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gait_planner.py
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gait_planner.py
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# Copyright 2021 I.S. "A. Sobrero" - SoRobotics Team. All rights reserved.
# Use of this source code is governed by the GPL 3.0 license that can be
# found in the LICENSE file.
# Partly based on https://github.com/miguelasd688/4-legged-robot-model/blob/master/src/gaitPlanner.py
import time
import numpy as np
#function neccesary to build a parametrized bezier curve
def f(n,k): #calculates binomial factor (n k)
return np.math.factorial(n)/(np.math.factorial(k)*np.math.factorial(n-k))
def b(t,k,point):
n = 9 #10 points bezier curve
return point*f(n,k)*np.power(t,k)*np.power(1-t,n-k)
#gait planner in order to move all feet
class GaitPlanner:
def __init__(self):
self.bodytoFeet = np.zeros([4,3])
self.phi = 0.
self.phiStance = 0.
self.lastTime = 0.
self.alpha = 0.
self.s = False
"""This trajectory planning is mostly based on:
https://www.researchgate.net/publication/332374021_Leg_Trajectory_Planning_for_Quadruped_Robots_with_High-Speed_Trot_Gait"""
def calculateStance(self , phi_st , V , angle):#phi_st between [0,1), angle in degrees
c = np.cos(np.deg2rad(angle))#cylindrical coordinates
s = np.sin(np.deg2rad(angle))
A = 0.05
halfStance = 5
p_stance=halfStance*(1-2*phi_st)
stanceX = c*p_stance*np.abs(V)
stanceY = -s*p_stance*np.abs(V)
stanceZ = -A*np.cos(np.pi/(2*halfStance)*p_stance)
return stanceX, stanceY , stanceZ
def calculateBezier_swing(self , phi_sw , V , angle):#phi between [0,1), angle in degrees
#curve generator https://www.desmos.com/calculator/xlpbe9bgll
c = np.cos(np.deg2rad(angle))#cylindrical coordinates
s = np.sin(np.deg2rad(angle))
# if (phi >= 0.75 or phi < 0.25):
# self.s = True
## print('foot DOWN' , self.s , phi)
#
# elif (phi <= 0.75 and phi > 0.25):
# self.s = False
## print('foot UP', self.s , phi)
X = np.abs(V)*c*np.array([-5. ,
-6.,
-7. ,
-7. ,
0. ,
0. ,
7. ,
7. ,
6. ,
5. ])
Y = np.abs(V)*s*np.array([ 5. ,
6. ,
7. ,
7. ,
0. ,
-0. ,
-7. ,
-7. ,
-6. ,
-5. ])
Z = np.abs(V)*np.array([0. ,
0. ,
5. ,
5. ,
5. ,
6. ,
6. ,
6. ,
0. ,
0. ])
swingX = 0.
swingY = 0.
swingZ = 0.
for i in range(10): #sum all terms of the curve
swingX = swingX + b(phi_sw,i,X[i])
swingY = swingY + b(phi_sw,i,Y[i])
swingZ = swingZ + b(phi_sw,i,Z[i])
return swingX, swingY , swingZ
def stepTrajectory(self , phi , V , angle , Wrot , centerToFoot): #phi belong [0,1), angles in degrees
if (phi >= 1):
phi = phi - 1.
#step describes a circuference in order to rotate
r = np.sqrt(centerToFoot[0]**2 + centerToFoot[1]**2) #radius of the ciscunscribed circle
footAngle = np.arctan2(centerToFoot[1],centerToFoot[0])
if Wrot >= 0.:#As it is defined inside cylindrical coordinates, when Wrot < 0, this is the same as rotate it 180ª
circleTrayectory = 90. - np.rad2deg(footAngle - self.alpha)
else:
circleTrayectory = 270. - np.rad2deg(footAngle - self.alpha)
stepOffset = 0.75
if phi <= stepOffset: #stance phase
phiStance = phi/stepOffset
stepX_long , stepY_long , stepZ_long = self.calculateStance(phiStance , V , angle)#longitudinal step
stepX_rot , stepY_rot , stepZ_rot = self.calculateStance(phiStance , Wrot , circleTrayectory)#rotational step
# print(phi,phiStance, stepX_long)
else: #swing phase
phiSwing = (phi-stepOffset)/(1-stepOffset)
stepX_long , stepY_long , stepZ_long = self.calculateBezier_swing(phiSwing , V , angle)#longitudinal step
stepX_rot , stepY_rot , stepZ_rot = self.calculateBezier_swing(phiSwing , Wrot , circleTrayectory)#rotational step
if (centerToFoot[1] > 0):#define the sign for every quadrant
if (stepX_rot < 0):
self.alpha = -np.arctan2(np.sqrt(stepX_rot**2 + stepY_rot**2) , r)
else:
self.alpha = np.arctan2(np.sqrt(stepX_rot**2 + stepY_rot**2) , r)
else:
if (stepX_rot < 0):
self.alpha = np.arctan2(np.sqrt(stepX_rot**2 + stepY_rot**2) , r)
else:
self.alpha = -np.arctan2(np.sqrt(stepX_rot**2 + stepY_rot**2) , r)
coord = np.empty(3)
coord[0] = stepX_long + stepX_rot
coord[1] = stepY_long + stepY_rot
coord[2] = stepZ_long + stepZ_rot
return coord
#computes step trajectory for every foot, defining L which is like velocity command, its angle,
#offset between each foot, period of time of each step and the initial vector from center of robot to feet.
def loop(self , V , angle , Wrot , T , offset , bodytoFeet_ ):
if T <= 0.01:
T = 0.01
if (self.phi >= 0.99):
self.lastTime= time.time()
self.phi = (time.time()-self.lastTime)/T
# print(self.phi)
#now it calculates step trajectory for every foot
step_coord = self.stepTrajectory(self.phi + offset[0] , V , angle , Wrot , np.squeeze(np.asarray(bodytoFeet_[0,:]))) #FR
self.bodytoFeet[0,0] = bodytoFeet_[0,0] + step_coord[0]
self.bodytoFeet[0,1] = bodytoFeet_[0,1] + step_coord[1]
self.bodytoFeet[0,2] = bodytoFeet_[0,2] + step_coord[2]
step_coord = self.stepTrajectory(self.phi + offset[1] , V , angle , Wrot , np.squeeze(np.asarray(bodytoFeet_[1,:])))#FL
self.bodytoFeet[1,0] = bodytoFeet_[1,0] + step_coord[0]
self.bodytoFeet[1,1] = bodytoFeet_[1,1] + step_coord[1]
self.bodytoFeet[1,2] = bodytoFeet_[1,2] + step_coord[2]
step_coord = self.stepTrajectory(self.phi + offset[2] , V , angle , Wrot , np.squeeze(np.asarray(bodytoFeet_[2,:])))#BR
self.bodytoFeet[2,0] = bodytoFeet_[2,0] + step_coord[0]
self.bodytoFeet[2,1] = bodytoFeet_[2,1] + step_coord[1]
self.bodytoFeet[2,2] = bodytoFeet_[2,2] + step_coord[2]
step_coord = self.stepTrajectory(self.phi + offset[3] , V , angle , Wrot , np.squeeze(np.asarray(bodytoFeet_[3,:])))#BL
self.bodytoFeet[3,0] = bodytoFeet_[3,0] + step_coord[0]
self.bodytoFeet[3,1] = bodytoFeet_[3,1] + step_coord[1]
self.bodytoFeet[3,2] = bodytoFeet_[3,2] + step_coord[2]
#
return self.bodytoFeet