Identification and Analysis of Robot Manipulator Singularities

The existence of singular positions inside the robot workspace is an inherent problem for task planning and robot control. At manipulator configurations near singular positions, very large joint motions are required to produce relatively small end-effector displacements. In the limit, when a singularity is encountered, the required joint motions become unbounded and the manipulator loses at least one degree of freedom. Identify ing the singularities in the robot workspace is not always an analytically tractable problem, except for manipulators with op portune placement of the joint axes. Typically, it is easier and more informative to evaluate the robot "arm" and "wrist" sin gularities, which reflect the limitations of the lower-order robot subsystems responsible for positioning and orienting, respec tively, the end effector in space. The objective of this article is to define analytically the interplay between the individual "arm" and "wrist" singularities and the global manipulator singularities. Specifically, a general formula that defines ma nipulator singularities in terms of the subsystem singularities is developed. The analysis leads to a novel, efficient method for identifying the singularities of six-axis manipulators. This is then illustrated through an example.