TapeMeasure
– Measuring distances between frames¶
-
class
trep.
TapeMeasure
(system, frames)¶ Parameters: 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 (\(\tfrac{dx}{dt}\)) and its derivatives.(figure here)
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
frames
. The length, \(x\) is calculated as follows.\[ \begin{align}\begin{aligned}v_k = p_{k+1} - p_k\\x_k = \sqrt{v_k^T v_k}\\x = \sum_{k=0}^{n-1} x_k\end{aligned}\end{align} \]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 Objects¶
-
TapeMeasure.
system
¶ The system that the
TapeMeasure
works in.(read-only)
-
TapeMeasure.
length
()¶ Return type: Float
Calculate the total length of the line segments at the system’s current configuration.
-
TapeMeasure.
length_dq
(q1)¶ Parameters: q1 ( Config
) – Derivative variableReturn type: Float
Calculate the derivative of the length with respect to the value of q1.
-
TapeMeasure.
length_dqdq
(q1, q2)¶ Parameters: Return type: 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)¶ Parameters: Return type: 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
()¶ Return type: Float
-
TapeMeasure.
velocity_dq
(q1)¶ Parameters: q1 ( Config
) – Derivative variableReturn type: Float
Calculate the derivative of the velocity with respect to the value of q1.
-
TapeMeasure.
velocity_ddq
(dq1)¶ Parameters: dq1 ( Config
) – Derivative variableReturn type: Float
Calculate the derivative of the velocity with respect to the velocity of q1.
-
TapeMeasure.
velocity_dqdq
(q1, q2)¶ Parameters: Return type: Float
Calculate the second derivative of the velocity with respect to the value of q1 and the value of q2.
Visualization¶
-
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 theSystem
.This method can be called by constraints, forces, and potentials that are based on the
TapeMeasure
.
Verifying Derivatives¶
-
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
, andForce
,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 aTapeMeasure
and having trouble.