tapemeasure.rst

:class:`TapeMeasure` -- Measuring distances between frames

.. currentmodule:: trep

param system:	The :class:`System` that the frames belong to.
param frames:	A list of :class:`Frame` objects or frame names.

A :class:`TapeMeasure` object calculates the length of the line you get from playing "connect the dots" with the origins of a list of coordinate frames. :class:`TapeMeasure` can calculate the length of the line and its derivatives with respect to configuration variables, and the velocity of the length (\tfrac{dx}{dt}) and its derivatives.

(figure here)

:class:`TapeMeasure` can be used as the basis for new constraints, potentials, and forces, or used independently for your own calculations.

Length and Velocity Calculations

Let (p_0, p_1, p_2 \dots p_{n} ) be the points at the origins of the frames specified by :attr:`frames`. The length, x is calculated as follows.

v_k = p_{k+1} - p_k

x_k = \sqrt{v_k^T v_k}

x = \sum_{k=0}^{n-1} x_k

The velocity is calculated by applying the chain rule to x:

\dot{x} = \sum_k \sum_i \frac{\partial x_k}{\partial q_i} \dot{q}_i

These calculations, and their derivatives, are optimized internally to take advantage of the fact that many of these terms are zero, significantly reducing the amount of calculation to do.

Warning

The derivatives of the length and velocity do not exist when the length of any part of the segment is zero. :class:`TapeMeasure` does not check for this condition and will return :data:`NaN` or cause a divide-by-zero error. Be careful to avoid these cases.

TapeMeasure Objects

.. attribute:: TapeMeasure.system

   The system that the :class:`TapeMeasure` works in.

   *(read-only)*

.. attribute:: TapeMeasure.frames

   A tuple of :class:`Frame` objects that define the lines being
   measured.

   *(read-only)*

.. method:: TapeMeasure.length()

   :rtype: :class:`Float`

   Calculate the total length of the line segments at the system's
   current configuration.

.. method:: TapeMeasure.length_dq(q1)

   :param q1: Derivative variable
   :type q1: :class:`Config`
   :rtype: :class:`Float`

   Calculate the derivative of the length with respect to the value of
   *q1*.

.. method:: TapeMeasure.length_dqdq(q1, q2)

   :param q1: Derivative variable
   :type q1: :class:`Config`
   :param q2: Derivative variable
   :type q2: :class:`Config`
   :rtype: :class:`Float`

   Calculate the second derivative of the length with respect to the
   value of *q1* and the value of *q2*.

.. method:: TapeMeasure.length_dqdqdq(q1, q2, q3)

   :param q1: Derivative variable
   :type q1: :class:`Config`
   :param q2: Derivative variable
   :type q2: :class:`Config`
   :param q3: Derivative variable
   :type q3: :class:`Config`
   :rtype: :class:`Float`

   Calculate the third derivative of the length with respect to the
   value of *q1*, the value of *q2*, and the value of *q3*.

.. method:: TapeMeasure.velocity()

   :rtype: :class:`Float`

.. method:: TapeMeasure.velocity_dq(q1)

   :param q1: Derivative variable
   :type q1: :class:`Config`
   :rtype: :class:`Float`

   Calculate the derivative of the velocity with respect to the value
   of *q1*.

.. method:: TapeMeasure.velocity_ddq(dq1)

   :param dq1: Derivative variable
   :type dq1: :class:`Config`
   :rtype: :class:`Float`

   Calculate the derivative of the velocity with respect to the
   velocity of *q1*.

.. method:: TapeMeasure.velocity_dqdq(q1, q2)

   :param q1: Derivative variable
   :type q1: :class:`Config`
   :param q2: Derivative variable
   :type q2: :class:`Config`
   :rtype: :class:`Float`

   Calculate the second derivative of the velocity with respect to the
   value of *q1* and the value of *q2*.

.. method:: TapeMeasure.velocity_dddqdq(dq1, dq2)

   :param dq1: Derivative variable
   :type dq1: :class:`Config`
   :param q2: Derivative variable
   :type q2: :class:`Config`
   :rtype: :class:`Float`

   Calculate the second derivative of the velocity with respect to the
   velocity of *q1* and the value of *q2*.

Visualization

.. method:: TapeMeasure.opengl_draw(width=1.0, color=(1.0,1.0,1.0))

   Draw a representation of the line defined by the
   :class:`TapeMeasure` with the specified width and color.  The
   current OpenGL coordinate system should be the root coordinate
   frame of the :class:`System`.

   This method can be called by constraints, forces, and potentials
   that are based on the :class:`TapeMeasure`.

Verifying Derivatives

.. method:: TapeMeasure.validate_length_dq([delta=1e-6, tolerance=1e-6, verbose=False])
            TapeMeasure.validate_length_dqdq([delta=1e-6, tolerance=1e-6, verbose=False])
            TapeMeasure.validate_length_dqdqdq([delta=1e-6, tolerance=1e-6, verbose=False])
            TapeMeasure.validate_velocity_dq([delta=1e-6, tolerance=1e-6, verbose=False])
            TapeMeasure.validate_velocity_ddq([delta=1e-6, tolerance=1e-6, verbose=False])
            TapeMeasure.validate_velocity_dqdq([delta=1e-6, tolerance=1e-6, verbose=False])
            TapeMeasure.validate_velocity_ddqdq([delta=1e-6, tolerance=1e-6, verbose=False])

   Unlike :class:`Constraint`, :class:`Potential`, and :class:`Force`,
   :class:`TapeMeasure` is used directly and all of the calculations
   are already implemented and verified.  These functions are
   primarily used for testing during developement, but they might be
   useful for debugging if you are using a :class:`TapeMeasure` and
   having trouble.