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get_plot.py
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get_plot.py
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#!/usr/bin/python
from tkinter import *
import math
import sys
import numpy
X=0
Y=1
Z=2
FL=0 # front left leg
FR=1 # front right leg
RL=2 # rear left leg
RR=3 # rear right leg
TIME_FACTOR=0.5
UPDATE_FREQ=100.0
#ORIGINS={FL:[-0.4,0.4,0],FR:[0.4,0.4,0],RL:[-0.4,-0.4,0],RR:[0.4,-0.4,0]}
#ANGLES={FL:3.0*math.pi/4.0,FR:math.pi/4.0,RL:5.0*math.pi/4.0,RR:7.0*math.pi/4.0}
#ANGLES_ORIG={FL:3.0*math.pi/4.0,FR:math.pi/4.0,RL:5.0*math.pi/4.0,RR:7.0*math.pi/4.0}
SPEED={'v1':80,'v2':40,'v3':20}
#MATRICES={}
#IMATRICES={}
LEGS={FL:{'origin':(-0.4,0.4,0), \
'angle':3.0*math.pi/4.0, \
'angle_orig':3.0*math.pi/4.0, \
'matrix': [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]], \
'imatrix':[[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]] }, \
FR:{'origin':(0.4,0.4,0), \
'angle':math.pi/4.0, \
'angle_orig':math.pi/4.0, \
'matrix': [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]], \
'imatrix':[[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]] }, \
RL:{'origin':(-0.4,-0.4,0), \
'angle':5.0*math.pi/4.0, \
'angle_orig': 5.0*math.pi/4.0, \
'matrix': [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]], \
'imatrix':[[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]] }, \
RR:{'origin':(0.4,-0.4,0), \
'angle':7.0*math.pi/4.0, \
'angle_orig':7.0*math.pi/4.0, \
'matrix': [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]], \
'imatrix':[[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]] } \
}
ROBOT={'LEGS':LEGS,'SPEED':SPEED}
for l in FL,FR,RL,RR:
LEGS[l]['v1sim']=550
LEGS[l]['v2sim']=550
LEGS[l]['v3sim']=550
LEGS_CANVAS={}
LEGS_SLIDER={FL:{},FR:{},RL:{},RR:{}}
def update_transformation_matrices_for(matrix,imatrix,angle,origin):
m = [ [math.cos(angle) , 0 , -math.sin(angle) , origin[X] ],
[math.sin(angle) , 0 , -math.cos(angle) , origin[Y] ],
[ 0 , 1 , 0 , origin[Z] ],
[ 0 , 0 , 0 , 1 ] ]
im = [ [math.cos(-angle) , -math.sin(-angle) , 0 , -origin[X] * math.cos(-angle) + origin[Y] * math.sin(-angle)],
[ 0 , 0 , 1 , -origin[Z] ],
[math.sin(angle) , -math.cos(angle) , 0 , origin[X] * math.sin(-angle) + origin[Y] * math.cos(-angle) ],
[ 0 , 0 , 0 , 1 ] ]
for l in range(len(matrix)):
for c in range(len(matrix[0])):
matrix[l][c]=m[l][c]
imatrix[l][c]=im[l][c]
# compute transformation matrices
def update_transformation_matrices(legs):
for l in FL,FR,RL,RR:
update_transformation_matrices_for(legs[l]['matrix'],legs[l]['imatrix'],legs[l]['angle'],legs[l]['origin'])
update_transformation_matrices(ROBOT['LEGS'])
def draw_points(canvas,points,lines,vectors,msg):
canvas_width = int(canvas['width'])
canvas_height = int(canvas['height'])
shift_x=canvas_width/2
shift_y=canvas_height/2
scale=CANVAS_SCALE
#print (points)
npoints={}
for k in points:
npoints[k]=(points[k][0]*scale+shift_x,-points[k][1]*scale+shift_y)
for k in npoints:
p=npoints[k]
#print p
canvas.create_oval(p[0],p[1],p[0]+5,p[1]+5,fill="#476042")
canvas.create_text(p[0]-50,p[1]-15,text=k+'\n(%.2f,%.2f)'%(points[k][0],points[k][1]))
#canvas.create_text(p[0]-10,p[1]-15,text=k)
for (a,b,c) in lines:
#print a,b,c
canvas.create_line(npoints[a][0],npoints[a][1],npoints[b][0],npoints[b][1],
fill=c,width=5)
#print vectors
for a in vectors:
canvas.create_line(npoints[a][0],npoints[a][1],npoints[a][0]+vectors[a][0]/10.0,npoints[a][1]-vectors[a][1]/10.0,
fill="magenta",width=5)
if msg!=None:
#canvas.create_text(200,200,text=msg,justify=LEFT)
pass
from math import sqrt
def norm2(v):
n=0
for x in v:
n+=x**2
return n
def norm(v):
return sqrt(norm2(v))
def normed(v):
n=norm(v)
assert(n!=0)
return tuple([a/n for a in v])
def dist(a,b):
return norm(((b[0]-a[0]),(b[1]-a[1])))
def p2v(a,b):
return tuple ([b[i] - a[i] for i in range(len(a))])
def plus(v1,v2):
return tuple ([ v1[i] + v2[i] for i in range(len(v1)) ])
def prod(v1,a):
return tuple([i*a for i in v1])
def one_line(centre, point , distance):
cp=p2v(centre,point)
d=normed(cp)
return plus(centre,prod(d,distance))
def scalaire(v1,v2):
n=0
for i in range(len(v1)):
n+=v1[i]*v2[i]
return n
def vectoriel(v1,v2):
return v1[0]*v2[1] - v1[1]*v2[0]
def vectoriel3D(v1,v2):
return (
v1[Y]*v2[Z] - v1[Z]*v2[Y],
v1[Z]*v2[X] - v1[X]*v2[Z],
v1[X]*v2[Y] - v1[Y]*v2[X]
)
def compute(xxx_todo_changeme, xxx_todo_changeme1,da,db):
(xa,ya) = xxx_todo_changeme
(xb,yb) = xxx_todo_changeme1
xa=float(xa)
ya=float(ya)
xb=float(xb)
yb=float(yb)
da=float(da)
db=float(db)
Dab = sqrt((xb-xa)**2 + (yb-ya)**2)
xp=(da**2-db**2 + Dab**2) / (2.0*Dab)
t=da**2-xp**2
if t<0:
return ()
if t==0:
yp1=0
yp2=0
else:
yp1=sqrt(t)
yp2=-yp1
i = normed( ((xb-xa), (yb-ya)) )
x1=xa + xp * i[0] - yp1*i[1]
y1=ya + xp * i[1] + yp1*i[0]
x2=xa + xp * i[0] - yp2*i[1]
y2=ya + xp * i[1] + yp2*i[0]
return ( (x1,y1) , (x2,y2) )
def middle(a,b):
return (a[0]+(b[0]-a[0])/2,a[1]+(b[1]-a[1])/2)
def get_gravity_center(points,weigths):
mw=[]
total_weigth=0
tweigths=[]
for p1 in range(len(points)):
np1=list(points.keys())[p1]
for p2 in range(p1+1,len(points)):
np2=list(points.keys())[p2]
if np1 in weigths and np2 in weigths[np1]:
tweigths.append((np1,np2,weigths[np1][np2]))
for a,b,w in tweigths:
m=middle(points[a],points[b])
mw.append((m,w))
total_weigth += w
g=[0,0]
for m,w in mw:
g[0]+=m[0]*w
g[1]+=m[1]*w
g[0]=g[0]/total_weigth
g[1]=g[1]/total_weigth
return (g,total_weigth)
#print compute( (1, 1) , (2 , 2) , 1 ,1)
def get_leg_points(V1,V2,AO,BC,AE,DE,EF,FG,FH,GI,BF,GJ):
#print 'get leg width V1: ',V1,' and V2: ',V2
points={'O':(0.0,0.0),'A':(-AO,0.0),'B':(0.10,0),'C':(BC+0.1,0.06),'Q':(-0.8,0),'R':(-0.8-0.79,-0.49)}
points['D'],p2= compute(points['A'],points['C'], AE-DE , V1)
points['E'] = one_line(points['A'], points['D'] , AE)
#print points['D']
#print points['E']
#print vectoriel(p2v(points['A'],points['D']) , p2v(points['A'],points['E']))
#print dist(points['A'],points['E'])
#print scalaire(p2v(points['A'],points['D']) , p2v(points['A'],points['E']))
points['F'],p2= compute(points['E'],points['B'], EF , BF)
points['H'] = one_line(points['B'], points['F'] , BF-FH)
points['G'] = one_line(points['E'], points['F'] , EF+FG)
points['I'],p2= compute(points['G'],points['H'], GI , V2)
points['J'] = one_line(points['G'], points['I'] , GJ)
return points
def get_leg_points_V1_V2(v1,v2):
return get_leg_points(v1,
v2,
int(ao.get())/1000.0,
int(bc.get())/1000.0,
int(ae.get())/1000.0,
int(de.get())/1000.0,
int(ef.get())/1000.0,
int(fg.get())/1000.0,
int(fh.get())/1000.0,
int(gi.get())/1000.0,
int(bf.get())/1000.0,
int(gj.get())/1000.0)
def compute_gravity_stengths_2points(points,gravity,a,b):
forces={}
forces['M'] = (0,-gravity[1]*9.81)
forces[b] = (0,gravity[1]*9.81 * (points['M'][0] - points[a][0]) / (points[b][0] - points[a][0]))
forces[a] = (0,gravity[1]*9.81 * (points[b][0] - points['M'][0]) / (points[b][0] - points[a][0]))
return forces
def compute_actuator_strengths_VE(points,weigths,Forces):
S2points={}
for p in ['R','Q','O','A','B','C','E','D','F','G','H']:
S2points[p]=points[p]
G2=get_gravity_center(S2points,weigths)
#print "Gravity for S2:",G2
S3points={}
for p in ['H','I']:
S3points[p]=points[p]
G3=get_gravity_center(S3points,weigths)
#G3=(G3[0],0.001)
#print "Gravity for S3:",G3
S4points={}
for p in ['G','I','J']:
S4points[p]=points[p]
G4=get_gravity_center(S4points,weigths)
#print "Gravity for S4:",G4
total_weight=G2[1]+G3[1]+G4[1]
#print "MX:",(G2[0][X]*G2[1] + G3[0][X]*G3[1] + G4[0][X]*G4[1]) / total_weight
#print "MY:",(G2[0][Y]*G2[1] + G3[0][Y]*G3[1] + G4[0][Y]*G4[1]) / total_weight
#print "W:",total_weight
#print "A :",points['R']
#print "B :",points['J']
#print "C :",points['H']
#print "D :",points['I']
#print "E :",points['G']
a12=G4[1]*9.81*(G4[0][X]-points['G'][X]) + (points['G'][X] - points['J'][X])*Forces['J'][Y]
a2 = points['I'][X]-points['H'][X]
a10 = points['I'][Y]-points['G'][Y]
a3 = points['H'][Y] - points['I'][Y]
a4 = G3[1]*9.81*(G3[0][X] - points['H'][X])
a5 = points['G'][X] - points['I'][X]
FD=[0,0]
FD[X] = (a12 * a2 - a5 * a4) / (a10 * a2 - a3 * a5 )
FD[Y] = (a12 * a3 - a10 * a4) / (a5 * a3 - a2 * a10)
#print "FD:",FD
FC1=[0,0]
FC1[X] = - FD[X]
FC1[Y] = G3[1]*9.81-FD[Y]
#print "FC1:",FC1
FC2=[0,0]
a=points['H'][Y] - points['G'][Y]
b=points['G'][X] - points['H'][X]
c=G2[1]*9.81*(G2[0][X] - points['G'][X]) + (points['G'][X]-points['R'][X]) * Forces['R'][Y]
ap=points['I'][Y] - points['H'][Y]
bp=points['H'][X] - points['I'][X]
cp=G3[1] * 9.81 * (G3[0][X] - points['I'][X])
FC2[X] = (cp * b - bp * c) / (ap*b-a*bp)
FC2[Y] = (cp*a-ap*c) / (bp*a-b*ap)
#print "FC2:",FC2
Forces['H'] = FC2
Forces['I'] = FD
Forces['G'] = [0,0]
Forces['G'][X] = Forces['I'][X] - Forces['J'][X]
Forces['G'][Y] = G4[0][1]*9.81 + Forces['I'][Y] - Forces['J'][Y]
def compute_actuator_strengths_VM(points,weigths,forces):
S21points={}
for p in ['E','F','G']:
S21points[p]=points[p]
G21=get_gravity_center(S21points,weigths)
#print "Gravity for S21:",G21
S22points={}
for p in ['A','D','E']:
S22points[p]=points[p]
G22=get_gravity_center(S22points,weigths)
#print "Gravity for S22:",G22
S23points={}
for p in ['R','A','B','C','O','Q']:
S23points[p]=points[p]
G23=get_gravity_center(S23points,weigths)
#print "Gravity for S23:",G23
S24points={}
for p in ['D','C']:
S24points[p]=points[p]
G24=get_gravity_center(S24points,weigths)
#print "Gravity for S24:",G24
S25points={}
for p in ['B','H','F']:
S25points[p]=points[p]
G25=get_gravity_center(S25points,weigths)
#print "Gravity for S25:",G25
S3points={}
for p in ['H','I']:
S3points[p]=points[p]
G3=get_gravity_center(S3points,weigths)
#G3=(G3[0],0.001)
#print "Gravity for S3:",G3
S4points={}
for p in ['G','I','J']:
S4points[p]=points[p]
G4=get_gravity_center(S4points,weigths)
#print "Gravity for S4:",G4
total_weight=G21[1]+G22[1]+G23[1]+G24[1]+G25[1]+G3[1]+G4[1]
#print "MX:",(G21[0][X]*G21[1] +G22[0][X]*G22[1] + G23[0][X]*G23[1] + G24[0][X]*G24[1] + G25[0][X]*G25[1] + G3[0][X]*G3[1] + G4[0][X]*G4[1]) / total_weight
#print "MY:",(G21[0][Y]*G21[1] +G22[0][Y]*G22[1] + G23[0][Y]*G23[1] + G24[0][Y]*G24[1] + G25[0][Y]*G25[1] + G3[0][Y]*G3[1] + G4[0][Y]*G4[1]) / total_weight
#print "W:",total_weight
a1 = G21[1]*9.81*(G21[0][X] - points['F'][X]) + (points['G'][X] - points['F'][X])*forces['G'][Y] + (points['F'][Y] - points['G'][Y]) * forces['G'][X] \
+(points['F'][X] - points['E'][X])*(G25[1]*9.81+G21[1]*9.81+forces['G'][Y] + forces['H'][Y]) \
+(points['E'][Y] - points['F'][Y])*(forces['H'][X] - forces['G'][X])
a2 = points['E'][Y] - points['F'][Y]
a3 = points['F'][X] - points['E'][X]
a4 = points['B'][X] - points['F'][X]
a5 = points['F'][Y] - points['B'][Y]
a6 = G25[1] * 9.81 * (G25[0][X] - points['F'][X]) + (points['H'][X] - points['F'][X]) * forces['H'][Y] + (points['F'][Y] - points['H'][Y])*forces['H'][X]
FB=[0,0]
FB[X] = (a6 * a3 - a4*a1) / (a3*a5 - a2*a4)
FB[Y] = -(a2*a6-a1*a5)/(a3*a5-a2*a4)
forces['B']=FB
FE=[0,0]
FE[X] = forces['H'][X] + forces['G'][X] - forces['B'][X]
FE[Y] = G25[1]*9.81 + G21[1]*9.81 + forces['G'][Y] + forces['H'][Y] - forces['B'][Y]
forces['E']=FE
b1 = G24[1]*9.81*(G24[0][X] - points['C'][X])
b2 = points['D'][Y] - points['C'][Y]
b3 = points['C'][X] - points['D'][X]
b4 = points['A'][X] - points['C'][X]
b5 = points['C'][Y] - points['A'][Y]
b6 = G23[1] * 9.81 * (G23[0][X] - points['A'][X]) + (points['A'][X] - points['R'][X]) * forces['R'][Y] - (points['A'][X] - points['B'][X])*forces['B'][Y] - (points['B'][Y] - points['A'][Y])*forces['B'][X]
FC=[0,0]
FC[X] = (b6 * b3 - b4*b1) / (b3*b5 - b2*b4)
FC[Y] = -(b2*b6-b1*b5)/(b3*b5-b2*b4)
forces['C']=FC
FD=[0,0]
FD[X] = - forces['C'][X]
FD[Y] = G24[1]*9.81 - forces['C'][Y]
forces['D']=FD
FA=[0,0]
FA[X] = forces['E'][X] + forces['D'][X]
FA[Y] = G22[1] * 9.81 + forces['E'][Y] + forces['D'][Y]
forces['A'] = FA
FF=[0,0]
FF[X] = forces['G'][X] - forces['E'][X]
FF[Y] = G21[1] * 9.81 + forces['G'][Y] - forces['E'][Y]
forces['F']=FF
def compute_forces_and_stress(points,weights,forces,stress):
gravity=get_gravity_center(points,weigths)
points['M'],weigth=gravity
f=compute_gravity_stengths_2points(points,gravity,'R','J')
for i in f:
forces[i]=f[i]
compute_actuator_strengths_VE(points,weigths,forces)
compute_actuator_strengths_VM(points,weigths,forces)
sup=normed(p2v(points['C'],points['D']))
stress['C']=math.fabs(scalaire(sup,forces['C']))
stress['D']=math.fabs(scalaire(sup,forces['D']))
sup=normed(p2v(points['H'],points['I']))
stress['I']=math.fabs(scalaire(sup,forces['I']))
stress['H']=math.fabs(scalaire(sup,forces['H']))
#points=get_leg_points(V1,V2)
lines=[('A','B','black'),('A','E','black'),('B','C','black'),('B','F','black'),('E','G','black'),
('G','J','black'),('D','C','red'),('H','I','red'),('J1','J2','blue'),('J2','J4','blue'),
('J4','J3','blue'),('J3','J1','blue'),('R','Q','black'),('Q','O','black')]
#weigths=[('A','B',2.0),('A','C',1.6),('A','E',3.6),('E','G',4.0),('B','F',3.45),('G','J',3.65),('D','C',5.3),('H','I',5.3),('R','Q',32),('O','Q',1)]
weigths={}
for p in 'ABCDEFGHIJO':
weigths[p]={}
weigths['Q']={}
weigths['R']={}
weigths['A']['B']=2.0
weigths['A']['C']=1.6
weigths['A']['E']=3.6
weigths['E']['G']=4.0
weigths['B']['F']=3.45
weigths['G']['J']=3.65
weigths['D']['C']=5.3
weigths['H']['I']=5.3
weigths['R']['Q']=32
weigths['O']['Q']=80
tweigths={}
for a in weigths:
for b in weigths[a]:
weigths[b][a]=weigths[a][b]
def update_robot(robot=None):
if robot==None:
irobot=ROBOT
ilegs=ROBOT['LEGS']
else:
irobot=robot
ilegs=robot['LEGS']
irobot['feets']={}
irobot['centers']={}
for leg in FL,FR,RL,RR:
if 'points' not in ilegs[leg]:
continue
feet=ilegs[leg]['points']['J']
feet=(feet[0],feet[1],0,1)
rfeet=numpy.matmul(ilegs[leg]['matrix'],feet).tolist()
irobot['feets'][leg]=rfeet[:3]
center=ilegs[leg]['points']['O']
center=(center[0],center[1],0,1)
rcenter=numpy.matmul(ilegs[leg]['matrix'],center).tolist()
irobot['centers'][leg] = rcenter[:3]
# compute gravity center of the robot
irobot['gravities']={}
for leg in FL,FR,RL,RR:
if 'gravity' not in ilegs[leg]:
return
lg=ilegs[leg]['gravity'][0]
lg=(lg[0],lg[1],0,1)
rlg=numpy.matmul(ilegs[leg]['matrix'],lg).tolist()
irobot['gravities'][leg]=(rlg[:3],ilegs[leg]['gravity'][1])
robot_gravity=[0,0,0]
total_weight=0
for leg in FL,FR,RL,RR:
g=irobot['gravities'][leg]
robot_gravity[X]+=g[0][X]*g[1]
robot_gravity[Y]+=g[0][Y]*g[1]
robot_gravity[Z]+=g[0][Z]*g[1]
total_weight+=g[1]
robot_gravity[X]/=total_weight
robot_gravity[Y]/=total_weight
robot_gravity[Z]/=total_weight
irobot['gravity']=(robot_gravity,total_weight)
irobot['projections']={}
irobot['projections']['FL_FR_RL']=get_point_projection_on_plane(irobot['feets'][FL],irobot['feets'][FR],irobot['feets'][RL],irobot['gravity'][0])
irobot['projections']['FR_RL_RR']=get_point_projection_on_plane(irobot['feets'][FR],irobot['feets'][RL],irobot['feets'][RR],irobot['gravity'][0])
irobot['projections']['RL_RR_FL']=get_point_projection_on_plane(irobot['feets'][RL],irobot['feets'][RR],irobot['feets'][FL],irobot['gravity'][0])
irobot['projections']['RR_FL_FR']=get_point_projection_on_plane(irobot['feets'][RR],irobot['feets'][FL],irobot['feets'][FR],irobot['gravity'][0])
def update_projections():
canvas_width = int(projections[FL]['width'])
canvas_height = int(projections[FL]['height'])
shift_x=canvas_width/2
shift_y=canvas_height/2
for i in projections:
projections[i].delete("all")
for triangle in [ ((FL,FR,RL) , 'FL_FR_RL') , ((FR,RL,RR),'FR_RL_RR'), ((RL,RR,FL),'RL_RR_FL'),((RR,FL,FR),'RR_FL_FR') ]:
points=[]
for l in triangle[0]:
px=ROBOT['feets'][l][X] * CANVAS_SCALE/2.0 + shift_x
py=ROBOT['feets'][l][Y] * CANVAS_SCALE/2.0 + shift_y
points.append((px,py))
for i in range(3):
projections[triangle[0][0]].create_line(points[i][X],points[i][Y],points[(i+1)%3][X],points[(i+1)%3][Y],fill="black",width=4)
px=ROBOT['projections'][triangle[1]][0][X]* CANVAS_SCALE/2.0 + shift_x
py=ROBOT['projections'][triangle[1]][0][Y]* CANVAS_SCALE/2.0 + shift_y
if ROBOT['projections'][triangle[1]][1]:
projections[triangle[0][0]].create_oval(px-2,py-2,px+2,py+2,fill="red")
else:
projections[triangle[0][0]].create_oval(px-2,py-2,px+2,py+2,fill="blue")
projections[triangle[0][0]].create_text(px-2,py-10,text="%.2f"%ROBOT['projections'][triangle[1]][2])
#for l in FL,FR,RL:
# c
#top_view.create_oval(px-1,py-1,px+1,py+1,fill="#FFFFFF")
def update_top_view():
global top_view
top_view.delete("all")
canvas_width = int(top_view['width'])
canvas_height = int(top_view['height'])
shift_x=canvas_width/2
shift_y=canvas_height/2
top_view.create_oval(shift_x,shift_y,shift_x+5,shift_y+5,fill="#476042")
feets={}
update_robot()
for leg in FL,FR,RL,RR:
if (leg in ROBOT['feets'])==False:
return
px=ROBOT['feets'][leg][X] * CANVAS_SCALE + shift_x
py=ROBOT['feets'][leg][Y] * CANVAS_SCALE + shift_y
top_view.create_oval(px-5,py-5,px+5,py+5,fill="#FF0000")
px=ROBOT['centers'][leg][X] * CANVAS_SCALE + shift_x
py=ROBOT['centers'][leg][Y] * CANVAS_SCALE + shift_y
top_view.create_oval(px-5,py-5,px+5,py+5,fill="#00FF00")
# compute gravity center of the robot
px=ROBOT['gravity'][0][X] * CANVAS_SCALE + shift_x
py=ROBOT['gravity'][0][Y] * CANVAS_SCALE + shift_y
top_view.create_oval(px-5,py-5,px+5,py+5,fill="#FF00FF")
#h=get_point_projection_on_plane(ROBOT['feets'][FL],ROBOT['feets'][FR],ROBOT['feets'][RL],ROBOT['gravity'][0])
#px=h[X] * CANVAS_SCALE + shift_x
#py=h[Y] * CANVAS_SCALE + shift_y
#top_view.create_oval(px-1,py-1,px+1,py+1,fill="#FFFFFF")
update_projections()
def update_angle_kin(x,leg,robot=ROBOT):
robot['LEGS'][leg]['angle']=robot['LEGS'][leg]['angle_orig'] + ((robot['LEGS'][leg]['v3sim'] - 0.45 ) / (0.650-0.45) - 0.5 ) * math.pi /3
def update_angle(x,leg,robot=ROBOT):
robot['LEGS'][leg]['angle']=robot['LEGS'][leg]['angle_orig'] + ((robot['LEGS'][leg]['v3sim'] - 450.0 ) / (650.0-450.0) - 0.5 ) * math.pi /3
#ANGLES[leg]=ANGLES_ORIG[leg] + ((LEGS[leg]['v3sim'] - 450.0 ) / (650.0-450.0) - 0.5 ) * math.pi /3
update_transformation_matrices(robot['LEGS'])
update_top_view()
def distance_point_to_line(p1,p2,p):
return math.fabs((p2[Y] - p1[Y]) * p[X] - (p2[X] - p1[X])* p[Y] + p2[X]*p1[Y] - p2[Y]*p1[X]) / math.sqrt((p2[Y]-p1[Y])**2 + (p2[X] - p1[X])**2)
def get_point_projection_on_plane(p1,p2,p3,m):
#print p1,p2,p3,m
normale=normed(
vectoriel3D(
p2v(p1,p2),
p2v(p1,p3)
)
)
p=plus(
m,
prod(
normale,
-scalaire(p2v(p1,m),normale)
)
)
# check if it is in triangle
w1 = ( p1[X]*(p3[Y]-p1[Y]) + (p[Y] - p1[Y])*(p3[X]-p1[X])-p[X]*(p3[Y]-p1[Y])) \
/ \
( (p2[Y] - p1[Y])*(p3[X]-p1[X]) - (p2[X]-p1[X])*(p3[Y]-p1[Y]) )
w2 = ( p[Y] - p1[Y] - w1*(p2[Y]-p1[Y]) ) / (p3[Y]-p1[Y])
d1 = distance_point_to_line(p1,p2,p)
d2 = distance_point_to_line(p1,p3,p)
d3 = distance_point_to_line(p2,p3,p)
return p , w1 >=0 and w2 >=0 and w1+w2<=1.0 , min(d1,d2,d3)
def update(x,leg):
global lines,ao,ae,ef
data=ROBOT['LEGS'][leg]
v1=data['v1sim']
v2=data['v2sim']
#print "update:",v1,v2
canvas=LEGS_CANVAS[leg]
canvas.delete("all")
msg=""
Cmax=0
Dmax=0
Imax=0
Hmax=0
points=get_leg_points_V1_V2(v1/1000.0,
v2/1000.0)
lpoints=dict(points)
del lpoints['R']
del lpoints['Q']
data['gravity']=get_gravity_center(lpoints,weigths)
tpoints=get_leg_points_V1_V2(450.0/1000.0,
450.0/1000.0)
forces={}
stress={}
compute_forces_and_stress(tpoints,weigths,forces,stress)
msg+="450 450: \n"
msg+="\tCD en C: %.2fN\n"%stress['C']
msg+="\tCD en D: %.2fN\n"%stress['D']
msg+="\tHI en I: %.2fN\n"%stress['I']
msg+="\tHI en H: %.2fN\n"%stress['H']
Cmax=max(Cmax,stress['C'])
Dmax=max(Dmax,stress['D'])
Imax=max(Imax,stress['I'])
Hmax=max(Hmax,stress['H'])
points['J1']=tpoints['J']
tpoints=get_leg_points_V1_V2(650.0/1000.0,
450.0/1000.0)
forces={}
stress={}
compute_forces_and_stress(tpoints,weigths,forces,stress)
msg+="650 450: \n"
msg+="\tCD en C: %.2fN\n"%stress['C']
msg+="\tCD en D: %.2fN\n"%stress['D']
msg+="\tHI en I: %.2fN\n"%stress['I']
msg+="\tHI en H: %.2fN\n"%stress['H']
Cmax=max(Cmax,stress['C'])
Dmax=max(Dmax,stress['D'])
Imax=max(Imax,stress['I'])
Hmax=max(Hmax,stress['H'])
points['J2']=tpoints['J']
tpoints=get_leg_points_V1_V2(450.0/1000.0,
650.0/1000.0)
forces={}
stress={}
compute_forces_and_stress(tpoints,weigths,forces,stress)
msg+="450 650: \n"
msg+="\tCD en C: %.2fN\n"%stress['C']
msg+="\tCD en D: %.2fN\n"%stress['D']
msg+="\tHI en I: %.2fN\n"%stress['I']
msg+="\tHI en H: %.2fN\n"%stress['H']
Cmax=max(Cmax,stress['C'])
Dmax=max(Dmax,stress['D'])
Imax=max(Imax,stress['I'])
Hmax=max(Hmax,stress['H'])
points['J3']=tpoints['J']
tpoints=get_leg_points_V1_V2(650.0/1000.0,
650.0/1000.0)
forces={}
stress={}
compute_forces_and_stress(tpoints,weigths,forces,stress)
msg+="650 650: \n"
msg+="\tCD en C: %.2fN\n"%stress['C']
msg+="\tCD en D: %.2fN\n"%stress['D']
msg+="\tHI en I: %.2fN\n"%stress['I']
msg+="\tHI en H: %.2fN\n"%stress['H']
Cmax=max(Cmax,stress['C'])
Dmax=max(Dmax,stress['D'])
Imax=max(Imax,stress['I'])
Hmax=max(Hmax,stress['H'])
points['J4']=tpoints['J']
forces={}
stress={}
compute_forces_and_stress(points,weigths,forces,stress)
msg+="CD en C: %.2fN (%.2f)\n"%(stress['C'],Cmax)
msg+="CD en D: %.2fN (%.2f)\n"%(stress['D'],Dmax)
msg+="HI en I: %.2fN (%.2f)\n"%(stress['I'],Imax)
msg+="HI en H: %.2fN (%.2f)\n"%(stress['H'],Hmax)
data['points']=points
data['forces']=forces
data['stress']=stress
draw_points(canvas,points,lines,forces,msg)
update_top_view()
def update_all(x):
update(x,FL)
update(x,FR)
update(x,RL)
update(x,RR)
from scipy.optimize import minimize
def inverse_kinetic_fun(v,dx,dy):
for k in v:
if k<0.449 or k>0.651:
print("!!!!! out of bounds",k)
return None
p=get_leg_points_V1_V2(v[0],v[1])
return norm(p2v(p['J'],(dx,dy)))
def inverse_kinetic(x,y):
res=minimize(inverse_kinetic_fun,(0.55,0.55),args=(x,y),\
#method='Nelder-Mead',\
bounds=((0.45,0.65),(0.45,0.65)),
tol=1e-6)
p=get_leg_points_V1_V2(res.x[0],res.x[1])
return (res.x[0],res.x[1],p,norm(p2v(p['J'],(x,y))))
import copy
def kinetic_for_gravity_center_fix_feet(center,triangle,legs):
# move center without moving feets from legs
robot=copy.deepcopy(ROBOT)
nv={}
for l in legs:
nv[l]={}
feet=robot['feets'][l]
nfeet=list(feet)
for v in range(len(center)):
nfeet[v]-=center[v]
# print "****"
# print "center ",center
# print "feet ",feet,"nfeet ",nfeet,"origin ",robot['LEGS'][l]['origin']
# print "angle ",robot['LEGS'][l]['angle']
# compute angle delta:
#t1=math.atan2(robot['LEGS'][l]['origin'][Y] - feet[Y],robot['LEGS'][l]['origin'][X] - feet[X])
t2=math.atan2(nfeet[Y]-robot['LEGS'][l]['origin'][Y] , nfeet[X] - robot['LEGS'][l]['origin'][X])
if t2<0:
t2+=math.pi*2.0
# print "t2:",t2
delta=t2-robot['LEGS'][l]['angle_orig']
if math.fabs(delta) > math.pi/3:
# is not possible for v3
delta = math.copysign(math.pi/3,delta)
robot['LEGS'][l]['angle'] = t2
# print "v3sim was ",robot['LEGS'][l]['v3sim']
robot['LEGS'][l]['v3sim'] = ((delta*3/math.pi + 0.5) * (0.65-0.45) + 0.45)*1000.0
# print "v3sim is ",delta,robot['LEGS'][l]['v3sim']
update_transformation_matrices(robot['LEGS'])
# print "point J in leg base was ",robot['LEGS'][l]['points']['J']
# print "J in robot base was ",numpy.matmul(robot['LEGS'][l]['matrix'],robot['LEGS'][l]['points']['J']+(0,1)).tolist()
# print "J in robot base was ",robot['feets'][l]
# print "point J in leg base using reverse matrix",numpy.matmul(robot['LEGS'][l]['imatrix'],robot['feets'][l]+[1]).tolist()[:3]
# print robot['LEGS'][l]['imatrix']
lfeet=numpy.matmul(robot['LEGS'][l]['imatrix'],nfeet+[1]).tolist()
# print "point J was ",robot['LEGS'][l]['points']['J']
# print "lfeet is ",lfeet[:3]
rev=inverse_kinetic(lfeet[X],lfeet[Y])
malus=0.0
if rev[3]>0.01:
print("OVER MOVE!")
malus=10.0
robot['LEGS'][l]['v1sim'] = rev[0]*1000.0
robot['LEGS'][l]['v2sim'] = rev[1]*1000.0
nv[l]['v1sim']=robot['LEGS'][l]['v1sim']
nv[l]['v2sim']=robot['LEGS'][l]['v2sim']
nv[l]['v3sim']=robot['LEGS'][l]['v3sim']
update_angle_kin(None,l,robot)
update_transformation_matrices(robot['LEGS'])
update_robot(robot)
if robot['projections'][triangle][1]:
#print v, -robot['projections'][triangle][2]
return -robot['projections'][triangle][2]+malus,nv
return robot['projections'][triangle][2]+malus,nv
def kinetic_for_gravity_center_fix_feet_fun(center,triangle,legs):
res=kinetic_for_gravity_center_fix_feet(center,triangle,legs)
return res[0]
# following is wrong and must be removed!
def kinetic_for_gravity_center(v,triangle,direction,legs):
#print v,triangle,direction,legs
for k in v:
if k<0.449 or k>0.651:
return 1000.0
robot=copy.deepcopy(ROBOT)
i=0
for l in legs:
robot['LEGS'][l]['v1sim']=v[i]
i+=1
robot['LEGS'][l]['v2sim']=v[i]
i+=1
robot['LEGS'][l]['v3sim']=v[i]
i+=1
for l in legs:
#print robot['LEGS'][l]['v1sim']
#print robot['LEGS'][l]['v2sim']
robot['LEGS'][l]['points']=get_leg_points_V1_V2(robot['LEGS'][l]['v1sim'],\
robot['LEGS'][l]['v2sim'])
robot['LEGS'][l]['gravity']=get_gravity_center(robot['LEGS'][l]['points'],weigths)
update_angle_kin(None,l,robot)
update_transformation_matrices(robot['LEGS'])
update_robot(robot)
#print "direction:",direction,"gravity projection:",robot['projections'][triangle]
#n=norm(p2v(robot['feets'][direction],robot['projections'][triangle][0]))
#if robot['projections'][triangle][1] and robot['projections'][triangle][2]>0.01:
# return n
#print "distance:",n
#return n*2
#print v, triangle, robot['projections'][triangle]
if robot['projections'][triangle][1]:
#print v, -robot['projections'][triangle][2]
return -robot['projections'][triangle][2]
return robot['projections'][triangle][2]
def onclick(event,leg):
v1 = LEGS_SLIDER[leg]['v1']
v2 = LEGS_SLIDER[leg]['v2']
canvas = LEGS_CANVAS[leg]
cx=float(event.x)
cy=float(event.y)
x=(cx-float(canvas['width'])/2.0) / CANVAS_SCALE
y=-(cy-float(canvas['height'])/2.0) / CANVAS_SCALE
res=inverse_kinetic(x,y)
v1.set(int(res[0]*1000))
v2.set(int(res[1]*1000))
# balance body on other three legs:
if leg==FL:
triangle='FR_RL_RR'
direction=FR
legs=(FR,RL,RR)
elif leg==FR:
triangle='RL_RR_FL'
direction=FL
legs=(RL,RR,FL)
elif leg==RL:
triangle='RR_FL_FR'
direction=FR
legs=(RR,FL,FR)
else:
triangle='FL_FR_RL'
direction=FL
legs=(FL,FR,RL)
initial_values=[0.0,0.0,0]
bounds=((-0.1,0.1),(-0.1,0.1),(-0.1,0.1))
res=minimize(kinetic_for_gravity_center_fix_feet_fun,initial_values,args=(triangle,legs),\
#method='Nelder-Mead',\
bounds=bounds,
tol=1e-6)
nv=kinetic_for_gravity_center_fix_feet(res.x,triangle,legs)
# nv=kinetic_for_gravity_center_fix_feet([0.0,0,0],triangle,legs)
print(res)
print(nv)
for l in legs:
LEGS_SLIDER[l]['v1'].set(int(round(nv[1][l]['v1sim'])))
LEGS_SLIDER[l]['v2'].set(int(round(nv[1][l]['v2sim'])))
LEGS_SLIDER[l]['v3'].set(int(round(nv[1][l]['v3sim'])))
# initial_values=[]
# bounds=[]
# for l in legs:
# initial_values.append(float(LEGS_SLIDER[l]['v1'].get())/1000.0)
# bounds.append((0.45,0.65))
# initial_values.append(float(LEGS_SLIDER[l]['v2'].get())/1000.0)
# bounds.append((0.45,0.65))
# initial_values.append(float(LEGS_SLIDER[l]['v3'].get())/1000.0)
# bounds.append((0.45,0.65))
# res=minimize(kinetic_for_gravity_center,initial_values,args=(triangle,direction,legs),\
# #method='Nelder-Mead',\
# bounds=bounds,
# tol=1e-9)
# i=0
# for l in legs:
# LEGS_SLIDER[l]['v1'].set(int(res.x[i]*1000.0))
# i+=1
# LEGS_SLIDER[l]['v2'].set(int(res.x[i]*1000.0))
# i+=1
# LEGS_SLIDER[l]['v3'].set(int(res.x[i]*1000.0))
# i+=1
# print res
def move_gravity_center(event):
global top_view
cx=float(event.x)
cy=float(event.y)
x=(cx-float(top_view['width'])/2.0) / CANVAS_SCALE
y=-(cy-float(top_view['height'])/2.0) / CANVAS_SCALE
print("move robot center to:",x,y)
res=kinetic_for_gravity_center_fix_feet((x,y),'FL_FR_RL',(FL,FR,RL,RR))
for l in (FL,FR,RL,RR):
LEGS_SLIDER[l]['v1'].set(int(res[1][l]['v1sim']))
LEGS_SLIDER[l]['v2'].set(int(res[1][l]['v2sim']))
LEGS_SLIDER[l]['v3'].set(int(res[1][l]['v3sim']))
master = Tk()
canvas=Frame(master)
flcanvas = Canvas(canvas,
width=400,
height=400)
CANVAS_SCALE=150
flcanvas.bind("<Button-1>",lambda e: onclick(e,FL))
flcanvas.pack(side=LEFT)
LEGS_CANVAS[FL]=flcanvas
frcanvas = Canvas(canvas,
width=400,
height=400)
frcanvas.bind("<Button-1>",lambda e: onclick(e,FR))
frcanvas.pack(side=LEFT)
LEGS_CANVAS[FR]=frcanvas
rlcanvas = Canvas(canvas,
width=400,
height=400)
rlcanvas.bind("<Button-1>",lambda e: onclick(e,RL))
rlcanvas.pack(side=LEFT)
LEGS_CANVAS[RL]=rlcanvas
rrcanvas = Canvas(canvas,
width=400,
height=400)
rrcanvas.bind("<Button-1>",lambda e: onclick(e,RR))
rrcanvas.pack(side=LEFT)
LEGS_CANVAS[RR]=rrcanvas
canvas.grid(row=0)
robot=Frame(master)
top_view=Canvas(robot,
width=400,
height=400)
top_view.bind("<Button-1>",move_gravity_center)
top_view.pack(side=LEFT)