A Nonlinear Constrained Optimization Framework for Comfortable and Customizable Motion Planning of Nonholonomic Mobile Robots - Part II

摘要

In this series of papers, we present a motion planning framework for planningcomfortable and customizable motion of nonholonomic mobile robots such asintelligent wheelchairs and autonomous cars. In Part I, we presented themathematical foundation of our framework, where we model motion discomfort as aweighted cost functional and define comfortable motion planning as a nonlinearconstrained optimization problem of computing trajectories that minimize thisdiscomfort given the appropriate boundary conditions and constraints. In this paper, we discretize the infinite-dimensional optimization problemusing conforming finite elements. We describe shape functions to handledifferent kinds of boundary conditions and the choice of unknowns to obtain asparse Hessian matrix. We also describe in detail how any trajectorycomputation problem can have infinitely many locally optimal solutions and ourmethod of handling them. Additionally, since we have a nonlinear andconstrained problem, computation of high quality initial guesses is crucial forefficient solution. We show how to compute them.