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

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 this first one we present themathematical foundation of our framework. The motion of a mobile robot that transports a human should be comfortableand customizable. We identify several properties that a trajectory must havefor comfort. We model motion discomfort as a weighted cost functional anddefine comfortable motion planning as a nonlinear constrained optimizationproblem of computing trajectories that minimize this discomfort given theappropriate boundary conditions and constraints. The optimization problem isinfinite-dimensional and we discretize it using conforming finite elements. Wealso outline a method by which different users may customize the motion toachieve personal comfort. There exists significant past work in kinodynamic motion planning, to thebest of our knowledge, our work is the first comprehensive formulation ofkinodynamic motion planning for a nonholonomic mobile robot as a nonlinearoptimization problem that includes all of the following - a careful analysis ofboundary conditions, continuity requirements on trajectory, dynamicconstraints, obstacle avoidance constraints, and a robust numericalimplementation. In this paper, we present the mathematical foundation of the motion planningframework and formulate the full nonlinear constrained optimization problem. Wedescribe, in brief, the discretization method using finite elements and theprocess of computing initial guesses for the optimization problem. Details ofthe above two are presented in Part II of the series.