Patent ID: 7869910

Claim:
A system to control motion of flapping foils positioned for maneuvering of an underwater vehicle, said system comprising: a non-linear oscillator operationally connected to the flapping foils; and a controller operationally connected to said oscillator wherein said controller is capable of resolving the equation {umlaut over (x)}+f,(x){dot over (x)}+ω 2 x=0 f(x)=α 0 x 2 −2ζ 0 ω, α 0 ,ζ 0 >0 with ω representing a frequency of oscillations, f representing a non-linearity, {umlaut over (x)} representing a second derivative and ζ representing a damping parameter; wherein said controller is capable of producing a limit cycle with a magnitude, frequency and phase characteristics depending on the parameters θ=(α 0 ,ζ 0 ,ω) such that periodic signals are produced to exhibit convergent and divergent behavior for responsive motion control of the flapping foils for maneuvering.