Semi-infinite Programming for Trajectory Optimization with Nonconvex Obstacles

Research output: Chapter in Book/Report/Conference proceedingChapter


This paper presents a novel optimization method that handles collision constraints with complex, non-convex 3D geometries. The optimization problem is cast as a semi-infinite program in which each collision constraint is implicitly treated as an infinite number of numeric constraints. The approach progressively generates some of these constraints for inclusion in a finite nonlinear program. Constraint generation uses an oracle to detect points of deepest penetration, and this oracle is implemented efficiently via signed distance field (SDF) versus point cloud collision detection. This approach is applied to pose optimization and trajectory optimization for both free-flying rigid bodies and articulated robots. Experiments demonstrate performance improvements compared to optimizers that handle only convex polyhedra, and demonstrate efficient collision avoidance between nonconvex CAD models and point clouds.

Original languageEnglish (US)
Title of host publicationSpringer Proceedings in Advanced Robotics
Number of pages16
StatePublished - 2020
Externally publishedYes

Publication series

NameSpringer Proceedings in Advanced Robotics
ISSN (Print)2511-1256
ISSN (Electronic)2511-1264


  • Collision avoidance
  • Optimization
  • Semi-infinite programming

ASJC Scopus subject areas

  • Mechanical Engineering
  • Artificial Intelligence
  • Engineering (miscellaneous)
  • Applied Mathematics
  • Electrical and Electronic Engineering
  • Control and Systems Engineering
  • Computer Science Applications


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