Collision-free trajectory planning for a 3-DoF robot with a passive joint

Kevin M. Lynch, Naoji Shiroma, Hirohiko Arai, Kazuo Tanie

Research output: Contribution to journalArticlepeer-review

83 Scopus citations


This paper studies motion planning from one zero-velocity state to another for a three-joint robot in a horizontal plane with a passive revolute third joint. Such a robot is small-time locally controllable on an open subset of its zero-velocity section, allowing it to follow any path in this subset arbitrarily closely. However, some paths are 'preferred' by the dynamics of the manipulator in that they can be followed at higher speeds. In this paper, the authors described a computationally efficient trajectory planner that finds fast, collision-free trajectories among obstacles. The planner decouples the problem of planning feasible trajectories in the robot's six-dimensional state space into the computationally simpler problems of planning paths in the three-dimensional configuration space and time scaling the paths according to the manipulator dynamics. This decoupling is made possible by the existence of velocity directions, fixed in the passive link frame, which can be executed at arbitrary speeds. Results of the planner have been implemented on an experimental underactuated manipulator. To the author's knowledge, it is the first implementation of a collision-free motion-planning algorithm for a manipulator subject to a second-order nonholonomic constraint.

Original languageEnglish (US)
Pages (from-to)1171-1184
Number of pages14
JournalInternational Journal of Robotics Research
Issue number12
StatePublished - Dec 2000

ASJC Scopus subject areas

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

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