Singularity control of robot manipulators using closed-form kinematic solutions

Abstract

In robotics, kinematic singularities of serial chain manipulators arise at places where the transformation from Cartesian coordinates to robot joint coordinates becomes ill-defined, with a loss of one or more degrees of freedom. Traveling close to a singularity while following a path in Cartesian coordinates typically results in unacceptably high joint velocities and accelerations. The problem of singularity control is to keep the joint velocities and accelerations bounded while still trying to stay close to the desired path. The paper explores an alternative method of singularity control which directly utilizes closed-form inverse kinematic solutions. While not all robots have closed-form solutions, most six degree-of-freedom robots in common use do. Closed form kinematic solutions offers the advantages of speed and computational stability. Perhaps most importantly, they also enable us to know exactly where the various singularities are. We specifically consider straight line Cartesian trajectories, and discuss a method for constructing a velocity profile that allows these trajectories to pass near or through singularities without any deviation in the spatial path, while keeping both the joint velocities and accelerations bounded. >