Kinematic Inversion of Parallel Manipulators in the Presence of Incompletely Specified Tasks

In this paper, the kinematic inversion of redundant parallel manipulators in the presence of incompletely specified tasks is formulated as an optimization problem. The performance index used is the condition number of the Jacobian matrix of the manipulator which is a measure of Jacobian invertibility. In order to optimize this index along a partially prescribed Cartesian trajectory, the concept of trajectory map is introduced. It is also shown that the optimum value of the free parameter that minimizes the condition number is not a continuous function of the prescribed Cartesian coordinates. An on-line algorithm producing continuous joint histories is then discussed. This method has been implemented and tested, as illustrated with the results presented here.