Chetan Jhurani

Chetan Jhurani, Travis M. Austin, Michael A. Heroux et al.

The Trilinos Project is an effort to facilitate the design, development, integration and ongoing support of mathematical software libraries within an object-oriented framework. It is intended for large-scale, complex multiphysics engineering and scientific applications. Epetra is one of its basic packages. It provides serial and parallel linear algebra capabilities. Before Trilinos version 11.0, released in 2012, Epetra used the C++ int data-type for storing global and local indices for degrees of freedom (DOFs). Since int is typically 32-bit, this limited the largest problem size to be smaller than approximately two billion DOFs. This was true even if a distributed memory machine could handle larger problems. We have added optional support for C++ long long data-type, which is at least 64-bit wide, for global indices. To save memory, maintain the speed of memory-bound operations, and reduce further changes to the code, the local indices are still 32-bit. We document the changes required to achieve this feature and how the new functionality can be used. We also report on the lessons learned in modifying a mature and popular package from various perspectives -- design goals, backward compatibility, engineering decisions, C++ language features, effects on existing users and other packages, and build integration.

Shilpa Gulati, Chetan Jhurani, Benjamin Kuipers

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.

Shilpa Gulati, Chetan Jhurani, Benjamin Kuipers

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 this first one we present the mathematical foundation of our framework. The motion of a mobile robot that transports a human should be comfortable and customizable. We identify several properties that a trajectory must have for comfort. 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. The optimization problem is infinite-dimensional and we discretize it using conforming finite elements. We also outline a method by which different users may customize the motion to achieve personal comfort. There exists significant past work in kinodynamic motion planning, to the best of our knowledge, our work is the first comprehensive formulation of kinodynamic motion planning for a nonholonomic mobile robot as a nonlinear optimization problem that includes all of the following - a careful analysis of boundary conditions, continuity requirements on trajectory, dynamic constraints, obstacle avoidance constraints, and a robust numerical implementation. In this paper, we present the mathematical foundation of the motion planning framework and formulate the full nonlinear constrained optimization problem. We describe, in brief, the discretization method using finite elements and the process of computing initial guesses for the optimization problem. Details of the above two are presented in Part II of the series.