Minimum control-switch motions for the snakeboard: A case study in kinematically controllable underactuated systems

Stefano Iannitti*, Kevin M. Lynch

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


We study the problem of computing an exact motion plan for the snakeboard, an underactuated system subject to nonholonomic constraints, by exploiting its kinematic controllability properties and its decoupling vector fields. Decoupling vector fields allow us to plan motions for the underactuated dynamic system as if it were kinematic, and rest-to-rest paths are the concatenation of integral curves of the decoupling vector fields. These paths can then be time-scaled according to actuator limits to yield fast trajectories. Switches between decoupling vector fields must occur at zero velocity, so, to find fast trajectories, we wish to find paths minimizing the number of switches. In this paper, we solve the minimum-switch path-planning problem for the snakeboard. We consider two problems: 1) finding motion plans achieving a desired position and orientation of the body of the snakeboard and 2) the full problem of motion planning for all five configuration variables of the snakeboard. The first problem is solvable in closed form by geometric considerations, while the second problem is solved by a numerical approach with guaranteed convergence. We present a complete characterization of the snakeboard's minimum-switch paths.

Original languageEnglish (US)
Pages (from-to)994-1006
Number of pages13
JournalIEEE Transactions on Robotics
Issue number6
StatePublished - Dec 2004


  • Decoupling vector field
  • Dynamic underactuated systems
  • Kinematic controllability
  • Kinematic reduction
  • Motion planning
  • Nonholonomic constraints
  • Snakeboard
  • Switch-optimal motions

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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