mathematical framework is established to prove that the closed-loop robotic system, with a discontin uous control applied, is asymptotically stable. Experimental results performed on a two-degree-of-freedom direct-drive robot support the theoretical claims made in this work.