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symbolic_computing_M_unitree.m
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aaaaaa=1
sym_var=SymVariable('q',[18,1]);
dsym_var=SymVariable('dq',[18,1]);
q=[sym_var(1);sym_var(2);sym_var(3);sym_var(4);sym_var(5);sym_var(6);sym_var(7);...
sym_var(8);sym_var(9);sym_var(10);sym_var(11);sym_var(12);sym_var(13);
sym_var(14);sym_var(15);sym_var(16);sym_var(17);sym_var(18)];
dq=[dsym_var(1);dsym_var(2);dsym_var(3);dsym_var(4);dsym_var(5);dsym_var(6);...
dsym_var(7);dsym_var(8);dsym_var(9);dsym_var(10);dsym_var(11);dsym_var(12);
dsym_var(13);dsym_var(14);dsym_var(15);dsym_var(16);dsym_var(17);dsym_var(18)];
Aw2bp = [1 0 0 q(1);
0 1 0 q(2);
0 0 1 q(3);
0 0 0 1];
Rb_roll = [1 0 0 0;
0 cos(q(4)) -sin(q(4)) 0;
0 sin(q(4)) cos(q(4)) 0;
0 0 0 1];
Rb_pitch = [cos(q(5)) 0 sin(q(5)) 0;
0 1 0 0;
-sin(q(5)) 0 cos(q(5)) 0;
0 0 0 1];
Rb_yaw = [cos(q(6)) -sin(q(6)) 0 0;
sin(q(6)) cos(q(6)) 0 0;
0 0 1 0;
0 0 0 1];
Rb_rpy = Rb_yaw*Rb_pitch*Rb_roll;
%Rb_rpy = Rb_roll*Rb_pitch*Rb_yaw;
Aw2b = Aw2bp*Rb_rpy;
%% base frame to FL
Ab2FL_hip_p = [1 0 0 0.21935;
0 1 0 0.0875;
0 0 1 0;
0 0 0 1];
AFL_hip_p2FL_hip = [1 0 0 0;
0 cos(q(10)) -sin(q(10)) 0;
0 sin(q(10)) cos(q(10)) 0;
0 0 0 1];
Ab2FL_hip = Ab2FL_hip_p*AFL_hip_p2FL_hip;
AFL_hip2upper_leg_p = [1 0 0 0.0;
0 1 0 0.037;
0 0 1 0;
0 0 0 1];
Aupper_leg_p2upper_leg = [cos(q(11)) 0 sin(q(11)) 0;
0 1 0 0;
-sin(q(11)) 0 cos(q(11)) 0;
0 0 0 1];
AFL_hip2upper_leg = AFL_hip2upper_leg_p*Aupper_leg_p2upper_leg;
AFL_upper_leg2lower_leg_p = [1 0 0 0;
0 1 0 0;
0 0 1 -0.25;
0 0 0 1];
AFL_lower_leg_p2lower_leg = [cos(q(12)) 0 sin(q(12)) 0;
0 1 0 0;
-sin(q(12)) 0 cos(q(12)) 0;
0 0 0 1];
AFL_upper_leg2lower_leg = AFL_upper_leg2lower_leg_p*AFL_lower_leg_p2lower_leg;
AFL_lower_leg2foot = [1 0 0 0.0;
0 1 0 0;
0 0 1 -0.27; %taken from mesh file (30degree offset)
0 0 0 1];
Aw2hip_FL = Aw2b*Ab2FL_hip;
Aw2upper_leg_FL = Aw2hip_FL*AFL_hip2upper_leg;
Aw2lower_leg_FL = Aw2upper_leg_FL*AFL_upper_leg2lower_leg;
Aw2foot_FL = Aw2lower_leg_FL*AFL_lower_leg2foot;
FL11=Aw2foot_FL(1,1);
FL11=FL11(1);
FL21=Aw2foot_FL(2,1);
FL21=FL21(1);
FL31=Aw2foot_FL(3,1);
FL31=FL31(1);
FL32=Aw2foot_FL(3,2);
FL32=FL32(1);
FL33=Aw2foot_FL(3,3);
FL33=FL33(1);
FL_Yaw=atan2(FL21,FL11);
FL_Pitch=atan2(-FL31,sqrt(FL32*FL32+FL33*FL33));
FL_Roll=atan2(FL32,FL33);
FLFoot = [Aw2foot_FL(1,4);Aw2foot_FL(2,4);Aw2foot_FL(3,4)]; %Foot no. 1, for constraints
%% base frame to FR
Ab2FR_hip_p = [1 0 0 0.21935;
0 1 0 -0.0875;
0 0 1 0;
0 0 0 1];
AFR_hip_p2FR_hip = [1 0 0 0;
0 cos(q(7)) -sin(q(7)) 0;
0 sin(q(7)) cos(q(7)) 0;
0 0 0 1];
Ab2FR_hip = Ab2FR_hip_p*AFR_hip_p2FR_hip;
AFR_hip2upper_leg_p = [1 0 0 0;
0 1 0 -0.0370;
0 0 1 0;
0 0 0 1];
Aupper_leg_p2upper_leg = [cos(q(8)) 0 sin(q(8)) 0;
0 1 0 0;
-sin(q(8)) 0 cos(q(8)) 0;
0 0 0 1];
AFR_hip2upper_leg = AFR_hip2upper_leg_p*Aupper_leg_p2upper_leg;
AFR_upper_leg2lower_leg_p = [1 0 0 0.0;
0 1 0 0.0;
0 0 1 -0.250;
0 0 0 1];
AFR_lower_leg_p2lower_leg =[cos(q(9)) 0 sin(q(9)) 0;
0 1 0 0;
-sin(q(9)) 0 cos(q(9)) 0;
0 0 0 1];
AFR_upper_leg2lower_leg = AFR_upper_leg2lower_leg_p*AFR_lower_leg_p2lower_leg;
AFR_lower_leg2foot = [1 0 0 0.0;
0 1 0 0;
0 0 1 -0.27; %taken from mesh file
0 0 0 1];
Aw2hip = Aw2b*Ab2FR_hip;
Aw2upper_leg = Aw2hip*AFR_hip2upper_leg;
Aw2lower_leg = Aw2upper_leg*AFR_upper_leg2lower_leg;
Aw2foot_FR = Aw2lower_leg*AFR_lower_leg2foot;
FR11=Aw2foot_FR(1,1);
FR11=FR11(1);
FR21=Aw2foot_FR(2,1);
FR21=FR21(1);
FR31=Aw2foot_FR(3,1);
FR31=FR31(1);
FR32=Aw2foot_FR(3,2);
FR32=FR32(1);
FR33=Aw2foot_FR(3,3);
FR33=FR33(1);
FR_Yaw=atan2(FR21,FR11);
FR_Pitch=atan2(-FR31,sqrt(FR32*FR32+FR33*FR33));
FR_Roll=atan2(FR32,FR33);
FRFoot = [Aw2foot_FR(1,4);Aw2foot_FR(2,4);Aw2foot_FR(3,4)]; %Foot no. 2, For constraints
%% base frame to RL
Ab2RL_hip_p = [1 0 0 -0.21935;
0 1 0 0.0875;
0 0 1 0;
0 0 0 1];
ARL_hip_p2RL_hip = [1 0 0 0;
0 cos(q(16)) -sin(q(16)) 0;
0 sin(q(16)) cos(q(16)) 0;
0 0 0 1];
Ab2RL_hip = Ab2RL_hip_p*ARL_hip_p2RL_hip;
ARL_hip2upper_leg_p = [1 0 0 0;
0 1 0 0.0370;
0 0 1 0;
0 0 0 1];
Aupper_leg_p2upper_leg = [cos(q(17)) 0 sin(q(17)) 0;
0 1 0 0;
-sin(q(17)) 0 cos(q(17)) 0;
0 0 0 1];
ARL_hip2upper_leg = ARL_hip2upper_leg_p*Aupper_leg_p2upper_leg;
ARL_upper_leg2lower_leg_p = [1 0 0 0;
0 1 0 0;
0 0 1 -0.250;
0 0 0 1];
ARL_lower_leg_p2lower_leg = [cos(q(18)) 0 sin(q(18)) 0;
0 1 0 0;
-sin(q(18)) 0 cos(q(18)) 0;
0 0 0 1];
ARL_upper_leg2lower_leg = ARL_upper_leg2lower_leg_p*ARL_lower_leg_p2lower_leg;
ARL_lower_leg2foot = [1 0 0 0.0;
0 1 0 0;
0 0 1 -0.27; %taken from mesh file
0 0 0 1];
Aw2hip = Aw2b*Ab2RL_hip;
Aw2upper_leg = Aw2hip*ARL_hip2upper_leg;
Aw2lower_leg = Aw2upper_leg*ARL_upper_leg2lower_leg;
Aw2foot_RL = Aw2lower_leg*ARL_lower_leg2foot;
RL11=Aw2foot_RL(1,1);
RL11=RL11(1);
RL21=Aw2foot_RL(2,1);
RL21=RL21(1);
RL31=Aw2foot_RL(3,1);
RL31=RL31(1);
RL32=Aw2foot_RL(3,2);
RL32=RL32(1);
RL33=Aw2foot_RL(3,3);
RL33=RL33(1);
RL_Yaw=atan2(RL21,RL11);
RL_Pitch=atan2(-RL31,sqrt(RL32*RL32+RL33*RL33));
RL_Roll=atan2(RL32,RL33);
RLFoot = [Aw2foot_RL(1,4);Aw2foot_RL(2,4);Aw2foot_RL(3,4)]; %Foot no. 3, For constraints
%% base frame to RR
Ab2RR_hip_p = [1 0 0 -0.21935;
0 1 0 -0.0875;
0 0 1 0;
0 0 0 1];
ARR_hip_p2RR_hip = [1 0 0 0;
0 cos(q(13)) -sin(q(13)) 0;
0 sin(q(13)) cos(q(13)) 0;
0 0 0 1];
Ab2RR_hip = Ab2RR_hip_p*ARR_hip_p2RR_hip;
ARR_hip2upper_leg_p = [1 0 0 0;
0 1 0 -0.0370;
0 0 1 0;
0 0 0 1];
Aupper_leg_p2upper_leg = [cos(q(14)) 0 sin(q(14)) 0;
0 1 0 0;
-sin(q(14)) 0 cos(q(14)) 0;
0 0 0 1];
ARR_hip2upper_leg = ARR_hip2upper_leg_p*Aupper_leg_p2upper_leg;
ARR_upper_leg2lower_leg_p = [1 0 0 0;
0 1 0 0;
0 0 1 -0.250;
0 0 0 1];
ARR_lower_leg_p2lower_leg = [cos(q(15)) 0 sin(q(15)) 0;
0 1 0 0;
-sin(q(15)) 0 cos(q(15)) 0;
0 0 0 1];
ARR_upper_leg2lower_leg = ARR_upper_leg2lower_leg_p*ARR_lower_leg_p2lower_leg;
ARR_lower_leg2foot = [1 0 0 0.0;
0 1 0 0;
0 0 1 -0.27; %taken from mesh file
0 0 0 1];
Aw2hip = Aw2b*Ab2RR_hip;
Aw2upper_leg = Aw2hip*ARR_hip2upper_leg;
Aw2lower_leg = Aw2upper_leg*ARR_upper_leg2lower_leg;
Aw2foot_RR = Aw2lower_leg*ARR_lower_leg2foot;
RR11=Aw2foot_RR(1,1);
RR11=RR11(1);
RR21=Aw2foot_RR(2,1);
RR21=RR21(1);
RR31=Aw2foot_RR(3,1);
RR31=RR31(1);
RR32=Aw2foot_RR(3,2);
RR32=RR32(1);
RR33=Aw2foot_RR(3,3);
RR33=RR33(1);
RR_Yaw=atan2(RR21,RR11);
RR_Pitch=atan2(-RR31,sqrt(RR32*RR32+RR33*RR33));
RR_Roll=atan2(RR32,RR33);
RRFoot = [Aw2foot_RR(1,4);Aw2foot_RR(2,4);Aw2foot_RR(3,4)]; %Foot no. 4, For constraints
%%
foot = [FLFoot;FRFoot;RLFoot;RRFoot];
j_foot = jacobian(foot,sym_var);
d_foot = j_foot*dq;
%%
foot_fun = SymFunction('foot_func',foot,sym_var);
j_foot_fun = SymFunction('j_foot_func',j_foot,sym_var);
d_foot_fun = SymFunction('d_foot_func',d_foot,sym_var,dsym_var);
%%
export(foot_fun,'')
export(j_foot_fun,'')
export(d_foot_fun,'')