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Copyright (C) 2016 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 <>.
import numpy as np
import matplotlib.pyplot as plt
import pydmps
import pydmps.dmp_discrete
beta = 20.0 / np.pi
gamma = 100
R_halfpi = np.array([[np.cos(np.pi / 2.0), -np.sin(np.pi / 2.0)],
[np.sin(np.pi / 2.0), np.cos(np.pi / 2.0)]])
num_obstacles = 5
obstacles = np.random.random((num_obstacles, 2))*2 - 1
def avoid_obstacles(y, dy, goal):
p = np.zeros(2)
for obstacle in obstacles:
# based on (Hoffmann, 2009)
# if we're moving
if np.linalg.norm(dy) > 1e-5:
# get the angle we're heading in
phi_dy = -np.arctan2(dy[1], dy[0])
R_dy = np.array([[np.cos(phi_dy), -np.sin(phi_dy)],
[np.sin(phi_dy), np.cos(phi_dy)]])
# calculate vector to object relative to body
obj_vec = obstacle - y
# rotate it by the direction we're going
obj_vec =, obj_vec)
# calculate the angle of obj relative to the direction we're going
phi = np.arctan2(obj_vec[1], obj_vec[0])
dphi = gamma * phi * np.exp(-beta * abs(phi))
R =, np.outer(obstacle - y, dy))
pval = -np.nan_to_num(, dy) * dphi)
# check to see if the distance to the obstacle is further than
# the distance to the target, if it is, ignore the obstacle
if np.linalg.norm(obj_vec) > np.linalg.norm(goal - y):
pval = 0
p += pval
return p
# test normal run
dmp = pydmps.dmp_discrete.DMPs_discrete(dmps=2, bfs=10, w=np.zeros((2,10)))
y_track = np.zeros((dmp.timesteps, dmp.dmps))
dy_track = np.zeros((dmp.timesteps, dmp.dmps))
ddy_track = np.zeros((dmp.timesteps, dmp.dmps))
goals = [[np.cos(theta), np.sin(theta)] for theta in np.linspace(0, 2*np.pi, 20)[:-1]]
for goal in goals:
dmp.goal = goal
for t in range(dmp.timesteps):
y_track[t], dy_track[t], ddy_track[t] = \
dmp.step(external_force=avoid_obstacles(dmp.y, dmp.dy, goal))
plt.figure(1, figsize=(6,6))
plot_goal, = plt.plot(dmp.goal[0], dmp.goal[1], 'gx', mew=3)
for obstacle in obstacles:
plot_obs, = plt.plot(obstacle[0], obstacle[1], 'rx', mew=3)
plot_path, = plt.plot(y_track[:,0], y_track[:, 1], 'b', lw=2)
plt.title('DMP system - obstacle avoidance')