Code covered by the BSD License  

Highlights from
Kinematic/Dynamic Control of a Two Link Manipulator

image thumbnail

Kinematic/Dynamic Control of a Two Link Manipulator

by

 

29 Apr 2009 (Updated )

Kinematic and Dynamic models of a Two Link Manipulator undergo non-linear feedback linearization.

[dX]=KIN_CLTS(t,X)
%% KINEMATIC ANALYSIS CLOSED LOOP TASK SPACE CONTROL

% Course: Robotic Manipulation and Mobility
% Advisor: Dr. V. Krovi
%
% Homework Number: 4
%
% Names: Sourish Chakravarty
% 	Hrishi Lalit Shah

function [dX]=KIN_CLTS(t,X)

global l1 l2 lc1 lc2 j1 j2 m1 m2 g rx ry ell_an w Kp Kx Kp1 Kd1 A B % Given parameters
global itr Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 t1 t2 t3 t4 t5 t6 t7 t8

th1=X(1);
th2=X(2);

%% Trajectory information
R1=rx;
R2=ry;
r=ell_an;

x_des= A + R1*cos(w*t)*cos(r)-R2*sin(w*t)*sin(r);
y_des= B + R1*cos(w*t)*sin(r)+R2*sin(w*t)*cos(r);

xd_des= -R1*w*sin(w*t)*cos(r)-R2*w*cos(w*t)*sin(r);
yd_des= -R1*w*sin(w*t)*sin(r)+R2*w*cos(w*t)*cos(r);

xdd_des = -R1*(w^2)*cos(w*t)*cos(r)+R2*(w^2)*sin(w*t)*sin(r);
ydd_des = -R1*(w^2)*cos(w*t)*sin(r)-R2*(w^2)*sin(w*t)*cos(r);
% th_des=invbot_new([x_des, y_des]); % position in joint space
% th_des=invbot([x_des, y_des]); % position in joint space
th_des=invbot2([x_des, y_des],[th1, th2]); % position in joint space

% J=[-l1*sin(th_des(1)) -l2*sin(th_des(2));
%    l1*cos(th_des(1))  l2*cos(th_des(2))];
%% Simulation update
J=[-l1*sin(th1) -l2*sin(th2);
    l1*cos(th1)  l2*cos(th2)];
x1= l1*cos(th1) + l2*cos(th2);
y1= l1*sin(th1) + l2*sin(th2);

THD=inv(J)*([xd_des,yd_des]' + Kx*([x_des-x1;y_des-y1]) );
dX=THD;

%% Determining angular accelerations
th1d=THD(1);
th2d=THD(2);

Jdot= [-l1*cos(th1)*th1d, -l2*cos(th2)*th2d;
        -l1*sin(th1)*th1d, -l2*sin(th2)*th2d;];
    
THDD= inv(J)*([xdd_des;ydd_des] - Jdot*THD);    


%% Storage
itr=itr+1;
t3(itr)=t;
Q3(itr,1:2) = [th1, th2];
Q3(itr,3:4) = [th1d, th2d];
Q3(itr, 5:6) = [THDD]';

Contact us