190 lines
6.7 KiB
Matlab
190 lines
6.7 KiB
Matlab
clc; clear all; close all;
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% ------------------------------------------------------------------------
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% Load data and procces it (filter and estimate accelerations)
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% ------------------------------------------------------------------------
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% idntfcnTrjctry = parseURData('ur-19_12_23_free.csv', 1, 2005);
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% idntfcnTrjctry = parseURData('ur-20_01_31-unload.csv', 300, 2623);
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% idntfcnTrjctry = parseURData('ur-20_02_06-20sec_5harm.csv', 545, 2417); % 713
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idntfcnTrjctry = parseURData('ur-20_02_05-20sec_8harm.csv', 320, 2310);
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% idntfcnTrjctry = parseURData('ur-20_02_06-20sec_10harm.csv', 713, 2800); % 713
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% idntfcnTrjctry = parseURData('ur-20_02_05-20sec_12harm.csv', 605, 2710);
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idntfcnTrjctry = filterData(idntfcnTrjctry);
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%{
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idntfcnTrjctry1 = parseURData('ur-20_02_05-20sec_8harm.csv', 320, 2310);
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idntfcnTrjctry2 = parseURData('ur-20_02_06-20sec_10harm.csv', 713, 2800);
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idntfcnTrjctry1 = filterData(idntfcnTrjctry1);
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idntfcnTrjctry2 = filterData(idntfcnTrjctry2);
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idntfcnTrjctry3.t = [idntfcnTrjctry1.t; idntfcnTrjctry2.t + idntfcnTrjctry1.t(end)];
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idntfcnTrjctry3.q = [idntfcnTrjctry1.q; idntfcnTrjctry2.q];
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idntfcnTrjctry3.qd_fltrd = [idntfcnTrjctry1.qd_fltrd; idntfcnTrjctry2.qd_fltrd];
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idntfcnTrjctry3.q2d_est = [idntfcnTrjctry1.q2d_est; idntfcnTrjctry2.q2d_est];
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idntfcnTrjctry3.i_fltrd = [idntfcnTrjctry1.i_fltrd; idntfcnTrjctry2.i_fltrd];
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%}
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% -------------------------------------------------------------------
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% Generate Regressors based on data
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% ------------------------------------------------------------------------
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% Load matrices that map standard set of paratmers to base parameters
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% load('full2base_mapping.mat');
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load('baseQR.mat'); % load mapping from full parameters to base parameters
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% load identified drive gains
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% load('driveGains.mat')
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drvGains = [14.87; 13.26; 11.13; 10.62; 11.03; 11.47]; % deLuca gains
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Tau = {}; Wb = {};
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[Tau{1}, Wb{1}] = buildObservationMatrices(idntfcnTrjctry, baseQR, drvGains);
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[Tau{2}, Wb{2}] = buildObservationMatrices(idntfcnTrjctry, baseQR, drvGains2);
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[Tau{3}, Wb{3}] = buildObservationMatrices(idntfcnTrjctry, baseQR, drvGains3);
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% Usual least squares
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[pib_OLS(:,1), pifrctn_OLS(:,1)] = ordinaryLeastSquareEstimation(Tau{1}, Wb{1});
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[pib_OLS(:,2), pifrctn_OLS(:,2)] = ordinaryLeastSquareEstimation(Tau{2}, Wb{2});
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[pib_OLS(:,3), pifrctn_OLS(:,3)] = ordinaryLeastSquareEstimation(Tau{3}, Wb{3});
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% Set-up SDP optimization procedure
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[pib_SDP(:,1), pifrctn_SDP(:,1)] = physicallyConsistentEstimation(Tau{1}, Wb{1}, baseQR);
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[pib_SDP(:,2), pifrctn_SDP(:,2)] = physicallyConsistentEstimation(Tau{2}, Wb{2}, baseQR);
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[pib_SDP(:,3), pifrctn_SDP(:,3)] = physicallyConsistentEstimation(Tau{3}, Wb{3}, baseQR);
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return
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%% Saving identified parameters
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pi_full = baseQR.permutationMatrix*[eye(baseQR.numberOfBaseParameters), ...
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-baseQR.beta; ...
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zeros(26,baseQR.numberOfBaseParameters), ...
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eye(26) ]*[value(pi_b); value(pi_d)];
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t1 = reshape(pi_full, [11, 6]);
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identifiedUR10E = struct;
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identifiedUR10E.baseParameters = pi_b;
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identifiedUR10E.standardParameters = pi_full;
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identifiedUR10E.linearFrictionParameters = pi_frctn;
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%% Statisitical analysis
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% unbiased estimation of the standard deviation
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sqrd_sgma_e = norm(Tau_uldd - Wb_uldd*[pi_b; pi_frctn], 2)^2/...
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(size(Wb_uldd, 1) - size(Wb_uldd, 2));
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% the covariance matrix of the estimation error
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Cpi = sqrd_sgma_e*inv(Wb_uldd'*Wb_uldd);
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sgma_pi = sqrt(diag(Cpi));
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% relative standard deviation
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sgma_pi_rltv = sgma_pi./abs([pi_b; pi_frctn]);
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%% Functions
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function [Tau, Wb] = buildObservationMatrices(idntfcnTrjctry, baseQR, drvGains)
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% --------------------------------------------------------------------
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% The function builds observation matrix for UR10E
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% --------------------------------------------------------------------
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E1 = baseQR.permutationMatrix(:,1:baseQR.numberOfBaseParameters);
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Wb = []; Tau = [];
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for i = 1:1:length(idntfcnTrjctry.t)
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Yi = regressorWithMotorDynamics(idntfcnTrjctry.q(i,:)',...
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idntfcnTrjctry.qd_fltrd(i,:)',...
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idntfcnTrjctry.q2d_est(i,:)');
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Yfrctni = frictionRegressor(idntfcnTrjctry.qd_fltrd(i,:)');
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Ybi = [Yi*E1, Yfrctni];
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Wb = vertcat(Wb, Ybi);
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Tau = vertcat(Tau, diag(drvGains)*idntfcnTrjctry.i_fltrd(i,:)');
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end
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end
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function [pib_OLS, pifrctn_OLS] = ordinaryLeastSquareEstimation(Tau, Wb)
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pi_OLS = (Wb'*Wb)\(Wb'*Tau);
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pib_OLS = pi_OLS(1:40); % variables for base paramters
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pifrctn_OLS = pi_OLS(41:end);
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end
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function [pib_SDP, pifrctn_SDP] = physicallyConsistentEstimation(Tau, Wb, baseQR)
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physicalConsistency = 1;
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pi_frctn = sdpvar(18,1); % variables for dependent parameters
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pi_b = sdpvar(baseQR.numberOfBaseParameters,1); % variables for base paramters
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pi_d = sdpvar(26,1); % variables for dependent paramters
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% Bijective mapping from [pi_b; pi_d] to standard parameters pi
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pii = baseQR.permutationMatrix*[eye(baseQR.numberOfBaseParameters), ...
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-baseQR.beta; ...
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zeros(26,baseQR.numberOfBaseParameters), ...
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eye(26) ]*[pi_b; pi_d];
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% Feasibility contrraints of the link paramteres and rotor inertia
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mass_indexes = 10:11:66;
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massValuesURDF = [7.778 12.93 3.87 1.96 1.96 0.202]';
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errorRange = 0.10;
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massUpperBound = massValuesURDF*(1 + errorRange);
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cnstr = [];
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for i = 1:6
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cnstr = [cnstr, pii(mass_indexes(i))> 0, ...
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pii(mass_indexes(i)) < massUpperBound(i)];
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end
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if physicalConsistency
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for i = 1:11:66
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link_inertia_i = [pii(i), pii(i+1), pii(i+2); ...
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pii(i+1), pii(i+3), pii(i+4); ...
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pii(i+2), pii(i+4), pii(i+5)];
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frst_mmnt_i = pii(i+6:i+8);
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Di = [0.5*trace(link_inertia_i)*eye(3) - link_inertia_i, ...
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frst_mmnt_i; frst_mmnt_i', pii(i+9)];
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cnstr = [cnstr, Di>0, pii(i+10)>0];
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end
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else
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for i = 1:11:66
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link_inertia_i = [pii(i), pii(i+1), pii(i+2); ...
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pii(i+1), pii(i+3), pii(i+4); ...
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pii(i+2), pii(i+4), pii(i+5)];
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frst_mmnt_i = vec2skewSymMat(pii(i+6:i+8));
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Di = [link_inertia_i, frst_mmnt_i'; frst_mmnt_i, pii(i+9)*eye(3)];
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cnstr = [cnstr, Di>0, pii(i+10)>0];
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end
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end
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% Feasibility constraints on the friction prameters
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for i = 1:6
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cnstr = [cnstr, pi_frctn(3*i-2)>0, pi_frctn(3*i-1)>0];
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end
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% Defining pbjective function
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obj = norm(Tau - Wb*[pi_b; pi_frctn]);
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% Solving sdp problem
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sol2 = optimize(cnstr, obj, sdpsettings('solver','sdpt3'));
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pib_SDP = value(pi_b); % variables for base paramters
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pifrctn_SDP = value(pi_frctn);
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end |