# Source code for morse.sensors.imu

```import logging; logger = logging.getLogger("morse." + __name__)
import math
import morse.core.sensor
from morse.core import mathutils, blenderapi
from morse.sensors.magnetometer import MagnetoDriver
from morse.helpers.velocity import linear_velocities, angular_velocities
from copy import copy

"""
Important note:

The 'logger.debug' instructions take some processor work, even if they are
not displayed. For this reason, it is best to comment out these lines in
the 'default_action' method.
"""

[docs]class IMU(morse.core.sensor.Sensor):
"""
This sensor emulates an Inertial Measurement Unit (IMU), measuring
the angular velocity and linear acceleration including acceleration
due to gravity.
For the magnetic field part, refer to the documentation of
:doc:`./magnetometer`.

If the robot has a physics controller, the velocities are directly
read from it's properties ``localAngularVelocity`` and
``worldLinearVelocity``. Otherwise the velocities are calculated by
simple differentiation. Linear acceleration is always computed by
differentiation of the linear velocity. The measurements are given
in the IMU coordinate system, so the location and rotation of the
IMU with respect to the robot is taken into account.
"""

_name = "Inertial measurement unit"

'rates in IMU x, y, z axes (in radian . sec ^ -1)')
'acceleration in IMU x, y, z axes (in m . sec ^ -2)')
'magnetic field along x, y, z axes (in nT)')
"Kind of computation, can be one of ['Velocity', 'Position']. "
"Only robot with dynamic and Velocity control can choose Velocity "
"computation. Default choice is Velocity for robot with physics, "
"and Position for others")

def __init__(self, obj, parent=None):
""" Constructor method.

Receives the reference to the Blender object.
The second parameter should be the name of the object's parent.
"""
logger.info('%s initialization' % obj.name)
# Call the constructor of the parent class
morse.core.sensor.Sensor.__init__(self, obj, parent)

has_physics = bool(self.robot_parent.bge_object.getPhysicsId())
if self._type == 'Automatic':
if has_physics:
self._type = 'Velocity'
else:
self._type = 'Position'

if self._type == 'Velocity' and not has_physics:
logger.error("Invalid configuration : Velocity computation without "
"physics")
return

if self._type == 'Velocity':
# make new references to the robot velocities and use those.
self.robot_w = self.robot_parent.bge_object.localAngularVelocity
self.robot_vel = self.robot_parent.bge_object.worldLinearVelocity
else:
self.pp = copy(self.position_3d)

# previous linear velocity
self.plv = mathutils.Vector((0.0, 0.0, 0.0))
# previous angular velocity
self.pav = mathutils.Vector((0.0, 0.0, 0.0))

self.gravity = - blenderapi.gravity()

# imu2body will transform a vector from imu frame to body frame
self.imu2body = self.sensor_to_robot_position_3d()
# rotate vector from body to imu frame
self.rot_b2i = self.imu2body.rotation.conjugated()
logger.debug("imu2body rotation RPY [% .3f % .3f % .3f]" % tuple(math.degrees(a) for a in self.imu2body.euler))
logger.debug("imu2body translation [% .3f % .3f % .3f]" % tuple(self.imu2body.translation))

if self.imu2body.translation.length > 0.01:
self.compute_offset_acceleration = True
else:
self.compute_offset_acceleration = False

# reference for rotating a vector from imu frame to world frame
self.rot_i2w = self.bge_object.worldOrientation

self.mag = MagnetoDriver()

logger.info("IMU Component initialized, runs at %.2f Hz ", self.frequency)

[docs]    def sim_imu_simple(self):
"""
Simulate angular velocity and linear acceleration measurements via simple differences.
"""
# linear and angular velocities
lin_vel = linear_velocities(self.pp, self.position_3d, 1 / self.frequency)
ang_vel = angular_velocities(self.pp, self.position_3d, 1 / self.frequency)

# linear acceleration in imu frame
dv_imu = self.rot_i2w.transposed() * (lin_vel - self.plv) * self.frequency

# measurement includes gravity and acceleration
accel_meas = dv_imu + self.rot_i2w.transposed() * self.gravity

# save current position and attitude for next step
self.pp = copy(self.position_3d)

# save velocity for next step
self.plv = lin_vel
self.pav = ang_vel

return ang_vel, accel_meas

[docs]    def sim_imu_with_physics(self):
"""
Simulate angular velocity and linear acceleration measurements using the physics of the robot.
"""

# rotate the angular rates from the robot frame into the imu frame
rates = self.rot_b2i * self.robot_w
#logger.debug("rates in robot frame (% .4f, % .4f, % .4f)", self.robot_w, self.robot_w, self.robot_w)
#logger.debug("rates in imu frame   (% .4f, % .4f, % .4f)", rates, rates, rates)

# differentiate linear velocity in world (inertial) frame
# and rotate to imu frame
dv_imu = self.rot_i2w.transposed() * (self.robot_vel - self.plv) * self.frequency
#logger.debug("velocity_dot in imu frame (% .4f, % .4f, % .4f)", dv_imu, dv_imu, dv_imu)

# rotate acceleration due to gravity into imu frame
g_imu = self.rot_i2w.transposed() * self.gravity

# measurement includes gravity and acceleration
accel_meas = dv_imu + g_imu

if self.compute_offset_acceleration:
# acceleration due to rotation (centripetal)
# is zero if imu is mounted in robot center (assumed axis of rotation)
a_centripetal = self.rot_b2i * rates.cross(rates.cross(self.imu2body.translation))
#logger.debug("centripetal acceleration (% .4f, % .4f, % .4f)", a_rot, a_rot, a_rot)

# linear acceleration due to angular acceleration
a_alpha = self.rot_b2i * (self.robot_w - self.pav).cross(self.imu2body.translation) * self.frequency

# final measurement includes acceleration due to rotation center not in IMU
accel_meas += a_centripetal + a_alpha

# save velocity for next step
self.plv = self.robot_vel.copy()
self.pav = self.robot_w.copy()

return rates, accel_meas

[docs]    def default_action(self):
"""
Get the speed and acceleration of the robot and transform it into the imu frame
"""
if self._type == 'Velocity':
(rates, accel) = self.sim_imu_with_physics()
else:
(rates, accel) = self.sim_imu_simple()

# Store the important data
self.local_data['angular_velocity'] = rates
self.local_data['linear_acceleration'] = accel
self.local_data['magnetic_field'] = self.mag.compute(self.position_3d)
```