The effect of dynamic singularities on robotic control and design

This paper presents the definition of a new type of dynamic singularity for robotic manipulators. It is applicable to all underactuated robotic systems that can be described by Lagrange's equations where the Lagrangian is the kinetic minus potential energy. The approach is to decompose the velocity at every point in the configuration space into velocity directions that can be directly controlled and those that are uncontrolled and orthogonal to the directly controlled directions. These uncontrolled directions are controlled only through the dynamic coupling with the controlled directions and the measure of a dynamic singularity is then a measure of this degree of coupling. When this coupling is zero, the mechanism is said to be at a dynamic singularity. The practical implication is that, at such points, the dynamics are decoupled and control over the uncontrolled directions is very weak in that the mechanism will have to move away from the singularity before the inputs can affect the uncontrolled velocity directions. An example that is realistically complicated is presented and simulations show the effect on control inputs when the system is operating near a dynamic singularity.