Chapter

Global Optimization

Volume 85 of the series Nonconvex Optimization and Its Applications pp 331-360

A Collaborative Solution Methodology for Inverse Position Problem

  • Chandra Sekhar PedamalluAffiliated withSchool of Mechanical and Production Engineering, Systems and Engineering Management Division, Nanyang Technological University
  • , Linet OzdamarAffiliated withSchool of Mechanical and Production Engineering, Systems and Engineering Management Division, Nanyang Technological University

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Abstract

In this study, a difficult advanced kinematics problem is presented and solved with a collaborative methodology that integrates an effective symbolic inference scheme and a local search method into a global interval partitioning algorithm. The resulting methodology proves to be very effective in discarding infeasible sub-spaces, because with some exceptions, the symbolic inference scheme guarantees to reduce infeasibility in each re-partitioning iteration. Thus, the local search method is called much less frequently as compared to a subdivision scheme without symbolic inference. Empirical results are obtained on two applications, the 6R inverse position and modified kinematics problems. The first test problem is quite difficult to solve as compared to the second one, however, our available commercial solvers were not able to solve any of them. The proposed collaborative methodology is generic and can handle any Constraint Satisfaction Problem where the goal might be to cover all solutions or identify a first feasible solution.

Key words

Inverse Kinematics Interval Analysis Symbolic-Interval cooperation Sequential Quadratic Programming