Multi-modal motion planning in non-expansive spaces

Kris Hauser, Jean Claude Latombe

Research output: Contribution to journalArticlepeer-review


Motion planning problems encountered in manipulation and legged locomotion have a distinctive multi-modal structure, where the space of feasible configurations consists of intersecting submanifolds, often of different dimensionalities. Such a feasible space does not possess expansiveness, a property that characterizes whether planning queries can be solved efficiently with traditional probabilistic roadmap (PRM) planners. In this paper we present a new PRM-based multi-modal planning algorithm for problems where the number of intersecting manifolds is finite. We also analyze the completeness properties of this algorithm. More specifically, we show that the algorithm converges quickly when each submanifold is individually expansive and establish a bound on the expected running time in that case. We also present an incremental variant of the algorithm that has the same convergence properties, but works better for problems with a large number of submanifolds by considering subsets of submanifolds likely to contain a solution path. These algorithms are demonstrated in geometric examples and in a legged locomotion planner.

Original languageEnglish (US)
Pages (from-to)897-915
Number of pages19
JournalInternational Journal of Robotics Research
Issue number7
StatePublished - Jun 2010
Externally publishedYes


  • Hybrid systems
  • Legged locomotion
  • Motion planning
  • Probablistic completeness

ASJC Scopus subject areas

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


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