Quantifying and Optimizing Failure Tolerance of a Class of Parallel Manipulators

For any robotic system, fault tolerance is a desirable property. This work uses a comparative approach to investigate fault tolerance and the associated problem of reduced manipulability of robots. An important result in combinatorial matrix theory is first obtained. Its consequent modifications are then applied to the theory of fault tolerance of robotic manipulators. It is shown that for a certain class of parallel manipulators, the mean squared relative manipulability over all possible cases of a given number of actuator failures is always constant irrespective of the geometry of the manipulator. A theorem formulates the value of the mean squared relative manipulability. It is shown that this value depends only upon the number of simultaneous joint failures, the nominal number of joint degrees of freedom and the nominal task degrees of freedom. It is difficult to predict specific failures at the design stage and as such failure of any actuator is considered equally likely. In this context, optimal fault tolerant manipulability is quantified. The theory is applied to a special class of parallel manipulators called Orthogonal Gough-Stewart Platforms (Orthogonal GSPs or OGSPs). A class of two-group symmetric OGSPs which inherently provide for optimal fault tolerant manipulability under a single failure is developed.