Lift-Off Dynamics in a Simple Jumping Robot

Jeffery AguilarAlex Lesov , Kurt Wiesenfeld , Daniel I. Goldman

光電四

吳卓宇

Experiment & model linear motor actuator

(Dunkermotoren ServoTube STA11)

1D mass spring system

Xa : Actuator position

A = Amplitude f = frequence

ψ = initial phase offset

Xp : video tracked position of the

thrust rod

Linear motor

(Dunkermotoren ServoTube STA11)

Equation of motion K = stiffness

C = damping

g = gravity

m = total mass of the actuator

ma = air-bearing mass

α = 1 , if Xp 0

0 , if Xp 0

(the piecewise constant)

White robot : airborne(when Xp > 0)

(a)A = 4 mm

ST = Stutter jump

S = Single jump

MJ = Multijump

(b)The model with the sameparameters

Optimal jump height

Solid — experimentalDashed — simulation

A = 0.19 mm (not lift off) 0.30 mm (lift off)

ϕ=3/2 , α=1 , c=1 , ma = m

P = Fext Vm

Fext : total external forceVm : center-of-mass robot velosity

vertical dotted line :

when the actuator stops

Light gray area : Xp>0 (aerial)

Dark gray area : mg/k < Xp 0

(negative forve)

White area : 0 mg/k

(positive force)

Conclusion Stutter jumps is achieves comparable jump height but uses less power

than single jumps.

&

A quick single jump that resembles a

squat jump is beneficial when a fast escape is essential,

while a slower stutter jump similar to a countermovement

can achieve comparable jump height

Thanks for listening.