Stabilizability of Nonholonomic Control Systems

We consider here the problem of stabilization of nonlinear Hamiltonian control systems with nonholonomic constraints. Such systems are of interest in various applications including the control of robotic systems. We discuss the formulation of Hamiltonian systems with nonholonomic constraints, in particular considering the differences between the Dirac theory of constraints, the classical theory of nonholonomic constraints, and Weber's theory of generalized nonholonomic constraints. Stabilization of systems with these constraints is discussed using the theory of Hamiltonian control systems, and a reduced stabilization criterion is given. The effects of symmetries in the presence of constraints are also discussed.