Abstract
This work develops a concept of singular configurations of non-holonomic systems, rooted in the endogenous configuration space approach. The approach takes as a starting point a control system representation of the equations of motion of a non-holonomic robotic system in the form of a control affine system with output. The input-output map is introduced whose derivative is defined as the system’s Jacobian. Dynamic singular configurations are defined as control functions at which the input-output map is not surjective, i.e. the system’s Jacobian gets rank deficient. It is shown that the dynamic singularities coincide with the singular optimal controls of the control affine system. As a by-product of the Jacobian setting dynamic dexterity measures of the non-holonomic systems are designed. The concept of dynamic singularities is illustrated with an example of the front wheel driven car.
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