I am using MD49 Motor Drive with its motors
https://www.robot-electronics.co.uk/htm/md49tech.htm
http://wiki.ros.org/md49_base_controller
How to subscribe (encoder_l and encoder_r) from md49_base_controller package and publish (vx , vy ,and vth ) as a form odom (nav_msgs/Odometry) ?
There are two problem:
1-The first is that the encoders outputs are not correct "the package needs to be modified.
2-The second is the I want to create a package that subscribe the right and left wheels encoder counts (encoder_l and encoder_r) and publish (vx , vy ,and vth) as a form odom (nav_msgs/Odometry) to be compatable wth imu MPU9250
http://wiki.ros.org/robot_pose_ekf
The proposed package is:
1- We have to convert (encoder_l and encoder_r) to (RPM_l and RPM_r) as follow:
if (speed_l>128){newposition1 = encoder_l;}
else if (speed_l<128){ newposition1 = 0xFFFFFFFF-encoder_l;}
else if (speed_l==128) {newposition1=0;}
newtime1 = millis();
RPM_l = ((newposition1-oldposition1)*1000*60)/((newtime1-oldtime1)*980);
oldposition1 = newposition1;
oldtime1 = newtime1;
delay(250);
if (speed_r>128){ newposition2 = encoder_r;}
else if (speed_r<128){ newposition2 = 0xFFFFFFFF-encoder_r;}
else if (speed_r==128) { newposition2=0;}
newtime2 = millis();
RPM_r = ((newposition2-oldposition2)*1000*60)/((newtime2-oldtime2)*980);
oldposition2 = newposition2;
oldtime2= newtime2;
delay(250);
2- We have to convert (RPM_l and RPM_r) to (vx, vy, and vth) as follow:
vx=(r/2)*RPM_l*math.cos(th)+(r/2)*RPM_r*math.cos(th);
vx=(r/2)*RPM_l*math.sin(th)+(r/2)*RPM_r*math.sin(th);
vth=(r/B)*omega_l-(r/B)*omega_r;
Hint: r and B are wheel radius and vehicle width respectively.
3- The odom (nav_msgs/Odometry) package is:
#!/usr/bin/env python
import math
from math import sin, cos, pi
import rospy
import tf
from nav_msgs.msg import Odometry
from geometry_msgs.msg import Point, Pose, Quaternion, Twist, Vector3
from md49_messages.msg import md49_encoders
rospy.init_node('odometry_publisher')
odom_pub = rospy.Publisher("odom", Odometry, queue_size=50)
odom_broadcaster = tf.TransformBroadcaster()
x = 0.0
y = 0.0
th = 0.0
vx =0.1
vy = -0.1
vth = 0.1
current_time = rospy.Time.now()
last_time = rospy.Time.now()
r = rospy.Rate(1.0)
while not rospy.is_shutdown():
current_time = rospy.Time.now()
# compute odometry in a typical way given the velocities of the robot
dt = (current_time - last_time).to_sec()
delta_x = (vx * cos(th) - vy * sin(th)) * dt
delta_y = (vx * sin(th) + vy * cos(th)) * dt
delta_th = vth * dt
x += delta_x
y += delta_y
th += delta_th
# since all odometry is 6DOF we'll need a quaternion created from yaw
odom_quat = tf.transformations.quaternion_from_euler(0, 0, th)
# first, we'll publish the transform over tf
odom_broadcaster.sendTransform(
(x, y, 0.),
odom_quat,
current_time,
"base_link",
"odom"
)
# next, we'll publish the odometry message over ROS
odom = Odometry()
odom.header.stamp = current_time
odom.header.frame_id = "odom"
# set the position
odom.pose.pose = Pose(Point(x, y, 0.), Quaternion(*odom_quat))
# set the velocity
odom.child_frame_id = "base_link"
odom.twist.twist = Twist(Vector3(vx, vy, 0), Vector3(0, 0, vth))
# publish the message
odom_pub.publish(odom)
last_time = current_time
r.sleep()
The problem was in serial comunication setup not for the code.
Setup UART on the raspi 3 GPIO
For some strange reason the default for Pi3 using the latest 4.4.9 kernel is to DISABLE UART. To enable it you need to change enable_uart=1 in /boot/config.txt. (There is no longer necessary to add core_freq=250 to fix the core frequency to get stable baudrate.)
If you don’t use Bluetooth (or have undemanding uses) it is possible to swap the ports back in the Device Tree. There is a pi3-miniuart-bt and pi3-disable-bt module which are described in /boot/overlays/README here.
As mentioned, by default the new GPIO UART is not enabled so the first thing to do is to edit the config.txt file to enable the serial UART:
sudo nano /boot/config.txt
and add the line (at the bottom):
enable_uart=1
You have to reboot for the changes to take effect.
To check where your serial ports are pointing you can use the list command with the long “-l” listing format:
ls -l /dev
In the long listing you will find:
serial0 -> ttyS0
serial1 -> ttyAMA0
Thus on a Raspberry Pi 3 and Raspberry Pi Zero W, serial0 will point to GPIO J8 pins 8 and 10 and use the /dev/ttyS0. On other Raspberry Pi’s it will point to /dev/ttyAMA0.
So where possible refer to the serial port via it’s alias of “serial0” and your code should work on both Raspberry Pi 3 and other Raspberry Pi’s.
You also need to remove the console from the cmdline.txt. If you edit this with:
sudo nano /boot/cmdline.txt
you will see something like this:
dwc_otg.lpm_enable=0 console=serial0,115200 console=tty1 root=/dev/mmcblk0p2 rootfstype=ext4 elevator=deadline fsck.repair=yes root wait
remove the line: console=serial0,115200 and save and reboot for changes to take effect:
reboot
First off, you need to import nav_msgs/Odometry as the following:
from nav_msgs.msg import Odometry
You must have a function that performs those conversions and then in rospy.Subscriber import those variables, like this:
def example(data):
data.vx=<conversion>
data.vth=<conversion>
def listener():
rospy.Subscriber('*topic*', Odometry, example)
rospy.spin()
if __name__ == 'main':
listener()
I think this would work
Related
I'm working on a simulation of a Soft Robot using the Piecewise Constant Curvature (PCC) assumption and representing each PCC segment with an Augmented Rigid Body Model (ARBM). For this I first would like to implement a manual slider for curvature control, i.e., a slider where I can input the two curvature parameters (Theta and Phi) and after mapping it to the ARBM via some known map m(Theta, Phi) showcase the robot in meshcat.
I'm already displaying the ARBM, however, am struggling to get the slider to run. As a result, I'd like to have something similar to the Let's get you a Robot notebook from the Manipulation course. So ideally a kinematic simulation in which I can set the curvatures to show the resulting ARBM configuration.
As of right now, my approach is the following:
Create a Custom Slider Class that is based on LeafSystem that creates two slides
Create a Transformation System based on a VectorSystem that applies the map m(Theta, Phi) to the output of the sliders yielding the ARBM joint states on its output
Set the Robot Joints to this State (This is where I'm struggling)
The problem seems to be that I cannot connect the desired output directly to the Joint positions in the same way that, e.g., the Joint sliders are. Is there a way to do this or should I follow a different approach?
See below for the code of the individual instances:
CurvatureSlider.py:
from dataclasses import dataclass
import numpy as np
from pydrake.systems.framework import LeafSystem
class CurvatureSliders(LeafSystem):
#dataclass
class SliderDefault:
"""Default values for the meshcat sliders."""
name: str
"""The name that is used to add / query values from."""
default: float
"""The initial value of the slider."""
_THETA = SliderDefault("Theta", 0.0)
_PHI = SliderDefault("Phi", 0.0)
def __init__(self, meshcat):
"""
#param meshcat The already created pydrake.geometry.Meshcat instance.
"""
LeafSystem.__init__(self)
self.DeclareVectorOutputPort("theta_phi", 2, self.DoCalcOutput)
self.meshcat = meshcat
# Curvature Control Sliders
self.meshcat.AddSlider(
name=self._THETA.name, min=-2.0 * np.pi,
max=2.0 * np.pi, step=0.01,
value=self._THETA.default)
self.meshcat.AddSlider(
name=self._PHI.name, min=-2.0 * np.pi,
max=2.0 * np.pi, step=0.01,
value=self._PHI.default)
def SetConfiguration(self, config: tuple):
"""
#param pose Tuple of floats that is ordered (Theta, Phi)
"""
assert(len(config) == 2)
self.meshcat.SetSliderValue(self._THETA.name, config[0])
self.meshcat.SetSliderValue(self._PHI.name, config[1])
def DoCalcOutput(self, context, output):
theta = self.meshcat.GetSliderValue(self._THETA.name)
phi = self.meshcat.GetSliderValue(self._PHI.name)
output.SetAtIndex(0, theta)
output.SetAtIndex(1, phi)
CC2ARBM.py:
import numpy as np
from pydrake.systems.framework import VectorSystem
class CC2ARBM(VectorSystem):
def __init__(self, L: float):
"""
#param L The length of the segment.
"""
VectorSystem.__init__(self, 2, 10)
# Define length of the segment
self._L = L
def DoCalcVectorOutput(self, context, u, x, y):
# Extract Input
theta = u[0]
phi = u[1]
# Compute ARBM equivalent configuration
b = 0.5 * self._L
eta = 0
if not theta == 0:
b = self._L / theta * np.sqrt(1
+ 4 * np.sin(0.5 * theta) / theta
* (np.sin(0.5 * theta) / theta)
- np.cos(0.5 * theta))
eta = np.arccos(1 / b * self._L / theta * np.sin(0.5 * theta))
print("Computed ARBM Joint Position")
# Aggreate Output
y.SetAtIndex(0, phi)
y.SetAtIndex(1, 0.5 * theta - eta)
y.SetAtIndex(2, b)
y.SetAtIndex(3, eta)
y.SetAtIndex(4, - phi)
y.SetAtIndex(5, phi)
y.SetAtIndex(6, eta)
y.SetAtIndex(7, b)
y.SetAtIndex(8, 0.5 * theta - eta)
y.SetAtIndex(9, - phi)
Main.py:
import sys
import time
import matplotlib.pyplot as plt
import numpy as np
from CurvatureSliders import CurvatureSliders
from CC2ARBM import CC2ARBM
from pydrake.geometry import (
MeshcatVisualizerCpp,
MeshcatVisualizerParams,
Role,
StartMeshcat
)
from pydrake.math import (
RigidTransform,
RotationMatrix
)
from pydrake.multibody.meshcat import JointSliders
from pydrake.multibody.tree import FixedOffsetFrame
from pydrake.multibody.parsing import Parser
from pydrake.multibody.plant import AddMultibodyPlantSceneGraph
from pydrake.systems.analysis import Simulator
from pydrake.systems.framework import DiagramBuilder
from pydrake.systems.primitives import LogVectorOutput
def do_main(teleop: bool,
target_realtime_rate: float,
simulation_time: float,
max_time_step: float,
description_path: str) -> None:
# Start the visualizer.
# The cell will output an HTTP link after the execution.
# Click the link and a MeshCat tab should appear in your browser.
meshcat = StartMeshcat()
# Reset Meshcat Simulator
meshcat.Delete()
meshcat.DeleteAddedControls()
# Init the Diagram Builder
builder = DiagramBuilder()
# Note: the time_step here is chosen arbitrarily.
plant, scene_graph = AddMultibodyPlantSceneGraph(
builder, time_step=max_time_step)
# Load the files into the plant/scene_graph.
parser = Parser(plant)
# L - Mount
mount = parser.AddModelFromFile("../mount.sdf")
# Robot
model = parser.AddModelFromFile(description_path)
# Create an offset frame located half the link height above the origin
base_frame = plant.GetFrameByName("mount_base")
offset_frame = plant.AddFrame(
frame=FixedOffsetFrame(
name="offset_frame",
P=plant.world_frame(),
X_PF=RigidTransform(
R=RotationMatrix.Identity(),
p=np.array([0, 0, 0.5])
),
model_instance=None)
)
# Weld the base link to the offset frame
plant.WeldFrames(offset_frame, base_frame)
# Weld the robot base to the L-Mount
robot_base_frame = plant.GetFrameByName("robot_base")
robot_mounting_frame = plant.GetFrameByName("robot_location")
plant.WeldFrames(robot_mounting_frame, robot_base_frame)
# Finalize Plant
plant.Finalize()
#############################################################
# Post Plant Finalization Code #
#############################################################
# Set the Default states of the Joints
for i in plant.GetJointIndices(model):
j = plant.get_joint(i)
if j.num_positions() == 1:
j.set_default_positions([-0.2])
# Make the control inputs of the model an input to the diagram.
builder.ExportInput(plant.get_actuation_input_port())
# Add two visualizers, one to publish the "visual" geometry, and one to
# publish the "collision" geometry.
visual = MeshcatVisualizerCpp.AddToBuilder(
builder, scene_graph, meshcat,
MeshcatVisualizerParams(
role=Role.kPerception, prefix="visual")
)
collision = MeshcatVisualizerCpp.AddToBuilder(
builder, scene_graph, meshcat,
MeshcatVisualizerParams(role=Role.kProximity, prefix="collision"))
# Disable the collision geometry at the start; it can be enabled by the
# checkbox in the meshcat controls.
meshcat.SetProperty("collision", "visible", False)
# Setup Loggers
plant_logger = LogVectorOutput(plant.get_state_output_port(), builder)
# Joint Sliders Work like this
# sliders = builder.AddSystem(JointSliders(meshcat, plant))
# Add Curvature Sliders
curv_sliders = builder.AddSystem(CurvatureSliders(meshcat))
cc2arbm = builder.AddSystem(CC2ARBM(0.2))
# Connect the Sliders to the transformation block
builder.Connect(curv_sliders.get_output_port(0),
cc2arbm.get_input_port(0))
# Build the diagram
diagram = builder.Build()
# Start runnin the teleoperation
# Start Running the Slider similar to the Joint slider
# e.g. sliders.Run(diagram)
if __name__ == '__main__':
if len(sys.argv) <= 1:
do_main(target_realtime_rate=1,
simulation_time=10.0,
max_time_step=1.0e-3,
description_path="single_cc_segment.sdf")
else:
do_main(target_realtime_rate=float(sys.argv[1]),
simulation_time=float(sys.argv[2]),
max_time_step=float(sys.argv[3]),
description_path=sys.argv[4])
There are a few moving parts here. First, you say "kinematic simulation", but the demonstration in "Let's get you a robot" does not simulate (physics), it only visualizes the kinematics as set by the sliders. Assuming that is sufficient for your goal, then you could pass a callback into your sliders.Run method (as I do in the notebook corresponding to this chapter), and I believe that if you call plant.SetPositions in that callback, it should work?
I eventually ran the custom slider using a reimplementation of JointSlider.Run(...). For me, the following was sufficient (Two planar constant curvature segments, represented by 4 rigid joints each):
from dataclasses import dataclass
import numpy as np
import functools
import operator
import logging
import time
from typing import List, Tuple
from pydrake.systems.framework import LeafSystem
class CurvatureSliders(LeafSystem):
#dataclass
class SliderDefault:
"""Default values for the meshcat sliders."""
name: str
"""The name that is used to add / query values from."""
default: float
"""The initial value of the slider."""
_Q1 = SliderDefault("q1", 0.0)
_Q2 = SliderDefault("q2", 0.0)
def __init__(self, meshcat, plant, L=0.2):
"""
#param meshcat The already created pydrake.geometry.Meshcat instance.
#param plant The plant the sliders are connected to
#param L the restlength of the segment
"""
# Call Super Constructor
LeafSystem.__init__(self)
# Declare System Output
output = self.DeclareVectorOutputPort(
"q1_q2", 2, self.DoCalcOutput)
output.disable_caching_by_default()
# Init Class Variables
self._meshcat = meshcat
self._plant = plant
self._L = L
# Curvature Control Sliders
self._meshcat.AddSlider(
name=self._Q1.name, min=-2.0 * np.pi,
max=2.0 * np.pi, step=0.1,
value=self._Q1.default)
self._meshcat.AddSlider(
name=self._Q2.name, min=-2.0 * np.pi,
max=2.0 * np.pi, step=0.1,
value=self._Q2.default)
def SetConfiguration(self, q: Tuple):
"""
#param q configuration for each CC segment descriped by (q1, q2)
"""
self._meshcat.SetSliderValue(self._Q1.name, q[0])
self._meshcat.SetSliderValue(self._Q2.name, q[1])
def CC2AGRB(self, q: Tuple) -> List[float]:
# Extract input
q1 = q[0]
q2 = q[1]
# Compute ARBM equivalent configuration
config1 = [0, 0.5 * self._L, 0.5 * self._L, 0]
config2 = [0, 0.5 * self._L, 0.5 * self._L, 0]
if q1 != 0:
config1 = [
0.5 * q1,
self._L * np.sin(0.5 * q1) / q1,
self._L * np.sin(0.5 * q1) / q1,
0.5 * q1
]
if q2 != 0:
config2 = [
0.5 * q2,
self._L * np.sin(0.5 * q2) / q2,
self._L * np.sin(0.5 * q2) / q2,
0.5 * q2
]
return functools.reduce(operator.iconcat, [config1, config2], [])
def DoCalcOutput(self, context, output):
q1 = self._meshcat.GetSliderValue(self._Q1.name)
q2 = self._meshcat.GetSliderValue(self._Q2.name)
output.SetAtIndex(0, q1)
output.SetAtIndex(1, q2)
def Run(self, diagram, timeout=1e5):
# Get all the contextes
root_context = diagram.CreateDefaultContext()
sliders_context = self.GetMyContextFromRoot(root_context)
plant_context = self._plant.GetMyMutableContextFromRoot(root_context)
# Add Stop Button
kButtonName = "Stop Curvature Sliders"
logging.info("Press the '{}' button in Meshcat to continue.",
kButtonName)
self._meshcat.AddButton(kButtonName)
# Greb current time to implement the timeout
t0 = time.time()
# Loop until the button is clicked, or
# the timeout (when given) is reached.
diagram.Publish(root_context)
while self._meshcat.GetButtonClicks(kButtonName) < 1:
# Break out of loop if timeout elapsed
elapsed_t = time.time() - t0
if elapsed_t >= timeout:
break
# If the sliders have not changed, avoid invalidating the context.
old_positions = self._plant.GetPositions(plant_context)
new_positions = self.CC2AGRB(
self.get_output_port().Eval(sliders_context))
if (np.abs(new_positions - old_positions) < 0.001).all():
time.sleep(0.01)
continue
# Publish the new positions.
self._plant.SetPositions(plant_context, new_positions)
diagram.Publish(root_context)
And then just add them using the builder and calling the Run() function.
I am currently exploring how to handle memory in dask-cuda in order to write a function that will interpolate values along lines that cross an image.
My machine is a very basic windows 10 laptop with a single gpu (GeForce GTX 1050 4GB memory) and 16GB of RAM. I am using the following packages:
cupy 10.2.0
cudatoolkit 11.6.0
dask 2022.1.0
dask-cuda 22.2
A minimal version of my code is as follows:
import cupy as cp
import numpy as np
import dask.array as da
from dask_cuda import LocalCUDACluster
from dask.distributed import Client
from dask import compute
from math import pi
def bilinear_interpolate(im, x, y):
x0 = np.floor(x).astype(np.int32)
x1 = x0 + 1
y0 = np.floor(y).astype(np.int32)
y1 = y0 + 1
# keep coordinates within bounds
x0 = np.clip(x0, 0, im.shape[1]-1)
x1 = np.clip(x1, 0, im.shape[1]-1)
y0 = np.clip(y0, 0, im.shape[0]-1)
y1 = np.clip(y1, 0, im.shape[0]-1)
# retrieve values
Ia = im[ y0, x0 ]
Ib = im[ y1, x0 ]
Ic = im[ y0, x1 ]
Id = im[ y1, x1 ]
# calculate weights
wa = (x1-x) * (y1-y)
wb = (x1-x) * (y-y0)
wc = (x-x0) * (y1-y)
wd = (x-x0) * (y-y0)
return (wa*Ia + wb*Ib + wc*Ic + wd*Id).astype(np.float32)
# image used 5000x5000
im = cp.asarray(im)
# Set cuda-dask Client
cluster = LocalCUDACluster(
CUDA_VISIBLE_DEVICES = "0",
device_memory_limit = 0.4,
jit_unspill= True
)
client = Client(cluster)
# location
loc = im.shape[0] // 2, im.shape[1] //2
# radius
radius = [1,3000]
# pts per line
pts_line = radius[1]-radius[0]
# lines per degree factor
factor = 200
# radial chunks
rchunks = 180
# generate lines
r = cp.linspace(radius[0], radius[1], pts_line , dtype=np.int32)
psi = cp.linspace(0, 2*pi, 360*factor, dtype=np.float32)
R, PSI = cp.meshgrid(r, psi, sparse= True)
dR = da.from_array(R, chunks=(-1,pts_line), asarray=False).astype(np.float32)
dPSI = da.from_array(PSI, chunks=(rchunks,-1), asarray=False).astype(np.float32)
# Use polar coordinate to generate lines
rr = loc[0] + dR*np.cos(dPSI)
cc = loc[1] + dR* np.sin(dPSI)
rslt= da.map_blocks(bilinear_interpolate, im, cc, rr)
z = cp.asnumpy(rslt.compute().T)
I have managed, through trial and error, to interpolate +90k lines (each with 3000 points) across a single band image with 5000x5000 in size. However, as mentioned above, I am trying to write this function so that it will compute regardless of image size and number of lines to interpolate.
Much of the information I have found does not refer to windows machines (e.g. it appears that one cannot set rmm_pool_limit in a LocalCUDACluster as RAPIDS rmm package only works in linux). I am also familiar, thanks to the video by Mads Kristensen, with the limitations of the device_memory_limit parameter (i.e., it being a soft target) and the use of jit_unspill = True parameter as a way to minimize GPU memory spikes, etc. Yet, despite maintaining chuck sizes way below what I have available as GPU memory, I am still running into out of memory errors.
What is the best way to determine memory requirements? I had imagine that chuck size was the most crucial aspect (I thought that regardless of the original size of the array provided the chunk size was way below GPU memory limits I would be okay).
I'm trying to implement an addition to the loss function of the ppo algorithm in stable-baselines3. For this I collected additional observations for the states s(t-10) and s(t+1) which I can access in the train-function of the PPO class in ppo.py as part of the rollout_buffer.
I'm using a 3-layer-mlp as my network architecture and need the outputs of the second layer for the triplet (s(t-α), s(t), s(t+1)) to use them to calculate L = max(d(s(t+1) , s(t)) − d(s(t+1) , s(t−α)) + γ, 0), where d is the L2-distance.
Finally I want to add this term to the old loss, so loss = loss + 0.3 * L
This is my implementation starting with the original loss in line 242:
loss = policy_loss + self.ent_coef * entropy_loss + self.vf_coef * value_loss
###############################
net1 = nn.Sequential(*list(self.policy.mlp_extractor.policy_net.children())[:-1])
L_losses = []
a = 0
obs = rollout_data.observations
obs_alpha = rollout_data.observations_alpha
obs_plusone = rollout_data.observations_plusone
inds = rollout_data.inds
for i in inds:
if i > alpha: # only use observations for which L can be calculated
fs_t = net1(obs[a])
fs_talpha = net1(obs_alpha[a])
fs_tone = net1(obs_plusone[a])
L = max(
th.norm(th.subtract(fs_tone, fs_t)) - th.norm(th.subtract(fs_tone, fs_talpha)) + 1.0, 0.0)
L_losses.append(L)
else:
L_losses.append(0)
a += 1
L_loss = th.mean(th.FloatTensor(L_losses))
loss += 0.3 * L_loss
So with net1 I tried to get a clone of the original network with the outputs from the second layer. I am unsure if this is the right way to do this.
I do have some questions about my approach as the resulting performance is slightly worse compared to without the added term although it should be slightly better:
Is my way of getting the outputs of the second layer of the mlp network working?
When loss.backward() is called can the gradient be calculated correctly (with the new term included)?
In ROS turtlesim, how can we move turtle in sine path? I know we need to use proportional controller to achieve this. But am not getting actual method to do so. I have attached the code for the same which i have tried till now
Note: in callback function i have converted 0 to 2pi scale to -pi to pi scale which is used in ros
#!/usr/bin/env python
import rospy
from geometry_msgs.msg import Twist
from turtlesim.msg import Pose
PI = 3.1415926535897
import math
# Initial value of theta is 0
theta = 0
# Subscriber callback function
def pose_callback(pose):
global theta
req = 2 * math.pi
if pose.theta < 0:
alpha = req - (pose.theta + (2 * math.pi))
else:
alpha = req - pose.theta
alpha = 2 * math.pi - alpha
theta = alpha
# sin_graph function
def sin_graph():
# Starts a new node
global theta
rospy.init_node('sin_graph', anonymous=True)
# Initialization of publisher
velocity_publisher = rospy.Publisher(
'/turtle1/cmd_vel', Twist, queue_size=10)
# Subscribing to topic Pose
rospy.Subscriber("/turtle1/pose", Pose, pose_callback)
vel_msg = Twist()
# Initializing basic data
speed = 0.2
radius = 1
vel_msg.linear.x = speed
vel_msg.linear.y = 0
vel_msg.linear.z = 0
vel_msg.angular.x = 0
vel_msg.angular.y = 0
vel_msg.angular.z = speed/radius
# Rate at which message is published (10 times per second)
rate = rospy.Rate(10)
# Loop until current distance is re-initialized to zero(theta = 0)
while not rospy.is_shutdown():
vel_msg.linear.x = speed * math.cos(theta)
vel_msg.angular.z = math.sin(theta)
velocity_publisher.publish(vel_msg)
rospy.loginfo("Moving in a sine curve")
print(theta)
rate.sleep()
# Forcing our robot to stop
print("Goal Reached")
vel_msg.linear.x = 0
vel_msg.angular.z = 0
velocity_publisher.publish(vel_msg)
rospy.spin()
if __name__ == '__main__':
try:
# Testing our function
sin_graph()
except rospy.ROSInterruptException:
pass
I have some data that consists of a sequence of video frames which represent changes in luminance over time relative to a moving baseline. In these videos there are two kinds of 'event' that can occur - 'localised' events, which consist of luminance changes in small groups of clustered pixels, and contaminating 'diffuse' events, which affect most of the pixels in the frame:
I'd like to be able to isolate local changes in luminance from diffuse events. I'm planning on doing this by subtracting an appropriately low-pass filtered version of each frame. In order to design an optimal filter, I'd like to know which spatial frequencies of my frames are modulated during diffuse and local events, i.e. I'd like to generate a spectrogram of my movie over time.
I can find lots of information about generating spectrograms for 1D data (e.g. audio), but I haven't come across much on generating spectrograms for 2D data. What I've tried so far is to generate a 2D power spectrum from the Fourier transform of the frame, then perform a polar transformation about the DC component and then average across angles to get a 1D power spectrum:
I then apply this to every frame in my movie, and generate a raster plot of spectral power over time:
Does this seem like a sensible approach to take? Is there a more 'standard' approach to doing spectral analysis on 2D data?
Here's my code:
import numpy as np
# from pyfftw.interfaces.scipy_fftpack import fft2, fftshift, fftfreq
from scipy.fftpack import fft2, fftshift, fftfreq
from matplotlib import pyplot as pp
from matplotlib.colors import LogNorm
from scipy.signal import windows
from scipy.ndimage.interpolation import map_coordinates
def compute_2d_psd(img, doplot=True, winfun=windows.hamming, winfunargs={}):
nr, nc = img.shape
win = make2DWindow((nr, nc), winfun, **winfunargs)
f2 = fftshift(fft2(img*win))
psd = np.abs(f2*f2)
pol_psd = polar_transform(psd, centre=(nr//2, nc//2))
mpow = np.nanmean(pol_psd, 0)
stdpow = np.nanstd(pol_psd, 0)
freq_r = fftshift(fftfreq(nr))
freq_c = fftshift(fftfreq(nc))
pos_freq = np.linspace(0, np.hypot(freq_r[-1], freq_c[-1]),
pol_psd.shape[1])
if doplot:
fig,ax = pp.subplots(2,2)
im0 = ax[0,0].imshow(img*win, cmap=pp.cm.gray)
ax[0,0].set_axis_off()
ax[0,0].set_title('Windowed image')
lnorm = LogNorm(vmin=psd.min(), vmax=psd.max())
ax[0,1].set_axis_bgcolor('k')
im1 = ax[0,1].imshow(psd, extent=(freq_c[0], freq_c[-1],
freq_r[0], freq_r[-1]), aspect='auto',
cmap=pp.cm.hot, norm=lnorm)
# cb1 = pp.colorbar(im1, ax=ax[0,1], use_gridspec=True)
# cb1.set_label('Power (A.U.)')
ax[0,1].set_title('2D power spectrum')
ax[1,0].set_axis_bgcolor('k')
im2 = ax[1,0].imshow(pol_psd, cmap=pp.cm.hot, norm=lnorm,
extent=(pos_freq[0],pos_freq[-1],0,360),
aspect='auto')
ax[1,0].set_ylabel('Angle (deg)')
ax[1,0].set_xlabel('Frequency (cycles/px)')
# cb2 = pp.colorbar(im2, ax=(ax[0,1],ax[1,1]), use_gridspec=True)
# cb2.set_label('Power (A.U.)')
ax[1,0].set_title('Polar-transformed power spectrum')
ax[1,1].hold(True)
# ax[1,1].fill_between(pos_freq, mpow - stdpow, mpow + stdpow,
# color='r', alpha=0.3)
ax[1,1].axvline(0, c='k', ls='--', alpha=0.3)
ax[1,1].plot(pos_freq, mpow, lw=3, c='r')
ax[1,1].set_xlabel('Frequency (cycles/px)')
ax[1,1].set_ylabel('Power (A.U.)')
ax[1,1].set_yscale('log')
ax[1,1].set_xlim(-0.05, None)
ax[1,1].set_title('1D power spectrum')
fig.tight_layout()
return mpow, stdpow, pos_freq
def make2DWindow(shape,winfunc,*args,**kwargs):
assert callable(winfunc)
r,c = shape
rvec = winfunc(r,*args,**kwargs)
cvec = winfunc(c,*args,**kwargs)
return np.outer(rvec,cvec)
def polar_transform(image, centre=(0,0), n_angles=None, n_radii=None):
"""
Polar transformation of an image about the specified centre coordinate
"""
shape = image.shape
if n_angles is None:
n_angles = shape[0]
if n_radii is None:
n_radii = shape[1]
theta = -np.linspace(0, 2*np.pi, n_angles, endpoint=False).reshape(-1,1)
d = np.hypot(shape[0]-centre[0], shape[1]-centre[1])
radius = np.linspace(0, d, n_radii).reshape(1,-1)
x = radius * np.sin(theta) + centre[0]
y = radius * np.cos(theta) + centre[1]
# nb: map_coordinates can give crazy negative values using higher order
# interpolation, which introduce nans when you take the log later on
output = map_coordinates(image, [x, y], order=1, cval=np.nan,
prefilter=True)
return output
I believe that the approach you describe is in general the best way to do this analysis.
However, i did spot an error in your code. as:
np.abs(f2*f2)
is not the PSD of complex array f2, you need to multiply f2 by it's complex conjugate instead of itself (|f2^2| is not the same as |f2|^2).
Instead you should do something like
(f2*np.conjugate(f2)).astype(float)
Or, more cleanly:
np.abs(f2)**2.
The oscillations in the 2D power-spectrum are a tell-tale sign of this kind of error (I've done this before myself!)