Directional manipulability constrained by the condition number

There is often such a situation that the condition number of the optimization results based on the directional manipulability is very large, which is not conductive for control. To solve this problem, a new dexterity index-directional manipulability constrained by the condition number is proposed. The changing pattern of the partial derivative of this index with the increase of the condition number is analyzed. When the condition number is small, the index is mainly influenced by the directional manipulability. While the condition number increases, the impact of the directional manipulability on the index declines, and the impact of the condition number increases. Through changing the partial derivative, the condition number of the optimization results based on this index is less than the maximum of the task requirements. Moreover, the directional manipulability can be retained to maximum. The simulation researches for planar 3R and BUAA-RR robot and the experiment research for planar 3R manipulator demonstrate the superiority of this new index. Besides, this new index is used for tolerant performance of redundant robots. When one robot's joint fails at any moment during the task, the reduced robot based on this new index has a good manipulability on the task direction. A small condition number of the reduced robot also can be assured, which is benefit for singularity avoidance.