Statistical Calibration

Package for the kinematic calibration of mechanisms based on the covariance of sensor measurements and calibrated dimension.

Usage

The only exported method calibrate(f,Cp,Cq,p̄,Q̄,tol;kwargs...) takes as arguments

1. residual function of constraint equations f(p,q)=0 where p is a vector of calibrated dimesions and q a vector of sensor measurements
2. np x np and nq x nq covariance matrices for p and q respectively
3. vector of designed dimensions p̄ and a matrix Q̄ where each vector represents a measurement of q
4. vector (or number) tol determining the tolerance of individual (or all) constraint equation
5. kwargs in the form of stopping criteria for NLopt problems which are formulated internaly.

It's output are corrections p̂ and Q̂ the optimal value of f and the return code of the optimization ret.

Example

here is an example on a single arm measuring it's endpoint in 2D Cartesian coordinates

Installation

To install this package on your system simply paste

] add https://github.com/lieskjur/StatisticalCalibration.jl

into your julia repl

Algorithm and Approach information

The approach is based around the density function of a multivariate normal distribution. The problem itself is then defined by a quadratic objective function corresponding to the probability of the corrections and equality constraints in the form of the mechanism's kinematic constaints.

The objective function being quadratic the COBYLA algorithm is used for finding the optimization's solution.