Rotations in ROS

Notation

Fixed Axis vs Euler Angles

In these APIs there are two notations.

• Fixed Axis: For more information on the fixed axis can be found at the following Wikipedia article Rotation around a fixed axis. Fixed axis rotation also includes Euler extrinsic rotation around fixed axis, like RPY around fixed X-Y-Z used below, which is explained in the following Wikipedia article Euler angles

• Euler Angles: Euler angles specified here are intrinsic rotations around rotating axis, like YPR around rotating Z-Y-X, explained in the following Wikipedia article Euler angles.

C++

There are a number of math libraries including bullet and eigen and kdl. Bullet is the primary linear math library used in the system at the moment.

Bullet

There are two classes within bullet which deal with rotations, btMatrix3x3 and btQuaternion.

btMatrix3x3

Accessors

• getRPY(double roll, double pitch, double yaw)

  • This will get the roll pitch and yaw from the matrix about fixed axes X, Y, Z respectively.

  getEulerYPR(double yaw, double pitch, double roll)

  • This will get the yaw, pitch and roll from the matrix about the euler angles Z, Y, X respectively.

Mutators

• setRPY(double roll, double pitch, double yaw)

  • Set the rotation using fixed axis notation about X, Y, Z axes respectively.

  setEulerYPR(double yaw, double pitch, double roll) 

  • Set the rotation using euler angles about Z, Y, X respectively.

btQuaternion

Accessors

To get angles out construct a btMatrix3x3 and use it's accessors. For example:  btQuaternion q; btMatrix3x3(q).getRPY(roll, pitch, yaw);

Mutators

• setRPY(double roll, double pitch, double yaw)

  • Set the rotation using fixed axis notation about X, Y, Z axes respectively.

  setEulerZYX

  • Set the rotation using euler angles about Z, Y, X respectively.

Eigen

See Eigen's geometry tutorial.

KDL::Rotation

Constructors

• Rotation::RPY(double roll, double pitch, double yaw)

  • This will return a Rotation with roll pitch and yaw about fixed axes X, Y, Z respectively.

  Rotation::EulerZYX(double Alfa,double Beta,double Gamma)

  • Gives back a Rotation created by the EulerZYZ convention. First rotate around Z with alfa, then around the new Y with beta, then around new X with gamma.

  Rotation::EulerZYZ(double Alfa,double Beta,double Gamma)

  • Gives back a Rotation created by the EulerZYZ convention. First rotate around Z with alfa, then around the new Y with beta, then around new Z with gamma.

  Rotation::Quaternion(double x,double y,double z, double w)

  • Gives back a Rotation constructed by the 4 quaternion parameters. xyz first, and then rotation w. the norm of (x,y,z,w)) should be equal to 1.

Accessors

• GetRPY(double roll, double pitch, double yaw)

  • This will get the roll pitch and yaw angles about fixed axes X, Y, Z respectively.

  GetEulerZYX(double alpha, double beta, double gamma)

  • Gives back the EulerZYX convention description of the rotation matrix. First rotate around Z with alfa, then around the new Y with beta, then around new X with gamma.

  GetEulerZYZ(double alpha, double beta, double gamma)

  • Gives back the EulerZYZ convention description of the rotation matrix. First rotate around Z with alfa, then around the new Y with beta, then around new Z with gamma.

  GetQuaternion(double x,double y,double z, double w)

  • Gives back the 4 quaternion parameters. xyz first, and then rotation w. the norm of (x,y,z,w)) is equal to 1.

Python

Python euler angle support comes from transformations.py

transformations.py

The tf package also includes the popular transformations.py module. TransformerROS uses transformations.py to perform conversions between quaternions and matrices. transformations.py does has useful conversion on numpy matrices; it can convert between transformations as Euler angles, quaternions, and matrices.

To use these methods, include something similar to the following line:

   1 from tf.transformations import euler_from_quaternion