ABSTRACT
In this chapter, we study motion planning and control for systems subject to nonholonomic and underactuation constraints. All such systems can be written in the form
x˙ = f (x)+ m∑
i=1 uigi(x), ui ∈ R, (42.1)
where f (x) is a drift vector field, gi(x) are linearly independent control vector fields, and u = [u1, . . . , um]T is the control. Unless otherwise specified, we work in local coordinates and treat the state as x ∈ M = Rp.
