170 lines
6.8 KiB
Matlab
170 lines
6.8 KiB
Matlab
function sol = estimate_dynamic_params(path_to_data, idx, drvGains, baseQR, method)
|
|
% -----------------------------------------------------------------------
|
|
% In this script identification of inertial parameters of the UR10E
|
|
% is carried out. Two approaches are implemented: ordinary least squares
|
|
% and ordinary least squares with physical feasibility constraint.
|
|
% Moreover, statistical analysis of the estimated parmaeters is performed
|
|
%
|
|
% Inputs:
|
|
% path_to_data - measured data from the robot
|
|
% idx - specifies indeces for data to be used in estimation. Used
|
|
% to remove garbage data
|
|
% drvGains - drive gains
|
|
% baseQR - QR decomposition of the observation matrix used for
|
|
% calculatung base regressor
|
|
% method - method for estimation. Could be OLS or PC-OLS
|
|
%
|
|
% Ouputs:
|
|
% sol - structre with the estimate and its statistical abalysis
|
|
% sol.pi_b - estimated base parameters
|
|
% sol.pi_fr - estimated friction parameters
|
|
% sol.pi_s - estimated standard parameters only if PC-OLS was used
|
|
% sol.std - standard deviation of the estimated parameters
|
|
% sol.rel_std - relative standatrd deviation of the estimated parameters
|
|
% -----------------------------------------------------------------------
|
|
|
|
% ------------------------------------------------------------------------
|
|
% Load raw data and procces it (filter and estimate accelerations).
|
|
% A lot of different trajectories were recorded for identificatio. Each of
|
|
% them result in slightly different dynamic parameters. Some of them
|
|
% describe the dynamics better than others.
|
|
% ------------------------------------------------------------------------
|
|
idntfcnTrjctry = parseURData(path_to_data, idx(1), idx(2));
|
|
idntfcnTrjctry = filterData(idntfcnTrjctry);
|
|
|
|
% -------------------------------------------------------------------
|
|
% Generate Regressors based on data
|
|
% ------------------------------------------------------------------------
|
|
[Tau, Wb] = buildObservationMatrices(idntfcnTrjctry, baseQR, drvGains);
|
|
|
|
% ---------------------------------------------------------------------
|
|
% Estimate parameters
|
|
% ---------------------------------------------------------------------
|
|
sol = struct;
|
|
if strcmp(method, 'OLS')
|
|
% Usual least squares
|
|
[sol.pi_b, sol.pi_fr] = ordinaryLeastSquareEstimation(Tau, Wb);
|
|
elseif strcmp(method, 'PC-OLS')
|
|
% Physically consistent OLS using SDP optimization
|
|
[sol.pi_b, sol.pi_fr, sol.pi_s] = physicallyConsistentEstimation(Tau, Wb, baseQR);
|
|
else
|
|
error("Chosen method for dynamic parameter estimation does not exist");
|
|
end
|
|
|
|
% ------------------------------------------------------------------
|
|
% Statistical analysis
|
|
% -----------------------------------------------------------------
|
|
% unbiased estimation of the standard deviation
|
|
sqrd_sgma_e = norm(Tau - Wb*[sol.pi_b; sol.pi_fr], 2)^2/...
|
|
(size(Wb, 1) - size(Wb, 2));
|
|
|
|
% the covariance matrix of the estimation error
|
|
Cpi = sqrd_sgma_e*inv(Wb'*Wb);
|
|
sol.std = sqrt(diag(Cpi));
|
|
|
|
% relative standard deviation
|
|
sol.rel_std = 100*sol.std./abs([sol.pi_b; sol.pi_fr]);
|
|
end
|
|
|
|
|
|
% Local unctions
|
|
function [Tau, Wb] = buildObservationMatrices(idntfcnTrjctry, baseQR, drvGains)
|
|
% The function builds observation matrix for UR10E
|
|
E1 = baseQR.permutationMatrix(:,1:baseQR.numberOfBaseParameters);
|
|
|
|
Wb = []; Tau = [];
|
|
for i = 1:1:length(idntfcnTrjctry.t)
|
|
Yi = regressorWithMotorDynamics(idntfcnTrjctry.q(i,:)',...
|
|
idntfcnTrjctry.qd_fltrd(i,:)',...
|
|
idntfcnTrjctry.q2d_est(i,:)');
|
|
Yfrctni = frictionRegressor(idntfcnTrjctry.qd_fltrd(i,:)');
|
|
Ybi = [Yi*E1, Yfrctni];
|
|
|
|
Wb = vertcat(Wb, Ybi);
|
|
Tau = vertcat(Tau, diag(drvGains)*idntfcnTrjctry.i_fltrd(i,:)');
|
|
end
|
|
end
|
|
|
|
|
|
function [pib_OLS, pifrctn_OLS] = ordinaryLeastSquareEstimation(Tau, Wb)
|
|
% Function perfroms ordinary least squares estimation of parameters
|
|
pi_OLS = (Wb'*Wb)\(Wb'*Tau);
|
|
|
|
pib_OLS = pi_OLS(1:40); % variables for base paramters
|
|
pifrctn_OLS = pi_OLS(41:end);
|
|
end
|
|
|
|
|
|
function [pib_SDP, pifrctn_SDP, pi_full] = physicallyConsistentEstimation(Tau, Wb, baseQR)
|
|
% Function estimation physically consistent parameters
|
|
% Ideally the user can choose between physical consistency and
|
|
% so called semi-physical consistency, but right now it is hardcoded
|
|
physicalConsistency = 1;
|
|
|
|
pi_frctn = sdpvar(18,1); % variables for dependent parameters
|
|
pi_b = sdpvar(baseQR.numberOfBaseParameters,1); % variables for base paramters
|
|
pi_d = sdpvar(26,1); % variables for dependent paramters
|
|
|
|
% Bijective mapping from [pi_b; pi_d] to standard parameters pi
|
|
pii = baseQR.permutationMatrix*[eye(baseQR.numberOfBaseParameters), ...
|
|
-baseQR.beta; ...
|
|
zeros(26,baseQR.numberOfBaseParameters), ...
|
|
eye(26) ]*[pi_b; pi_d];
|
|
|
|
% Feasibility contrraints of the link paramteres and rotor inertia
|
|
mass_indexes = 10:11:66;
|
|
massValuesURDF = [7.778 12.93 3.87 1.96 1.96 0.202]';
|
|
errorRange = 0.10;
|
|
massUpperBound = massValuesURDF*(1 + errorRange);
|
|
|
|
cnstr = [];
|
|
for i = 1:6
|
|
cnstr = [cnstr, pii(mass_indexes(i))> 0, ...
|
|
pii(mass_indexes(i)) < massUpperBound(i)];
|
|
end
|
|
|
|
if physicalConsistency
|
|
for i = 1:11:66
|
|
link_inertia_i = [pii(i), pii(i+1), pii(i+2); ...
|
|
pii(i+1), pii(i+3), pii(i+4); ...
|
|
pii(i+2), pii(i+4), pii(i+5)];
|
|
frst_mmnt_i = pii(i+6:i+8);
|
|
|
|
Di = [0.5*trace(link_inertia_i)*eye(3) - link_inertia_i, ...
|
|
frst_mmnt_i; frst_mmnt_i', pii(i+9)];
|
|
|
|
cnstr = [cnstr, Di>0, pii(i+10)>0];
|
|
end
|
|
else
|
|
for i = 1:11:66
|
|
link_inertia_i = [pii(i), pii(i+1), pii(i+2); ...
|
|
pii(i+1), pii(i+3), pii(i+4); ...
|
|
pii(i+2), pii(i+4), pii(i+5)];
|
|
|
|
frst_mmnt_i = vec2skewSymMat(pii(i+6:i+8));
|
|
|
|
Di = [link_inertia_i, frst_mmnt_i'; frst_mmnt_i, pii(i+9)*eye(3)];
|
|
cnstr = [cnstr, Di>0, pii(i+10)>0];
|
|
end
|
|
end
|
|
|
|
% Feasibility constraints on the friction prameters
|
|
for i = 1:6
|
|
cnstr = [cnstr, pi_frctn(3*i-2)>0, pi_frctn(3*i-1)>0];
|
|
end
|
|
|
|
% Defining pbjective function
|
|
obj = norm(Tau - Wb*[pi_b; pi_frctn]);
|
|
|
|
% Solving sdp problem
|
|
sol2 = optimize(cnstr, obj, sdpsettings('solver','sdpt3'));
|
|
|
|
pib_SDP = value(pi_b); % variables for base paramters
|
|
pifrctn_SDP = value(pi_frctn);
|
|
|
|
pi_full = baseQR.permutationMatrix*[eye(baseQR.numberOfBaseParameters), ...
|
|
-baseQR.beta; ...
|
|
zeros(26,baseQR.numberOfBaseParameters), ...
|
|
eye(26)]*[value(pi_b); value(pi_d)];
|
|
end
|