Algorithm for Serial Robots Passing Through the Singular Point Spanning a Lie Algebra

Abstract

When the end effecter of a serial robot passes through the vicinity of a singular point, some joint must move about 180 degrees in a short period, and, in many cases, a robot must be stopped by the limitation of the velocities of actuators. Though the velocities at a singular point cannot be determined by the Jacobian matrix, it is shown that they can be determined mathematically when the linearly independent joints span a Lie algebra. Thus the end effecter can path through a Lie algebraic singular point. The novel method for passing through a singular point is proposed for a serial robot by changing the orientation path at the vicinity of a singular point. This modification makes it possible for a robot to pass through the singular point located at the most vicinity of the original trajectory. Some numerical examples show that the robot can passes through the singular point in the permissive velocities.