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Numerically optimized versions of *EI shapers have been tuned for specific ranges of damping ratios and will show poor stability outside of these designated ranges. Signed-off-by: Dmitry Butyugin <dmbutyugin@google.com>
122 lines
4.3 KiB
Python
122 lines
4.3 KiB
Python
# Definitions of the supported input shapers
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#
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# Copyright (C) 2020-2021 Dmitry Butyugin <dmbutyugin@google.com>
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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 collections, math
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SHAPER_VIBRATION_REDUCTION=20.
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DEFAULT_DAMPING_RATIO = 0.1
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InputShaperCfg = collections.namedtuple(
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'InputShaperCfg',
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('name', 'init_func', 'min_freq', 'max_damping_ratio'))
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def get_none_shaper():
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return ([], [])
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def get_zv_shaper(shaper_freq, damping_ratio):
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df = math.sqrt(1. - damping_ratio**2)
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K = math.exp(-damping_ratio * math.pi / df)
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t_d = 1. / (shaper_freq * df)
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A = [1., K]
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T = [0., .5*t_d]
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return (A, T)
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def get_zvd_shaper(shaper_freq, damping_ratio):
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df = math.sqrt(1. - damping_ratio**2)
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K = math.exp(-damping_ratio * math.pi / df)
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t_d = 1. / (shaper_freq * df)
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A = [1., 2.*K, K**2]
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T = [0., .5*t_d, t_d]
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return (A, T)
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def get_mzv_shaper(shaper_freq, damping_ratio):
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df = math.sqrt(1. - damping_ratio**2)
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K = math.exp(-.75 * damping_ratio * math.pi / df)
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t_d = 1. / (shaper_freq * df)
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a1 = 1. - 1. / math.sqrt(2.)
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a2 = (math.sqrt(2.) - 1.) * K
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a3 = a1 * K * K
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A = [a1, a2, a3]
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T = [0., .375*t_d, .75*t_d]
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return (A, T)
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def get_ei_shaper(shaper_freq, damping_ratio):
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v_tol = 1. / SHAPER_VIBRATION_REDUCTION # vibration tolerance
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df = math.sqrt(1. - damping_ratio**2)
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t_d = 1. / (shaper_freq * df)
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dr = damping_ratio
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a1 = (0.24968 + 0.24961 * v_tol) + (( 0.80008 + 1.23328 * v_tol) +
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( 0.49599 + 3.17316 * v_tol) * dr) * dr
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a3 = (0.25149 + 0.21474 * v_tol) + ((-0.83249 + 1.41498 * v_tol) +
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( 0.85181 - 4.90094 * v_tol) * dr) * dr
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a2 = 1. - a1 - a3
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t2 = 0.4999 + ((( 0.46159 + 8.57843 * v_tol) * v_tol) +
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(((4.26169 - 108.644 * v_tol) * v_tol) +
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((1.75601 + 336.989 * v_tol) * v_tol) * dr) * dr) * dr
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A = [a1, a2, a3]
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T = [0., t2 * t_d, t_d]
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return (A, T)
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def _get_shaper_from_expansion_coeffs(shaper_freq, damping_ratio, t, a):
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tau = 1. / shaper_freq
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T = []
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A = []
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n = len(a)
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k = len(a[0])
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for i in range(n):
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u = t[i][k-1]
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v = a[i][k-1]
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for j in range(k-1):
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u = u * damping_ratio + t[i][k-j-2]
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v = v * damping_ratio + a[i][k-j-2]
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T.append(u * tau)
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A.append(v)
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return (A, T)
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def get_2hump_ei_shaper(shaper_freq, damping_ratio):
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t = [[0., 0., 0., 0.],
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[0.49890, 0.16270, -0.54262, 6.16180],
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[0.99748, 0.18382, -1.58270, 8.17120],
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[1.49920, -0.09297, -0.28338, 1.85710]]
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a = [[0.16054, 0.76699, 2.26560, -1.22750],
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[0.33911, 0.45081, -2.58080, 1.73650],
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[0.34089, -0.61533, -0.68765, 0.42261],
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[0.15997, -0.60246, 1.00280, -0.93145]]
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return _get_shaper_from_expansion_coeffs(shaper_freq, damping_ratio, t, a)
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def get_3hump_ei_shaper(shaper_freq, damping_ratio):
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t = [[0., 0., 0., 0.],
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[0.49974, 0.23834, 0.44559, 12.4720],
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[0.99849, 0.29808, -2.36460, 23.3990],
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[1.49870, 0.10306, -2.01390, 17.0320],
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[1.99960, -0.28231, 0.61536, 5.40450]]
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a = [[0.11275, 0.76632, 3.29160 -1.44380],
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[0.23698, 0.61164, -2.57850, 4.85220],
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[0.30008, -0.19062, -2.14560, 0.13744],
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[0.23775, -0.73297, 0.46885, -2.08650],
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[0.11244, -0.45439, 0.96382, -1.46000]]
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return _get_shaper_from_expansion_coeffs(shaper_freq, damping_ratio, t, a)
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# min_freq for each shaper is chosen to have projected max_accel ~= 1500
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INPUT_SHAPERS = [
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InputShaperCfg(name='zv', init_func=get_zv_shaper,
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min_freq=21., max_damping_ratio=0.99),
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InputShaperCfg(name='mzv', init_func=get_mzv_shaper,
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min_freq=23., max_damping_ratio=0.99),
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InputShaperCfg(name='zvd', init_func=get_zvd_shaper,
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min_freq=29., max_damping_ratio=0.99),
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InputShaperCfg(name='ei', init_func=get_ei_shaper,
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min_freq=29., max_damping_ratio=0.4),
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InputShaperCfg(name='2hump_ei', init_func=get_2hump_ei_shaper,
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min_freq=39., max_damping_ratio=0.3),
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InputShaperCfg(name='3hump_ei', init_func=get_3hump_ei_shaper,
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min_freq=48., max_damping_ratio=0.2),
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]
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