Unified formulation of robotic systems with holonomic and nonholonomic constraints

Many robotic systems are subject to nonholonomic as well as holonomic constraints. Rolling contact between two rigid bodies is a typical example of such a system. In the study, a unified state space formulation of robotic systems subject to both holonomic and nonholonomic constraints is presented. The position-level holonomic constraints are first replaced by a set of velocity-level constraint equations that asymptotically converge to the original holonomic constraints. Having represented both holonomic and nonholonomic constraints in a common form, a state space representation of the constrained systems is then developed. A numerical algorithm for implementing the state space representation is also described. The proposed formulation eliminates the need to solve holonomic constraints either analytically or numerically, and ensures that holonomic constraints are always satisfied, particularly in computer simulations. The formulation makes it possible to treat systems with holonomic constraints, with nonholonomic constraints, or with both holonomic and nonholonomic constraints in a unified framework. Two examples are presented to illustrate the application of the unified formulation.