TY - JOUR
T1 - Minimum control-switch motions for the snakeboard
T2 - A case study in kinematically controllable underactuated systems
AU - Iannitti, Stefano
AU - Lynch, Kevin M.
N1 - Funding Information:
Manuscript received March 10, 2003; revised November 11, 2003. This paper was recommended by Associate Editor A. Maciejewski and Editor I. Walker upon evaluation of the reviewers’ comments.The work of S. Iannitti was supported in part by the Antonio Ruberti grant funded by the Universitá di Roma “La Sapienza.” The work of K. M. Lynch was supported by the National Science Foundation under Grant IIS-9811571. This paper was presented in part at the IEEE/RSJ International Conference on Intelligent Robots and Systems, Las Vegas, NV, October 2003.
PY - 2004/12
Y1 - 2004/12
N2 - 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.
AB - 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.
KW - Decoupling vector field
KW - Dynamic underactuated systems
KW - Kinematic controllability
KW - Kinematic reduction
KW - Motion planning
KW - Nonholonomic constraints
KW - Snakeboard
KW - Switch-optimal motions
UR - http://www.scopus.com/inward/record.url?scp=10944262670&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=10944262670&partnerID=8YFLogxK
U2 - 10.1109/TRO.2004.829455
DO - 10.1109/TRO.2004.829455
M3 - Article
AN - SCOPUS:10944262670
SN - 1552-3098
VL - 20
SP - 994
EP - 1006
JO - IEEE Transactions on Robotics
JF - IEEE Transactions on Robotics
IS - 6
ER -