The snakeboard is a well-studied example for mechanical systems analysis, largely because of its simultaneous richness in behavior and simplicity in design. However, few snakeboard models incorporate dissipative friction in the traveling direction and skidding as a violation of the rigid nonholonomic constraints. In this paper we investigate these effects on trajectory planning by evaluating a previously proposed friction model as well as a novel skidding model based on the addition of Rayleigh dissipation functions. We show how these additions change the usual behavior of gaits in the forward planning problem, and incorporate the changes into the solutions of the inverse planning problem by utilizing body coordinates along with a curvature parameterization for trajectories.

In this paper, we present a method of locomotion control for underwater vehicles that are propelled by a periodic deformation of the vehicle body, which is similar to the way a fish moves. We have developed control laws employing ldquoextremum seekingrdquo for two different ldquofishrdquo models. The first model consists of three rigid body links and relies on a 2-degree-of-freedom (DOF) movement that propels the fish without relying on vortices. The second fish model uses a Joukowski airfoil that has only 1 DOF in its movement and, thus, relies on vortex shedding for propulsion. We achieve model-free and position-free ldquosource seeking,rdquo and, if position is available, navigation along a predetermined path.

We describe basic considerations in the Lagrangian modeling of aquatic vehicles developing liftlike forces in a controlled way. We introduce the aquatic Flettner rotor as prototypical of this class of vehicles, and demonstrate the compatibility of Lagrangian formalism with experimental data describing a laboratory rotor. We analyze the controllability of a model for the rotor, connect its structure to that of models for Lagrangian systems subject to nonholonomic constraints, and present numerical evidence that our model can behave chaotically given physically motivated inputs and disturbances. We conclude with a description of a fishlike robotic vehicle employing a rotor in place of a caudal fin