  In this series of papers, we present a motion planning framework for planning
comfortable and customizable motion of nonholonomic mobile robots such as
intelligent wheelchairs and autonomous cars. In Part I, we presented the
mathematical foundation of our framework, where we model motion discomfort as a
weighted cost functional and define comfortable motion planning as a nonlinear
constrained optimization problem of computing trajectories that minimize this
discomfort given the appropriate boundary conditions and constraints.
  In this paper, we discretize the infinite-dimensional optimization problem
using conforming finite elements. We describe shape functions to handle
different kinds of boundary conditions and the choice of unknowns to obtain a
sparse Hessian matrix. We also describe in detail how any trajectory
computation problem can have infinitely many locally optimal solutions and our
method of handling them. Additionally, since we have a nonlinear and
constrained problem, computation of high quality initial guesses is crucial for
efficient solution. We show how to compute them.
