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Copyright (C) 2013 Travis DeWolf
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <>.
from dmp import DMPs
import numpy as np
class DMPs_rhythmic(DMPs):
"""An implementation of discrete DMPs"""
def __init__(self, **kwargs):
# call super class constructor
super(DMPs_rhythmic, self).__init__(pattern='rhythmic', **kwargs)
# set variance of Gaussian basis functions
# trial and error to find this spacing
self.h = np.ones(self.bfs) * self.bfs # 1.75
def gen_centers(self):
"""Set the centre of the Gaussian basis
functions be spaced evenly throughout run time"""
c = np.linspace(0, 2*np.pi, self.bfs+1)
c = c[0:-1]
self.c = c
def gen_front_term(self, x, dmp_num):
"""Generates the front term on the forcing term.
For rhythmic DMPs it's non-diminishing, so this
function is just a placeholder to return 1.
x float: the current value of the canonical system
dmp_num int: the index of the current dmp
if isinstance(x, np.ndarray):
return np.ones(x.shape)
return 1
def gen_goal(self, y_des):
"""Generate the goal for path imitation.
For rhythmic DMPs the goal is the average of the
desired trajectory.
y_des np.array: the desired trajectory to follow
goal = np.zeros(self.dmps)
for n in range(self.dmps):
num_idx = ~np.isnan(y_des[n]) # ignore nan's when calculating goal
goal[n] = .5 * (y_des[n, num_idx].min() +
y_des[n, num_idx].max())
return goal
def gen_psi(self, x):
"""Generates the activity of the basis functions for a given
canonical system state or path.
x float, array: the canonical system state or path
if isinstance(x, np.ndarray):
x = x[:, None]
return np.exp(self.h * (np.cos(x - self.c) - 1))
def gen_weights(self, f_target):
"""Generate a set of weights over the basis functions such
that the target forcing term trajectory is matched.
f_target np.array: the desired forcing term trajectory
# calculate x and psi
x_track = self.cs.rollout()
psi_track = self.gen_psi(x_track)
# efficiently calculate BF weights using weighted linear regression
for d in range(self.dmps):
for b in range(self.bfs):
self.w[d, b] = ([:, b], f_target[:, d]) /
(np.sum(psi_track[:, b]) + 1e-10))
# ==============================
# Test code
# ==============================
if __name__ == "__main__":
import matplotlib.pyplot as plt
# test normal run
dmp = DMPs_rhythmic(dmps=1, bfs=10, w=np.zeros((1, 10)))
y_track, dy_track, ddy_track = dmp.rollout()
plt.figure(1, figsize=(6, 3))
plt.plot(np.ones(len(y_track))*dmp.goal, 'r--', lw=2)
plt.plot(y_track, lw=2)
plt.title('DMP system - no forcing term')
plt.xlabel('time (ms)')
plt.ylabel('system trajectory')
plt.legend(['goal', 'system state'], loc='lower right')
# test imitation of path run
plt.figure(2, figsize=(6, 4))
num_bfs = [10, 30, 50, 100, 10000]
# a straight line to target
path1 = np.sin(np.arange(0, 2*np.pi, .01)*5)
# a strange path to target
path2 = np.zeros(path1.shape)
path2[(len(path2) / 2.):] = .5
for ii, bfs in enumerate(num_bfs):
dmp = DMPs_rhythmic(dmps=2, bfs=bfs)
dmp.imitate_path(y_des=np.array([path1, path2]))
y_track, dy_track, ddy_track = dmp.rollout()
plt.plot(y_track[:, 0], lw=2)
plt.plot(y_track[:, 1], lw=2)
a = plt.plot(path1, 'r--', lw=2)
plt.title('DMP imitate path')
plt.xlabel('time (ms)')
plt.ylabel('system trajectory')
plt.legend([a[0]], ['desired path'], loc='lower right')
b = plt.plot(path2, 'r--', lw=2)
plt.title('DMP imitate path')
plt.xlabel('time (ms)')
plt.ylabel('system trajectory')
plt.legend(['%i BFs' % i for i in num_bfs], loc='lower right')