Kinematically Redundant Manipulator

being solved to determine the corresponding required joint values, 8(t;). A kinematically redundant manipulator can, in general, satisfy an end-effector positioning constraint, x(t;), with an infinite family of joint values satisfying (2). The underlying premise for advocating the use of redundant manipulators for critical applications is that if a joint should fail, then the redundancy of the manipulator may permit the completion of the task. Although commercial manipulators currently are not equipped with the necessary circuitry to detect failures and apply the brakes to any failing joint, the need for such a mechanism is well known [3]. If failed joints are locked then a single joint failure reduces the number of degrees of freedom (DOF) of the system by one and the new kinematic functions] and ]-1 differ markedly from the original ones. In [4] a method is described for designing manipulators to be fault tolerant with regard to a given point-topoint task. The authors assume that any joint may fail anywhere within its entire range of motion. A manipulator is said to be fault tolerant with respect to a given set of task points x(t;) only if there exist solutions to (2) for every possible failure in all joint configurations. With this assumption, the worst case typically occurs when a failing joint is folded in on itself. In the work described here, failure tolerance is achieved by imposing constraints on the motion of all joints prior to a failure. AbstractThe high cost involved in the retrieval and repair of robotic manipulators used for remediating nuclear waste, processing hazardous chemicals, or for exploring space or the deep sea, places a premium on the reliability of the system as a whole. For such applications, kinematically redundant manipulators are inherently more reliable since the additional degrees of freedom (DOF) may compensate for a failed joint. In this work, a redundant manipulator is considered to be fault tolerant with respect to a given task if it is guaranteed to be capable of performing the task after anyone of its joints has failed and is locked in place. A method is developed for insuring the failure tolerance of kinematically redundant manipulators with respect to a given critical task. Techniques are developed for analyzing the manipulator's workspace to find regions which are inherently suitable for critical tasks due to their relatively high level of failure tolerance. Then, constraints are imposed OIl the range of motion of the manipulator to guarantee that a given task is completable regardless of which joint fails. These concepts are illustrated for a PUMA 560 that is used for a three-dimensional positioning task.