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

• Published in: IEEE transactions on robotics Vol. 20; no. 6; pp. 994 - 1006
• Main Authors: Iannitti, S., Lynch, K.M.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.12.2004; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Automata. Logic controller; Computer aided software engineering; Computer science; control theory; systems; Control systems; Control theory. Systems; Controllability; Decoupling; Decoupling vector field; dynamic underactuated systems; Dynamical systems; Dynamics; Exact sciences and technology; Geometry; kinematic controllability; kinematic reduction; Kinematics; Material handling, hoisting. Storage. Packaging; Mathematical analysis; Mathematical models; Mechanical systems; Motion analysis; Motion control; motion planning; nonholonomic constraints; Optimal control; Path planning; Robotics; Robots; snakeboard; switch-optimal motions; Switches; Trajectories; Transfert equipment, manipulators; industrial robots; Vectors (mathematics); Velocity; Wheels; Decoupling; Board; Kinematic theory; Holonomic system; Hybrid; Selector switch; Motion control
• ISSN: 1552-3098; 1941-0468
• DOI: 10.1109/TRO.2004.829455

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.