Semi-infinite programming for trajectory optimization with non-convex obstacles

Research output: Contribution to journalArticlepeer-review


This article 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 with optimizers that handle only convex polyhedra, and demonstrate efficient collision avoidance between non-convex CAD models and point clouds in a variety of pose and trajectory optimization settings.

Original languageEnglish (US)
Pages (from-to)1106-1122
Number of pages17
JournalInternational Journal of Robotics Research
Issue number10-11
StatePublished - Sep 2021


  • Optimization
  • collision avoidance
  • motion planning
  • numerical methods

ASJC Scopus subject areas

  • Software
  • Modeling and Simulation
  • Mechanical Engineering
  • Electrical and Electronic Engineering
  • Artificial Intelligence
  • Applied Mathematics


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