trep
- param system
The
System
that the frames belong to.- param frames
A list of
Frame
objects or frame names.
A TapeMeasure
object calculates the length of the line you get from playing "connect the dots" with the origins of a list of coordinate frames. TapeMeasure
can calculate the length of the line and its derivatives with respect to configuration variables, and the velocity of the length (
(figure here)
TapeMeasure
can be used as the basis for new constraints, potentials, and forces, or used independently for your own calculations.
Let (p0, p1, p2…pn) be the points at the origins of the frames specified by
frames
. The length, x is calculated as follows.
vk = pk + 1 − pk$$x_k = \sqrt{v_k^T v_k}$$ $$x = \sum_{k=0}^{n-1} x_k$$ 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.
TapeMeasure
does not check for this condition and will returnNaN
or cause a divide-by-zero error. Be careful to avoid these cases.
TapeMeasure.system
The system that the TapeMeasure
works in.
(read-only)
TapeMeasure.frames
A tuple of Frame
objects that define the lines being measured.
(read-only)
TapeMeasure.length()
- rtype
Float
Calculate the total length of the line segments at the system's current configuration.
TapeMeasure.length_dq(q1)
- param q1
Derivative variable
- type q1
Config
- rtype
Float
Calculate the derivative of the length with respect to the value of q1.
TapeMeasure.length_dqdq(q1, q2)
- param q1
Derivative variable
- type q1
Config
- param q2
Derivative variable
- type q2
Config
- rtype
Float
Calculate the second derivative of the length with respect to the value of q1 and the value of q2.
TapeMeasure.length_dqdqdq(q1, q2, q3)
- param q1
Derivative variable
- type q1
Config
- param q2
Derivative variable
- type q2
Config
- param q3
Derivative variable
- type q3
Config
- rtype
Float
Calculate the third derivative of the length with respect to the value of q1, the value of q2, and the value of q3.
TapeMeasure.velocity()
- rtype
Float
TapeMeasure.velocity_dq(q1)
- param q1
Derivative variable
- type q1
Config
- rtype
Float
Calculate the derivative of the velocity with respect to the value of q1.
TapeMeasure.velocity_ddq(dq1)
- param dq1
Derivative variable
- type dq1
Config
- rtype
Float
Calculate the derivative of the velocity with respect to the velocity of q1.
TapeMeasure.velocity_dqdq(q1, q2)
- param q1
Derivative variable
- type q1
Config
- param q2
Derivative variable
- type q2
Config
- rtype
Float
Calculate the second derivative of the velocity with respect to the value of q1 and the value of q2.
TapeMeasure.velocity_dddqdq(dq1, dq2)
- param dq1
Derivative variable
- type dq1
Config
- param q2
Derivative variable
- type q2
Config
- rtype
Float
Calculate the second derivative of the velocity with respect to the velocity of q1 and the value of q2.
TapeMeasure.opengl_draw(width=1.0, color=(1.0,1.0,1.0))
Draw a representation of the line defined by the TapeMeasure
with the specified width and color. The current OpenGL coordinate system should be the root coordinate frame of the System
.
This method can be called by constraints, forces, and potentials that are based on the TapeMeasure
.
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 Constraint
, Potential
, and Force
, 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 TapeMeasure
and having trouble.