Kinematic-Sensitivity Indices for Dimensionally Nonhomogeneous Jacobian Matrices

• Published in: IEEE transactions on robotics 2010-02, Vol.26 (1), p.166-173
• Main Authors: Cardou, P., Bouchard, S., Gosselin, C.
• Format: Article
• Language: English
• Subjects: Accuracy; Actuators; Applied sciences; Arrays; Computer science; control theory; systems; condition number; Control theory. Systems; dexterity; Differential equations; Displacement control; End effectors; Exact sciences and technology; Jacobian matrices; Jacobian matrix; kinematic sensitivity; Kinematics; manipulability; Manipulators; Mathematical models; Matrix; matrix norm; parallel robot; Parallel robots; Robot kinematics; Robot sensing systems; Robotics; Robots; serial robot; Upper bound
• ISSN: 1552-3098; 1941-0468
• DOI: 10.1109/TRO.2009.2037252

Numerous performance indices have been proposed to compare robot architectures based on their kinematic properties. However, none of these indices seems to draw a consensus among the robotics community. The most notorious indices, which are manipulability and dexterity, still entail some drawbacks, which are mainly due to the impossibility to define a single invariant metric for the special Euclidean group. The natural consequence is to use two distinct metrics, i.e., one for rotations and one for point displacements, as has already been proposed by other researchers. This is the approach used in this paper, where we define the maximum rotation sensitivity and the maximum point-displacement sensitivity. These two indices provide tight upper bounds to the end-effector rotation and point-displacement sensitivity under a unit-magnitude array of actuated-joint displacements. Therefore, their meaning is thought to be clear and definite to the designer of a robotic manipulator. Furthermore, methods for the computation of the proposed indices are devised, some of their properties are established and interpreted in the context of robotic manipulator design, and an example is provided.