A probabilistic approach for measuring the fault tolerance of robotic manipulators

Fault tolerance is critical for various situations where robotic manipulators are applied, such as for hazardous waste disposal, exploring remote environments, or medical procedures. Metrics that are frequently applied to measure the degree of fault tolerance that a manipulator possesses have been focused on local kinematic properties of the Jacobian matrix, e.g., the worst-case manipulability (or relative manipulability) following a locked joint failure. These measures are useful for characterizing the manipulator's dexterity at a given configuration, however, they do not provide a measure for completion of a task within a specified workspace. This paper extends the use of local fault tolerance measures by using them to compute a global measure using a probabilistic analysis. Specifically, we compute cumulative density functions (CDF) that can be used to specify a desired fault tolerance threshold for completion of a task within a specified workspace region. We further show how this CDF can be improved by utilizing redundancy to optimize manipulator configurations throughout this region, using a modified nine degree of freedom Mitsubishi PA10-7C.