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kinematics_delta.py
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kinematics_delta.py
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import math
import numpy as np
# Constants
PI = math.pi
SIN30 = 0.5
COS30 = np.sqrt(3)/2
TAN30 = 1/np.sqrt(3)
TAN60 = np.sqrt(3)
# Kinematics Reference: https://www.ri.cmu.edu/app/uploads/2021/12/Masters-Thesis-Final-Version.pdf
class PDelta():
def __init__(self, ee_len=0.006, base_len=0.02, leg_len=0.05):
# Delta parameters as defined by CAD
# ee_len: distance from platform centroid to the side of the triangle (inradius)
# base_len: distance from base centroid to the vertex of the triangle (circumradius)
# leg_len: length of the delta leg
# Key for number labels of points on each triangle
# 0: Origin
# 1: Bottom
# 2: Top Right
# 3: Top Left
# Delta parameters as defined by kinematics reference
self.s_b = base_len * 2 * np.sqrt(3) # base side length
self.s_p = ee_len * 2 * np.sqrt(3) # platform side length
self.l = leg_len
self.u_b = base_len # base circumradius
self.u_p = ee_len # platform circumradius
# Base Joint Locations (these values should never change)
self.b0 = np.zeros(3)
self.b1 = self.b0 + np.array([0, -self.u_b, 0])
self.b2 = self.b0 + np.array([self.u_b * COS30, self.u_b * SIN30, 0])
self.b3 = self.b0 + np.array([-self.u_b * COS30, self.u_b * SIN30, 0])
# Motor Actuation Amounts
self.h1 = 0 # Motor 1
self.h2 = 0 # Motor 2
self.h3 = 0 # Motor 3
# Knee Joint positions
self.k1 = np.zeros(3) # Knee 1
self.k2 = np.zeros(3) # Knee 2
self.k3 = np.zeros(3) # Knee 3
self.update_knee_positions()
# Platform Joint Locations
self.p0 = np.zeros(3)
self.p1 = np.zeros(3)
self.p2 = np.zeros(3)
self.p3 = np.zeros(3)
self.update_platform_corners()
self.b0_prev = np.zeros(3)
self.h1_prev = 0
self.h2_prev = 0
self.h3_prev = 0
self.p0_prev = np.zeros(3)
self.go_home()
# TODO do i need to store previous positions?
# TODO do i need to tell it to just go to a fixed distance away as home?
# TODO update functions
# walker calls go_to for IK and go_to_distance for FK
# REPORTING
def report_distance(self):
print('AT DISTANCE {:0.2f}, {:0.2f}, {:0.2f}'.format(self.t1, self.t2, self.t3))
def report_position(self):
print('AT POS {:0.2f}, {:0.2f}, {:0.2f}'.format(self.x0, self.y0, self.z0))
# UPDATING PARAMETERS
def update_platform_corners(self):
self.p1 = self.p0 + np.array([0, -self.u_p, 0])
self.p2 = self.p0 + np.array([self.u_p * COS30, self.u_p * SIN30, 0])
self.p3 = self.p0 + np.array([-self.u_p * COS30, self.u_p * SIN30, 0])
return
def update_knee_positions(self):
self.k1 = self.b1 - np.array([0, 0, self.h1])
self.k2 = self.b2 - np.array([0, 0, self.h2])
self.k3 = self.b3 - np.array([0, 0, self.h3])
return
def update_prev_positions(self):
self.b0_prev = self.b0
self.h1_prev = self.h1
self.h2_prev = self.h2
self.h3_prev = self.h3
self.p0_prev = self.p0
return
# MOVE FUNCTIONS
def go_home(self):
self.h1, self.h2, self.h3 = 0, 0, 0
self.update_knee_positions()
self.go_to_distance(0, 0, 0)
# self.go_to_position(0, 0, -0.04)
return
# Given a position, use IK to calculate the motor actuation amounts
def go_to_position(self, x, y, z):
self.update_prev_positions()
self.p0 = np.array([x, y, z])
self.update_platform_corners()
state = self.delta_calc_inverse()
if state == 0:
pass
else:
# TODO fix this section
print("Err in IK!")
self.go_home()
return self.h1, self.h2, self.h3
# Given motor actuation amounts, use IK to calculate the EE position
def go_to_distance(self, dst_1, dst_2, dst_3):
self.update_prev_positions()
p0_prev = self.p0
state = self.delta_calc_forward(dst_1, dst_2, dst_3)
if state == 0:
self.h1, self.h2, self.h3 = dst_1, dst_2, dst_3
self.update_knee_positions()
else:
# TODO fix this section
print("Err in FK!")
self.go_home()
return self.p0[0], self.p0[1], self.p0[2]
# Calculate inverse kinematics based on EE position
# Returns a 0 if the position is feasible and -1 otherwise
def delta_calc_inverse(self):
# Calculate XY squared dist from the end effector center to prismatic actuator axis
d1 = np.sum(np.power(self.p1[0:2] - self.b1[0:2], 2))
d2 = np.sum(np.power(self.p2[0:2] - self.b2[0:2], 2))
d3 = np.sum(np.power(self.p3[0:2] - self.b3[0:2], 2))
# Check if the end effector center is too far to be feasible
l_squared = np.power(self.l, 2)
if d1 > l_squared or d2 > l_squared or d3 > l_squared:
return -1
# IK calculation of the motor actuation amounts
self.h1 = -1*(self.p0[2] + np.sqrt(l_squared - d1))
self.h2 = -1*(self.p0[2] + np.sqrt(l_squared - d2))
self.h3 = -1*(self.p0[2] + np.sqrt(l_squared - d3))
self.update_knee_positions()
return 0
# Calculate FK based on given motor actuation amounts
# Returns a 0 if the position is feasible and -1 otherwise
def delta_calc_forward(self, dst_1, dst_2, dst_3):
# Find corners of a new triangle
t = (self.s_b - self.s_p) * TAN30 / 2 # equivalent to u_b - u_p
# Corner 1 (x1 = 0)
y1 = -1 * t
z1 = -1 * dst_1
# Corner 2
x2 = t * COS30
y2 = t * SIN30
z2 = -1 * dst_2
# Corner 3
x3 = -t * COS30
y3 = t * SIN30
z3 = -1 * dst_3
# Detn Value
dnm = (y2 - y1) * x3 - (y3 - y1) * x2
w1 = y1 * y1 + z1 * z1
w2 = x2 * x2 + y2 * y2 + z2 * z2
w3 = x3 * x3 + y3 * y3 + z3 * z3
# x = (a1*z + b1)/dnm
a1 = (z2 - z1) * (y3 - y1) - (z3 - z1) * (y2 - y1)
b1 = -((w2 - w1) * (y3 - y1) - (w3 - w1) * (y2 - y1)) / 2.0
# y = (a2*z + b2)/dnm
a2 = -(z2 - z1) * x3 + (z3 - z1) * x2
b2 = ((w2 - w1) * x3 - (w3 - w1) * x2) / 2.0
# a*z^2 + b*z + c = 0
a = a1 * a1 + a2 * a2 + dnm * dnm
b = 2 * (a1 * b1 + a2 * (b2 - y1 * dnm) - z1 * dnm * dnm)
c = (b2 - y1 * dnm) * (b2 - y1 * dnm) + b1 * b1 + dnm * dnm * (z1 * z1 - self.l * self.l)
# discriminant
d = b * b - (4.0 * a * c)
if d < 0:
return -1 # non-existing point
z0 = -(0.5 * (b + np.sqrt(d)) / a)
x0 = (a1 * z0 + b1) / dnm
y0 = (a2 * z0 + b2) / dnm
self.p0 = np.array([x0, y0, z0])
self.update_platform_corners()
return 0