Data Analysis and Validation

This script outlines the process for analyzing and validating the NED-2 repeatability dataset using https://docs.niryo.com/dev/pyniryo/v1.1.2/en/index.html.

This script is designed to evaluate the repeatability of a robotic system by executing a series of movements to a defined reference pose and measuring the deviation from this pose over multiple repetitions. The key steps include:

Defining a Reference Pose: Specifies a target position and orientation for the robot. Executing Movements: The robot is instructed to move to the reference pose multiple times. Recording Final Poses: After each movement, the final pose of the robot is recorded. Analyzing Deviations: The script calculates the deviation of each final pose from the reference pose, then computes the average deviation across all repetitions. This process helps in assessing the precision and reliability of the robot's positioning capabilities, critical aspects of robotic systems used in applications requiring high levels of accuracy.

Repeatability Capability Data Analysis

Given a NED-2 repeatability dataset D consisting of N samples, our objective is to divide this dataset into k equal sets for analysis, where k = 4. Let D_i represent the i^{th} set. The division process is as follows:

Data Ordering

Ensure all samples in D maintain their original order.

Set Division

For each sample n in D, assign it to set D_i, where i = n mod k and i belongs to the set [0, k-1].

Standard Deviation Calculation for Each Set

The standard deviation (SD) for each set D_i is calculated using the formula:

SD(D_i) = sqrt((1/(N_i - 1)) * sum((x_j - x̄)^2 from j=1 to N_i))

where:

• N_i is the number of samples in set D_i,
• x_j is the j^{th} sample in set D_i,
• x̄ is the mean of all samples in D_i.

Pooled Standard Deviation Calculation

The pooled standard deviation (SD_pooled) is calculated by combining the variances of all k sets, weighted by their degrees of freedom (N_i - 1), and then taking the square root. The formula is: