matlab中lspb,lspb.m · 丁益武/robotics-toolbox-matlab - Gitee.com

%LSPB Linear segment with parabolic blend

%

% [S,SD,SDD] = LSPB(S0, SF, M) is a scalar trajectory (Mx1) that varies

% smoothly from S0 to SF in M steps using a constant velocity segment and

% parabolic blends (a trapezoidal velocity profile). Velocity and

% acceleration can be optionally returned as SD (Mx1) and SDD (Mx1)

% respectively.

%

% [S,SD,SDD] = LSPB(S0, SF, M, V) as above but specifies the velocity of

% the linear segment which is normally computed automatically.

%

% [S,SD,SDD] = LSPB(S0, SF, T) as above but specifies the trajectory in

% terms of the length of the time vector T (Mx1).

%

% [S,SD,SDD] = LSPB(S0, SF, T, V) as above but specifies the velocity of

% the linear segment which is normally computed automatically and a time

% vector.

%

% LSPB(S0, SF, M, V) as above but plots S, SD and SDD versus time in a single

% figure.

%

% Notes::

% - If M is given

% - Velocity is in units of distance per trajectory step, not per second.

% - Acceleration is in units of distance per trajectory step squared, not

% per second squared.

% - If T is given then results are scaled to units of time.

% - The time vector T is assumed to be monotonically increasing, and time

% scaling is based on the first and last element.

% - For some values of V no solution is possible and an error is flagged.

%

% References::

% - Robotics, Vision & Control, Chap 3,

% P. Corke, Springer 2011.

%

% See also TPOLY, JTRAJ.

% Copyright (C) 1993-2017, by Peter I. Corke

%

% This file is part of The Robotics Toolbox for MATLAB (RTB).

%

% RTB is free software: you can redistribute it and/or modify

% it under the terms of the GNU Lesser General Public License as published by

% the Free Software Foundation, either version 3 of the License, or

% (at your option) any later version.

%

% RTB is distributed in the hope that it will be useful,

% but WITHOUT ANY WARRANTY; without even the implied warranty of

% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the

% GNU Lesser General Public License for more details.

%

% You should have received a copy of the GNU Leser General Public License

% along with RTB. If not, see .

%

% http://www.petercorke.com

%TODO

% add a 'dt' option, to convert to everything to units of seconds

function [s,sd,sdd] = lspb(q0, q1, t, V)

t0 = t;

if isscalar(t)

t = (0:t-1)';

else

t = t(:);

end

plotsargs = {'Markersize', 16};

tf = max(t(:));

if nargin < 4

% if velocity not specified, compute it

V = (q1-q0)/tf * 1.5;

else

V = abs(V) * sign(q1-q0);

if abs(V) < abs(q1-q0)/tf

error('V too small');

elseif abs(V) > 2*abs(q1-q0)/tf

error('V too big');

end

end

if q0 == q1

s = ones(size(t)) * q0;

sd = zeros(size(t));

sdd = zeros(size(t));

return

end

tb = (q0 - q1 + V*tf)/V;

a = V/tb;

p = zeros(length(t), 1);

pd = p;

pdd = p;

for i = 1:length(t)

tt = t(i);

if tt <= tb

% initial blend

p(i) = q0 + a/2*tt^2;

pd(i) = a*tt;

pdd(i) = a;

elseif tt <= (tf-tb)

% linear motion

p(i) = (q1+q0-V*tf)/2 + V*tt;

pd(i) = V;

pdd(i) = 0;

else

% final blend

p(i) = q1 - a/2*tf^2 + a*tf*tt - a/2*tt^2;

pd(i) = a*tf - a*tt;

pdd(i) = -a;

end

end

switch nargout

case 0

if isscalar(t0)

% for scalar time steps, axis is labeled 1 .. M

xt = t+1;

else

% for vector time steps, axis is labeled by vector M

xt = t;

end

clf

subplot(311)

% highlight the accel, coast, decel phases with different

% colored markers

hold on

%plot(xt, p);

k = t<= tb;

plot(xt(k), p(k), 'r.-', plotsargs{:});

k = (t>=tb) & (t<= (tf-tb));

plot(xt(k), p(k), 'b.-', plotsargs{:});

k = t>= (tf-tb);

plot(xt(k), p(k), 'g.-', plotsargs{:});

grid; ylabel('$s$', 'FontSize', 16, 'Interpreter','latex');

hold off

subplot(312)

plot(xt, pd, '.-', plotsargs{:});

grid;

if isscalar(t0)

ylabel('$ds/dk$', 'FontSize', 16, 'Interpreter','latex');

else

ylabel('$ds/dt$', 'FontSize', 16, 'Interpreter','latex');

end

subplot(313)

plot(xt, pdd, '.-', plotsargs{:});

grid;

if isscalar(t0)

ylabel('$ds^2/dk^2$', 'FontSize', 16, 'Interpreter','latex');

else

ylabel('$ds^2/dt^2$', 'FontSize', 16, 'Interpreter','latex');

end

if ~isscalar(t0)

xlabel('t (seconds)')

else

xlabel('k (step)');

for c=findobj(gcf, 'Type', 'axes')

set(c, 'XLim', [1 t0]);

end

end

shg

case 1

s = p;

case 2

s = p;

sd = pd;

case 3

s = p;

sd = pd;

sdd = pdd;

end

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