mirror of https://github.com/Desuuuu/klipper.git
mathutil: Move trilateration code from delta.py to mathutil.py
Move the trilateration algorithm to mathutil.py. It may be useful outside of delta kinematics, and it complicates the delta code. Signed-off-by: Kevin O'Connor <kevin@koconnor.net>
This commit is contained in:
Kevin O'Connor
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77a2c95b5e
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3e88ffabf1
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@ -4,7 +4,7 @@
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#
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# This file may be distributed under the terms of the GNU GPLv3 license.
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import math, logging
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import stepper, homing, chelper
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import stepper, homing, chelper, mathutil
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# Slow moves once the ratio of tower to XY movement exceeds SLOW_RATIO
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SLOW_RATIO = 3.
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@ -85,8 +85,9 @@ class DeltaKinematics:
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self.set_position([0., 0., 0.], ())
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def get_rails(self, flags=""):
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return list(self.rails)
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def _actuator_to_cartesian(self, pos):
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return actuator_to_cartesian(self.towers, self.arm2, pos)
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def _actuator_to_cartesian(self, spos):
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sphere_coords = [(t[0], t[1], sp) for t, sp in zip(self.towers, spos)]
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return mathutil.trilateration(sphere_coords, self.arm2)
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def calc_position(self):
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spos = [rail.get_commanded_position() for rail in self.rails]
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return self._actuator_to_cartesian(spos)
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@ -183,57 +184,6 @@ class DeltaKinematics:
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'arm_a': self.arm_lengths[0], 'arm_b': self.arm_lengths[1],
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'arm_c': self.arm_lengths[2] }
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######################################################################
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# Matrix helper functions for 3x1 matrices
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######################################################################
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def matrix_cross(m1, m2):
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return [m1[1] * m2[2] - m1[2] * m2[1],
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m1[2] * m2[0] - m1[0] * m2[2],
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m1[0] * m2[1] - m1[1] * m2[0]]
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def matrix_dot(m1, m2):
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return m1[0] * m2[0] + m1[1] * m2[1] + m1[2] * m2[2]
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def matrix_magsq(m1):
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return m1[0]**2 + m1[1]**2 + m1[2]**2
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def matrix_add(m1, m2):
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return [m1[0] + m2[0], m1[1] + m2[1], m1[2] + m2[2]]
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def matrix_sub(m1, m2):
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return [m1[0] - m2[0], m1[1] - m2[1], m1[2] - m2[2]]
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def matrix_mul(m1, s):
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return [m1[0]*s, m1[1]*s, m1[2]*s]
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def actuator_to_cartesian(towers, arm2, pos):
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# Find nozzle position using trilateration (see wikipedia)
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carriage1 = list(towers[0]) + [pos[0]]
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carriage2 = list(towers[1]) + [pos[1]]
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carriage3 = list(towers[2]) + [pos[2]]
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s21 = matrix_sub(carriage2, carriage1)
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s31 = matrix_sub(carriage3, carriage1)
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d = math.sqrt(matrix_magsq(s21))
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ex = matrix_mul(s21, 1. / d)
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i = matrix_dot(ex, s31)
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vect_ey = matrix_sub(s31, matrix_mul(ex, i))
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ey = matrix_mul(vect_ey, 1. / math.sqrt(matrix_magsq(vect_ey)))
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ez = matrix_cross(ex, ey)
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j = matrix_dot(ey, s31)
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x = (arm2[0] - arm2[1] + d**2) / (2. * d)
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y = (arm2[0] - arm2[2] - x**2 + (x-i)**2 + j**2) / (2. * j)
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z = -math.sqrt(arm2[0] - x**2 - y**2)
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ex_x = matrix_mul(ex, x)
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ey_y = matrix_mul(ey, y)
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ez_z = matrix_mul(ez, z)
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return matrix_add(carriage1, matrix_add(ex_x, matrix_add(ey_y, ez_z)))
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def get_position_from_stable(spos, params):
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angles = [params['angle_a'], params['angle_b'], params['angle_c']]
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radius = params['radius']
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@ -242,6 +192,6 @@ def get_position_from_stable(spos, params):
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for angle in map(math.radians, angles)]
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arm2 = [a**2 for a in [params['arm_a'], params['arm_b'], params['arm_c']]]
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endstops = [params['endstop_a'], params['endstop_b'], params['endstop_c']]
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pos = [es + math.sqrt(a2 - radius2) - p
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for es, a2, p in zip(endstops, arm2, spos)]
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return actuator_to_cartesian(towers, arm2, pos)
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sphere_coords = [(t[0], t[1], es + math.sqrt(a2 - radius2) - p)
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for t, es, a2, p in zip(towers, endstops, arm2, spos)]
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return mathutil.trilateration(sphere_coords, arm2)
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@ -3,7 +3,12 @@
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# Copyright (C) 2018 Kevin O'Connor <kevin@koconnor.net>
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#
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# This file may be distributed under the terms of the GNU GPLv3 license.
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import logging
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import math, logging
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######################################################################
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# Coordinate descent
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######################################################################
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# Helper code that implements coordinate descent
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def coordinate_descent(adj_params, params, error_func):
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@ -38,3 +43,57 @@ def coordinate_descent(adj_params, params, error_func):
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dp[param_name] *= 0.9
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logging.info("Coordinate descent best_err: %s rounds: %d", best_err, rounds)
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return params
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######################################################################
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# Trilateration
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######################################################################
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# Trilateration finds the intersection of three spheres. See the
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# wikipedia article for the details of the algorithm.
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def trilateration(sphere_coords, radius2):
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sphere_coord1, sphere_coord2, sphere_coord3 = sphere_coords
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s21 = matrix_sub(sphere_coord2, sphere_coord1)
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s31 = matrix_sub(sphere_coord3, sphere_coord1)
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d = math.sqrt(matrix_magsq(s21))
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ex = matrix_mul(s21, 1. / d)
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i = matrix_dot(ex, s31)
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vect_ey = matrix_sub(s31, matrix_mul(ex, i))
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ey = matrix_mul(vect_ey, 1. / math.sqrt(matrix_magsq(vect_ey)))
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ez = matrix_cross(ex, ey)
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j = matrix_dot(ey, s31)
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x = (radius2[0] - radius2[1] + d**2) / (2. * d)
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y = (radius2[0] - radius2[2] - x**2 + (x-i)**2 + j**2) / (2. * j)
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z = -math.sqrt(radius2[0] - x**2 - y**2)
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ex_x = matrix_mul(ex, x)
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ey_y = matrix_mul(ey, y)
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ez_z = matrix_mul(ez, z)
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return matrix_add(sphere_coord1, matrix_add(ex_x, matrix_add(ey_y, ez_z)))
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######################################################################
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# Matrix helper functions for 3x1 matrices
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######################################################################
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def matrix_cross(m1, m2):
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return [m1[1] * m2[2] - m1[2] * m2[1],
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m1[2] * m2[0] - m1[0] * m2[2],
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m1[0] * m2[1] - m1[1] * m2[0]]
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def matrix_dot(m1, m2):
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return m1[0] * m2[0] + m1[1] * m2[1] + m1[2] * m2[2]
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def matrix_magsq(m1):
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return m1[0]**2 + m1[1]**2 + m1[2]**2
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def matrix_add(m1, m2):
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return [m1[0] + m2[0], m1[1] + m2[1], m1[2] + m2[2]]
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def matrix_sub(m1, m2):
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return [m1[0] - m2[0], m1[1] - m2[1], m1[2] - m2[2]]
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def matrix_mul(m1, s):
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return [m1[0]*s, m1[1]*s, m1[2]*s]
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