On Dynamic Evaluation of Dexterity of Robot Manipulators Considering Deviation of Acceleration

Abstract

In this paper, a new index for evaluation of dexterity is proposed on the basis of manipulator dynamics. It is called Stochastic Dynamic Manipulability Measure.
It can deal with deviation of end-effector acceleration according to the direction of motion, which is a characteristic of required manipulator motion. Therefore, it can evaluate how suitable a robot mechanism is for its objective task considering features of the motion. This ability is really important for a dexterity index because a manipulator mechanism is designed to be able to perform its objective task. It does not mean undexterity that it cannot accomplish other tasks efficiently.
The deviation is given by a probability density function. The evaluation is based on expected value of mean of joint torques which are necessary for stochastically described motion.
Applications to 2- and 3-DOF manipulators revealed the following.
1. It is important to consider deviation of motion in dexterity evaluation.
2. Stochastic dynamic manipulability always values worse when there is a direction in which it is extremely difficult for an end-effector to move.
3. Singular points sometimes substantially lose their singularity.
4. Optimal trajectory can be planned by using contour-line maps of stochastic dynamic manipulability in joint acceleration space.
5. Contour-line maps in task space help optimal mechanism design and installation planning of manipulators.
6. Maps in null space of Jacobian matrix can be used to determine configurations of redundant manipulators.