An example of a seven joint manipulator optimized for kinematic fault tolerance

It is common practice to design a robot´s kinematics from the desired properties that are locally specified by a manipulator Jacobian. For the case of local optimality with respect to fault tolerance, one common definition is that the post-failure Jacobian possesses the largest possible minimum singular value over all possible locked-joint failures. This work considers the global analysis of seven-joint manipulators that have been designed to be locally optimal in terms of fault tolerance when used for six-dimensional tasks. An algorithm for calculating a six-dimensional volume that is composed of a three-dimensional positioning component and a three-dimensional orientation component is presented. Two example manipulators are then analyzed and compared, illustrating a wide degree of variability between their global fault tolerant properties. It is further shown that there are 7! = 5040 different such manipulator designs due to the number of permutations of the Jacobian matrix.