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City Beest

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Project Description

The CityBeest is a walking robot that consist of 377 3D printed parts. It has two independent crank shafts that are powered by geared DC motors. These are controlled by an Arduino. Ultrasound range sensors provide the robot with rudimentary obstacle detection capability.

The robot’s legs are based on the famous Theo Jansen linkage. Jansen’s 11 holy numbers were however not used as linkage parameters in the construction.

Instead, I decided to follow in Jansen’s footsteps.

A genetic algorithm was implemented, in as an attempt to search parameter space for other sets of viable numbers – numbers that would give rise to a viable gait for the same mechanical linkage. A mechanical simulation was used to calculate the trajectory of point “G” for a full rotation of the AB segment. Certain aspects of the shape described by the trajectory, such as “stride length”, “lift”, “linearity of ground stroke” were then calulated and used as input to the scoring function for the genetic algoritm.

The genetic algorithm evaluated approximately 12 billion parameter sets over the course of 10 days. Parameters for eleven of the discovered parameter sets  are listed in the table below.

Theo Jansen’s Holy Numbers

a b(CD) c(CH) d(CF) e(DF) f(FE) g(HE) h(EG) i(HG) j(BD) k(BH) l m(AB)
38 41,5 39,3 40,1 55,8 39,4 36,7 65,7 49 50 61,9 7,8 15

Visualization of the mechanical simulation used by the genetic algorithm, showing the Theo Jansen linkage, parametrized with set #11 (see the parameter table below).

Other “Holy Numbers” discovered by the genetic algorithm. (AC is Jansen’s a-l diagonal)

# CD CH CF DF FE HE EG HG BD BH AC AB
#1 98,20 141,85 121,95 205,30 198,21 177,96 208,04 243,82 121,46 244,44 155,25 41,19
#2 105,65 137,24 136,73 152,88 207,52 193,32 191,63 252,14 184,67 251,84 176,56 44,03
#3 137,97 127,07 175,22 169,76 201,50 166,52 233,41 179,55 194,50 238,89 162,49 45,54
#4 106,63 126,00 163,98 144,98 191,21 113,67 236,64 160,97 144,35 253,47 165,45 34,11
#5 152,19 180,78 150,44 175,17 194,29 122,51 185,10 203,64 206,66 254,17 111,53 25,59
#6 145,83 122,53 101,70 196,10 217,52 101,24 213,72 219,86 183,15 255,95 229,75 54,47
#7 141,72 156,33 94,95 170,45 155,37 84,62 200,61 161,12 167,11 243,68 148,88 53,01
#8 144,36 147,38 114,60 253,02 193,30 142,71 203,55 206,07 178,70 234,28 218,97 73,15
#9 140,24 102,10 196,13 131,76 221,74 152,14 247,01 176,00 212,53 223,31 170,67 45,16
#10 128,21 157,95 164,60 155,33 194,10 140,18 236,24 153,45 181,72 249,81 155,64 51,38
#11 158,58 190,15 159,66 174,83 197,86 137,28 251,18 180,12 206,22 248,52 131,11 56,04

City Beest infographics

Timeline

December 2014

Silly walks – del 2

By |December 30th, 2014|Categories: City Beest|

Etter å ha sneket meg til noen klokkesykluser på jobbmaskina i natt (dual Xeon med 12 kjerner), så har jeg faktisk noen resultater, hvorav ett er slående likt Jansens eget. Med 12 prosesser, så klarer [...]

Silly walks – del 1

By |December 29th, 2014|Categories: City Beest|

Evolusjon i praksis. En av mine store helter er Theo Jansen. Han har med sine Strandbeests visket ut grensene mellom kunst og ingeniørdisiplinene. Han konstruerer skapninger som kan bevege seg, lagre energi, reagere på omgivelsene, og [...]

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