Visual analytics for nonlinear programming in robot motion planning

David Hägele,Moataz Abdelaal,Daniel Weiskopf,Ozgur S. Oguz,Marc Toussaint

doi:10.1007/s12650-021-00786-8

David Hägele, Moataz Abdelaal + Show 3 more

Open Access

https://doi.org/10.1007/s12650-021-00786-8

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Abstract

Nonlinear programming is a complex methodology where a problem is mathematically expressed in terms of optimality while imposing constraints on feasibility. Such problems are formulated by humans and solved by optimization algorithms. We support domain experts in their challenging tasks of understanding and troubleshooting optimization runs of intricate and high-dimensional nonlinear programs through a visual analytics system. The system was designed for our collaborators’ robot motion planning problems, but is domain agnostic in most parts of the visualizations. It allows for an exploration of the iterative solving process of a nonlinear program through several linked views of the computational process. We give insights into this design study, demonstrate our system for selected real-world cases, and discuss the extension of visualization and visual analytics methods for nonlinear programming.Graphic abstract

Highlights

Nonlinear constraint optimization, known as nonlinear programming (NLP), deals with finding optima within constrained sets of variables
We propose a visual analytics approach for a postmortem analysis of optimization runs of robot motion planning problems that we developed in tight collaboration with domain experts
We focus on visualizing the highdimensional optimization landscape as seen by the optimizer, to be able to reason about its behavior, and on representing the evolution of the solution throughout the optimization in order to be able to interpret highdimensional loci as intermediate solutions to the motion planning problem

Summary

Introduction

Known as nonlinear programming (NLP), deals with finding optima within constrained sets of variables. 3.1 Robot motion planning Motion planning is the problem of finding a collision-free path to move an object from an initial state to a desired goal state (Latombe 2012). It is a crucial problem in many fields, including robotics, computational biology (drug design, protein folding), virtual prototyping, manufacturing, and computer graphics. We expect that our visual analytics approach will carry over to other applications

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