Using redundancy to optimize manipulability of Stewart platforms

For any robotic system, fault tolerance is a desirable property. This paper uses a comparative approach to investigate fault tolerance and the associated problem of reduced manipulability of robots. It is shown that for a certain class of 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. 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 symmetric OGSPs that inherently provide for optimal fault tolerant manipulability under a single failure is developed.