89 lines
3.3 KiB
Matlab
89 lines
3.3 KiB
Matlab
% ---------------------------------------------------------------------
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% In this script trajectory optimization otherwise called experiment
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% design for dynamic paramters identification is carried out.
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% ---------------------------------------------------------------------
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run('main_ur.m'); % get robot description
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% Getting limits on posistion and velocities. Moreover we get some
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% constant parmeters of the robot that allow us to accelerate computation
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% of the robot regressor.
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q_min = zeros(6,1); q_max = zeros(6,1); qd_max = zeros(6,1);
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for i = 1:6
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rot_axes(:,i) = str2num(ur10.robot.joint{i}.axis.Attributes.xyz)';
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R_pj = RPY(str2num(ur10.robot.joint{i}.origin.Attributes.rpy));
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p_pj = str2num(ur10.robot.joint{i}.origin.Attributes.xyz)';
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T_pj(:,:,i) = [R_pj, p_pj; zeros(1,3), 1];
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r_com(:,i) = str2num(ur10.robot.link{i+1}.inertial.origin.Attributes.xyz)';
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q_min(i) = str2double(ur10.robot.joint{i}.limit.Attributes.lower);
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q_max(i) = str2double(ur10.robot.joint{i}.limit.Attributes.upper);
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qd_max(i) = str2double(ur10.robot.joint{i}.limit.Attributes.velocity);
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end
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ur10.rot_axes = rot_axes; % axis of rotation of each joint
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ur10.T_pj = T_pj;
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ur10.r_com = r_com;
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ur10.qd_max = qd_max;
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ur10.q2d_max = 2*ones(6,1);
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% Use different limit for positions for safety
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ur10.q_min = deg2rad([-180 -180 -90 -180 -90 -90]');
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ur10.q_max = deg2rad([180 0 90 0 90 90]');
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ur10.q0 = deg2rad([0 -90 0 -90 0 0 ]');
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% Trajectory parameters
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traj_par.T = 20; % period of signal
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traj_par.wf = 2*pi/traj_par.T; % fundamental frequency
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traj_par.t_smp = 1e-1; % sampling time
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traj_par.t = 0:traj_par.t_smp:traj_par.T; % time
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traj_par.N = 5; % number of harmonics
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% ------------------------------------------------------------------------
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% Otimization
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% ------------------------------------------------------------------------
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A = []; b = [];
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Aeq = []; beq = [];
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lb = []; ub = [];
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x0 = rand(6*2*traj_par.N,1);
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optns_pttrnSrch = optimoptions('patternsearch');
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optns_pttrnSrch.Display = 'iter';
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x = patternsearch(@(x)traj_cost_lgr(x,traj_par,ur10),x0,A,b,Aeq,beq,lb,ub,...
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@(x)traj_cnstr(x,traj_par,ur10), optns_pttrnSrch);
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return
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options = optimoptions('ga');
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options.Display = 'iter';
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options.PlotFcn = 'gaplotbestf'; % {'gaplotbestf', 'gaplotscores'}
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options.MaxGenerations = 50;
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options.PopulationSize = 1e+3; % in each generation.
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options.InitialPopulationRange = [-100; 100];
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options.SelectionFcn = 'selectionroulette';
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[x,fval,exitflag,output,population,scores] = ga(@(x)traj_cost(x,traj_par,ur10),...
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6*2*traj_par.N,A,b,Aeq,beq,lb,ub,@(x)traj_cnstr(x,traj_par,ur10),options);
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%% ------------------------------------------------------------------------
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% Verifying obtained trajectory
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% ------------------------------------------------------------------------
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ab = reshape(x,[12,traj_par.N]);
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a = ab(1:6,:); % sin coeffs
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b = ab(7:12,:); % cos coeffs
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c_pol = pol_coeffs(traj_par.T,a,b,traj_par.wf,traj_par.N); % polynomial coeffs
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[q,qd,q2d] = mixed_traj(traj_par.t,c_pol,a,b,traj_par.wf,traj_par.N);
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traj_cnstr(x,traj_par,ur10)
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figure
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subplot(3,1,1)
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plot(traj_par.t,q)
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legend('q1','q2','q3','q4','q5','q6')
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subplot(3,1,2)
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plot(traj_par.t,qd)
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legend('qd1','qd2','qd3','qd4','qd5','qd6')
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subplot(3,1,3)
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plot(traj_par.t,q2d)
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legend('q2d1','q2d2','q2d3','q2d4','q2d5','q2d6') |