Quantifying optimum fault tolerance of manipulators and robotic vision systems

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 and reduced perceptibility of vision systems. 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 and vision systems.;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. 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 symmetric OGSPs which inherently provide for optimal fault tolerant manipulability under a single failure is developed.;The theory is then extended to study failure tolerance of robotic vision systems. The problem of reduced perceptibility under failures in such systems is addressed. The concept of relative perceptibility, which is analogous to the concept of relative manipulability, is used to design vision systems capable of withstanding failures. It is shown that for a certain class of robotic vision systems analogous to the aforementioned class of robotic manipulators, the mean squared relative motion perceptibilities over all possible cases of a given number of sensing failures (or a given number of actuator failures) is always constant irrespective of the geometry of the robotic vision system.