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115 lines
3.4 KiB
115 lines
3.4 KiB
%TPOLY Generate scalar polynomial trajectory
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%
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% [S,SD,SDD] = TPOLY(S0, SF, M) is a scalar trajectory (Mx1) that varies
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% smoothly from S0 to SF in M steps using a quintic (5th order) polynomial.
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% Velocity and acceleration can be optionally returned as SD (Mx1) and SDD (Mx1).
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%
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% [S,SD,SDD] = TPOLY(S0, SF, T) as above but specifies the trajectory in
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% terms of the length of the time vector T (Mx1).
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%
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% Notes::
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% - If no output arguments are specified S, SD, and SDD are plotted.
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% Copyright (C) 1993-2011, by Peter I. Corke
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%
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% This file is part of The Robotics Toolbox for Matlab (RTB).
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%
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% RTB is free software: you can redistribute it and/or modify
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% it under the terms of the GNU Lesser General Public License as published by
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% the Free Software Foundation, either version 3 of the License, or
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% (at your option) any later version.
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%
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% RTB is distributed in the hope that it will be useful,
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% but WITHOUT ANY WARRANTY; without even the implied warranty of
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% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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% GNU Lesser General Public License for more details.
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%
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% You should have received a copy of the GNU Leser General Public License
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% along with RTB. If not, see <http://www.gnu.org/licenses/>.
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% [S,SD,SDD] = TPOLY(S0, SF, N, SD0, SDF) as above but specifies initial
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% and final joint velocity for the trajectory.
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%
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% [S,SD,SDD] = TPOLY(S0, SF, T, SD0, SDF) as above but specifies initial
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% and final joint velocity for the trajectory and time vector T.
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%
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% Notes::
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% - In all cases if no output arguments are specified S, SD, and SDD are plotted
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% against time.
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%
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% See also LSPB, JTRAJ.
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function [s,sd,sdd] = tpoly(q0, qf, t, qd0, qdf)
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t0 = t;
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if isscalar(t)
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t = (0:t-1)';
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else
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t = t(:);
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end
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if nargin < 4
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qd0 = 0;
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end
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if nargin < 5
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qdf = 0;
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end
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tf = max(t);
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% solve for the polynomial coefficients using least squares
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X = [
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0 0 0 0 0 1
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tf^5 tf^4 tf^3 tf^2 tf 1
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0 0 0 0 1 0
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5*tf^4 4*tf^3 3*tf^2 2*tf 1 0
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0 0 0 2 0 0
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20*tf^3 12*tf^2 6*tf 2 0 0
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];
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coeffs = (X \ [q0 qf qd0 qdf 0 0]')';
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% coefficients of derivatives
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coeffs_d = coeffs(1:5) .* (5:-1:1);
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coeffs_dd = coeffs_d(1:4) .* (4:-1:1);
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% evaluate the polynomials
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p = polyval(coeffs, t);
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pd = polyval(coeffs_d, t);
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pdd = polyval(coeffs_dd, t);
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switch nargout
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case 0
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if isscalar(t0)
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% for scalar time steps, axis is labeled 1 .. M
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xt = t+1;
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else
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% for vector time steps, axis is labeled by vector M
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xt = t;
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end
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clf
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subplot(311)
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plot(xt, p); grid; ylabel('s');
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subplot(312)
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plot(xt, pd); grid; ylabel('sd');
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subplot(313)
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plot(xt, pdd); grid; ylabel('sdd');
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if ~isscalar(t0)
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xlabel('time')
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else
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for c=get(gcf, 'Children');
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set(c, 'XLim', [1 t0]);
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end
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end
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shg
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case 1
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s = p;
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case 2
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s = p;
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sd = pd;
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case 3
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s = p;
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sd = pd;
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sdd = pdd;
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end
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