Controllability and stabilizability of higher-order nonholonomic systems

This paper studies the nonlinear modeling and control problem for systems with higher-order nonholonomic constraints using tools from differential geometry. A number of control-theoretic properties such as nonintegrability, controllability, and stabilizability are first derived. The applicability of the theoretical development is illustrated through a third-order nonholonomic system example: a planar PPR robot manipulator subject to a jerk constraint. In particular, it is shown that although the system is not asymptotically stabilizable to a given equilibrium configuration using a time-invariant continuous feedback, it is strongly accessible and small-time locally controllable at any equilibrium.