An Exact Solver for Geometric Constraints with Inequalities

Nikhil Somani, Markus Rickert, Alois Knoll

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


CAD/CAM approaches have been used in the manufacturing industry for a long time, and their use in robotic systems is becoming more popular. One common element in these approaches is the use of geometric constraints to define relative object poses. Hence, approaches for solving these geometric constraints are critical to their performance. In this paper, we present an exact solver for geometric constraints. Our approach is based on mathematical models of constraints and geometric properties of constraint nullspaces. Our constraint solver supports nonlinear constraints with inequalities, and also mixed transformation manifolds, i.e., cases where the rotation and translation components of the constraints are not independent. Through several applications, we show how inequality constraints and mixed transformation manifolds increase the expressive power of constraint-based task definitions. The exact solver provides repeatable solutions with deterministic runtimes and our experiments show that it is also much faster than comparable iterative solvers.

Original languageEnglish
Article number7822919
Pages (from-to)1148-1155
Number of pages8
JournalIEEE Robotics and Automation Letters
Issue number2
StatePublished - Apr 2017


  • Control architectures and programming
  • optimization and optimal control
  • robust/adaptive control of robotic systems


Dive into the research topics of 'An Exact Solver for Geometric Constraints with Inequalities'. Together they form a unique fingerprint.

Cite this