An Illustration of Generating Robots from Optimal Fault-tolerant Jacobians

The local kinematic properties of a robotic manipulator’s configuration can be described by its corresponding Jacobian matrix. Conversely, one can determine a manipulator that possesses certain desirable kinematic properties by specifying the required Jacobian. In this work, design criteria that require a manipulator to function in a configuration that is optimal under normal operation and after an arbitrary single joint fails and is locked in position is first described. Specifically, the desired Jacobian matrix must be isotropic, i.e., possess all equal singular values prior to a failure, and have equal minimum singular values for every possible single column being removed. Then a simple planar three degree-of-freedom example is used to illustrate how one can identify all of the possible manipulator designs that possess the desired local properties described by the required structure of the Jacobian matrix. This paper concludes by showing that despite having identical local properties, the resulting manipulator designs have significantly different global kinematic properties that can be used to match a design to additional application-specific performance criteria.