I noticed one particular gear causing a lot of slipping, the large one driving the bogie. It misbehaved in two ways:
The large gear was pushed sideways by the force of the motor, pushing apart the frame and causing the top gear to slip.
The large gear exerted force on the bogie, pushing one wheel off the ground under force.
To solve these issues, I used a smaller gear and reinforced the frame. This helps keep all the gears together and all the wheels on the ground. The robot can now climb much bigger obstacles.
I have tried before to make a Rocker-Bogie robot, similar to NASA’s Mars rovers. But with the NXT I always had a shortage of structural parts, leading to incomplete and unstable constructions.
With the EV3 it works surprisingly well, and I was able to power all the wheels with two motors, and leave enough parts to make a robotic arm.
It looks lovely, and the principle works, but the actual capabilities are slightly disappointing as the torque is very limited. Climbing any large obstacles pushes the bogie off the ground and rattles some of the many gears.
In various web pages and projects across the web lives a mysterious file that does a FFT in C. There are several different versions modified by various people to do various things. I have no idea where it came form.
All I know is that this particular version by yours truly runs on Arduino and 8-bit AVR chips in general.
#include<avr/pgmspace.h>
#include<Arduino.h>/* fix_fft.c - Fixed-point in-place Fast Fourier Transform *//*
All data are fixed-point short integers, in which -32768
to +32768 represent -1.0 to +1.0 respectively. Integer
arithmetic is used for speed, instead of the more natural
floating-point.
For the forward FFT (time -> freq), fixed scaling is
performed to prevent arithmetic overflow, and to map a 0dB
sine/cosine wave (i.e. amplitude = 32767) to two -6dB freq
coefficients. The return value is always 0.
For the inverse FFT (freq -> time), fixed scaling cannot be
done, as two 0dB coefficients would sum to a peak amplitude
of 64K, overflowing the 32k range of the fixed-point integers.
Thus, the fix_fft() routine performs variable scaling, and
returns a value which is the number of bits LEFT by which
the output must be shifted to get the actual amplitude
(i.e. if fix_fft() returns 3, each value of fr[] and fi[]
must be multiplied by 8 (2**3) for proper scaling.
Clearly, this cannot be done within fixed-point short
integers. In practice, if the result is to be used as a
filter, the scale_shift can usually be ignored, as the
result will be approximately correctly normalized as is.
Written by: Tom Roberts 11/8/89
Made portable: Malcolm Slaney 12/15/94 malcolm@interval.com
Enhanced: Dimitrios P. Bouras 14 Jun 2006 dbouras@ieee.org
AVR: Pepijn de Vos 8 March 2015
*/#define N_WAVE 1024 /* full length of Sinewave[] */
#define LOG2_N_WAVE 10 /* log2(N_WAVE) *//*
Henceforth "short" implies 16-bit word. If this is not
the case in your architecture, please replace "short"
with a type definition which *is* a 16-bit word.
*//*
Since we only use 3/4 of N_WAVE, we define only
this many samples, in order to conserve data space.
*/constshortSinewave[N_WAVE-N_WAVE/4]PROGMEM={0,201,402,603,804,1005,1206,1406,1607,1808,2009,2209,2410,2610,2811,3011,3211,3411,3611,3811,4011,4210,4409,4608,4807,5006,5205,5403,5601,5799,5997,6195,6392,6589,6786,6982,7179,7375,7571,7766,7961,8156,8351,8545,8739,8932,9126,9319,9511,9703,9895,10087,10278,10469,10659,10849,11038,11227,11416,11604,11792,11980,12166,12353,12539,12724,12909,13094,13278,13462,13645,13827,14009,14191,14372,14552,14732,14911,15090,15268,15446,15623,15799,15975,16150,16325,16499,16672,16845,17017,17189,17360,17530,17699,17868,18036,18204,18371,18537,18702,18867,19031,19194,19357,19519,19680,19840,20000,20159,20317,20474,20631,20787,20942,21096,21249,21402,21554,21705,21855,22004,22153,22301,22448,22594,22739,22883,23027,23169,23311,23452,23592,23731,23869,24006,24143,24278,24413,24546,24679,24811,24942,25072,25201,25329,25456,25582,25707,25831,25954,26077,26198,26318,26437,26556,26673,26789,26905,27019,27132,27244,27355,27466,27575,27683,27790,27896,28001,28105,28208,28309,28410,28510,28608,28706,28802,28897,28992,29085,29177,29268,29358,29446,29534,29621,29706,29790,29873,29955,30036,30116,30195,30272,30349,30424,30498,30571,30643,30713,30783,30851,30918,30984,31049,31113,31175,31236,31297,31356,31413,31470,31525,31580,31633,31684,31735,31785,31833,31880,31926,31970,32014,32056,32097,32137,32176,32213,32249,32284,32318,32350,32382,32412,32441,32468,32495,32520,32544,32567,32588,32609,32628,32646,32662,32678,32692,32705,32717,32727,32736,32744,32751,32757,32761,32764,32766,32767,32766,32764,32761,32757,32751,32744,32736,32727,32717,32705,32692,32678,32662,32646,32628,32609,32588,32567,32544,32520,32495,32468,32441,32412,32382,32350,32318,32284,32249,32213,32176,32137,32097,32056,32014,31970,31926,31880,31833,31785,31735,31684,31633,31580,31525,31470,31413,31356,31297,31236,31175,31113,31049,30984,30918,30851,30783,30713,30643,30571,30498,30424,30349,30272,30195,30116,30036,29955,29873,29790,29706,29621,29534,29446,29358,29268,29177,29085,28992,28897,28802,28706,28608,28510,28410,28309,28208,28105,28001,27896,27790,27683,27575,27466,27355,27244,27132,27019,26905,26789,26673,26556,26437,26318,26198,26077,25954,25831,25707,25582,25456,25329,25201,25072,24942,24811,24679,24546,24413,24278,24143,24006,23869,23731,23592,23452,23311,23169,23027,22883,22739,22594,22448,22301,22153,22004,21855,21705,21554,21402,21249,21096,20942,20787,20631,20474,20317,20159,20000,19840,19680,19519,19357,19194,19031,18867,18702,18537,18371,18204,18036,17868,17699,17530,17360,17189,17017,16845,16672,16499,16325,16150,15975,15799,15623,15446,15268,15090,14911,14732,14552,14372,14191,14009,13827,13645,13462,13278,13094,12909,12724,12539,12353,12166,11980,11792,11604,11416,11227,11038,10849,10659,10469,10278,10087,9895,9703,9511,9319,9126,8932,8739,8545,8351,8156,7961,7766,7571,7375,7179,6982,6786,6589,6392,6195,5997,5799,5601,5403,5205,5006,4807,4608,4409,4210,4011,3811,3611,3411,3211,3011,2811,2610,2410,2209,2009,1808,1607,1406,1206,1005,804,603,402,201,0,-201,-402,-603,-804,-1005,-1206,-1406,-1607,-1808,-2009,-2209,-2410,-2610,-2811,-3011,-3211,-3411,-3611,-3811,-4011,-4210,-4409,-4608,-4807,-5006,-5205,-5403,-5601,-5799,-5997,-6195,-6392,-6589,-6786,-6982,-7179,-7375,-7571,-7766,-7961,-8156,-8351,-8545,-8739,-8932,-9126,-9319,-9511,-9703,-9895,-10087,-10278,-10469,-10659,-10849,-11038,-11227,-11416,-11604,-11792,-11980,-12166,-12353,-12539,-12724,-12909,-13094,-13278,-13462,-13645,-13827,-14009,-14191,-14372,-14552,-14732,-14911,-15090,-15268,-15446,-15623,-15799,-15975,-16150,-16325,-16499,-16672,-16845,-17017,-17189,-17360,-17530,-17699,-17868,-18036,-18204,-18371,-18537,-18702,-18867,-19031,-19194,-19357,-19519,-19680,-19840,-20000,-20159,-20317,-20474,-20631,-20787,-20942,-21096,-21249,-21402,-21554,-21705,-21855,-22004,-22153,-22301,-22448,-22594,-22739,-22883,-23027,-23169,-23311,-23452,-23592,-23731,-23869,-24006,-24143,-24278,-24413,-24546,-24679,-24811,-24942,-25072,-25201,-25329,-25456,-25582,-25707,-25831,-25954,-26077,-26198,-26318,-26437,-26556,-26673,-26789,-26905,-27019,-27132,-27244,-27355,-27466,-27575,-27683,-27790,-27896,-28001,-28105,-28208,-28309,-28410,-28510,-28608,-28706,-28802,-28897,-28992,-29085,-29177,-29268,-29358,-29446,-29534,-29621,-29706,-29790,-29873,-29955,-30036,-30116,-30195,-30272,-30349,-30424,-30498,-30571,-30643,-30713,-30783,-30851,-30918,-30984,-31049,-31113,-31175,-31236,-31297,-31356,-31413,-31470,-31525,-31580,-31633,-31684,-31735,-31785,-31833,-31880,-31926,-31970,-32014,-32056,-32097,-32137,-32176,-32213,-32249,-32284,-32318,-32350,-32382,-32412,-32441,-32468,-32495,-32520,-32544,-32567,-32588,-32609,-32628,-32646,-32662,-32678,-32692,-32705,-32717,-32727,-32736,-32744,-32751,-32757,-32761,-32764,-32766,};/*
fix_mpy() - fixed-point multiplication & scaling.
Substitute inline assembly for hardware-specific
optimization suited to a particluar DSP processor.
Scaling ensures that result remains 16-bit.
*/shortfix_mpy(shorta,shortb){/* shift right one less bit (i.e. 15-1) */longc=((long)a*(long)b)>>14;/* last bit shifted out = rounding-bit */b=c&0x01;/* last shift + rounding bit */a=(c>>1)+b;returna;}/*
fix_fft() - perform forward/inverse fast Fourier transform.
fr[n],fi[n] are real and imaginary arrays, both INPUT AND
RESULT (in-place FFT), with 0 <= n < 2**m; set inverse to
0 for forward transform (FFT), or 1 for iFFT.
*/intfix_fft(shortfr[],shortfi[],shortm,shortinverse){longmr,nn,i,j,l,k,istep,n,scale,shift;shortqr,qi,tr,ti,wr,wi;n=1<<m;/* max FFT size = N_WAVE */if(n>N_WAVE)return-1;mr=0;nn=n-1;scale=0;/* decimation in time - re-order data */for(m=1;m<=nn;++m){l=n;do{l>>=1;}while(mr+l>nn);mr=(mr&(l-1))+l;if(mr<=m)continue;tr=fr[m];fr[m]=fr[mr];fr[mr]=tr;ti=fi[m];fi[m]=fi[mr];fi[mr]=ti;}l=1;k=LOG2_N_WAVE-1;while(l<n){if(inverse){/* variable scaling, depending upon data */shift=0;for(i=0;i<n;++i){j=fr[i];if(j<0)j=-j;m=fi[i];if(m<0)m=-m;if(j>16383||m>16383){shift=1;break;}}if(shift)++scale;}else{/*
fixed scaling, for proper normalization --
there will be log2(n) passes, so this results
in an overall factor of 1/n, distributed to
maximize arithmetic accuracy.
*/shift=1;}/*
it may not be obvious, but the shift will be
performed on each data point exactly once,
during this pass.
*/istep=l<<1;for(m=0;m<l;++m){j=m<<k;/* 0 <= j < N_WAVE/2 */wr=pgm_read_dword(&(Sinewave[j+N_WAVE/4]));wi=-pgm_read_dword(&(Sinewave[j]));if(inverse)wi=-wi;if(shift){wr>>=1;wi>>=1;}for(i=m;i<n;i+=istep){j=i+l;tr=fix_mpy(wr,fr[j])-fix_mpy(wi,fi[j]);ti=fix_mpy(wr,fi[j])+fix_mpy(wi,fr[j]);qr=fr[i];qi=fi[i];if(shift){qr>>=1;qi>>=1;}fr[j]=qr-tr;fi[j]=qi-ti;fr[i]=qr+tr;fi[i]=qi+ti;}}--k;l=istep;}returnscale;}/*
fix_fftr() - forward/inverse FFT on array of real numbers.
Real FFT/iFFT using half-size complex FFT by distributing
even/odd samples into real/imaginary arrays respectively.
In order to save data space (i.e. to avoid two arrays, one
for real, one for imaginary samples), we proceed in the
following two steps: a) samples are rearranged in the real
array so that all even samples are in places 0-(N/2-1) and
all imaginary samples in places (N/2)-(N-1), and b) fix_fft
is called with fr and fi pointing to index 0 and index N/2
respectively in the original array. The above guarantees
that fix_fft "sees" consecutive real samples as alternating
real and imaginary samples in the complex array.
*/intfix_fftr(shortf[],longm,shortinverse){longi,N=1<<(m-1),scale=0;shorttt,*fr=f,*fi=&f[N];if(inverse)scale=fix_fft(fi,fr,m-1,inverse);for(i=1;i<N;i+=2){tt=f[N+i-1];f[N+i-1]=f[i];f[i]=tt;}if(!inverse)scale=fix_fft(fi,fr,m-1,inverse);returnscale;}
The licensing and versioning on this thing apparently works as follows: Add your name and date to the list of authors and post it in your corner of the web. That’s all.
