92 lines
3.4 KiB
Matlab
92 lines
3.4 KiB
Matlab
function [taulist]= get_rb_dynamics(thetalist, dthetalist, ddthetalist, g,...
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dh_list, mass_list, mass_center_list, inertia_tensor_list, f_tip)
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%---------变量定义-----------------
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% thetalist:6x1,关节变量，dthetalist:6x1,关节变量一阶导数, ddthetalist:6x1,关节变量二阶导数
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% g: 1x1,重力加速度
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% dh_list:6x4,modified_DH参数
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% mass_list:6x1,连杆质量，mass_center_list:6x3,连杆质心相对于坐标系{i}坐标，
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% inertia_tensor_list: 3x3x6,连杆相对于质心坐标系的惯量张量
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% f_tip: 2x3,机械臂末端施加外力和力矩
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%taulist:6x1,各关节所需力矩
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%R：3x3x6,旋转矩阵，P：3x6,后一连杆坐标系在前一连杆坐标系中的位置
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%w：3x6,连杆角速度，dw：3x6,连杆角加速度，dv：3x6,连杆线加速度，dvc：3x6,连杆质心线加速度
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%Ic:3x3x6,等同于inertia_tensor_list
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%Pc:3x6, mass_center_list的转置
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%F:3x6,各轴所受合力，N:3x6,各轴所受合力矩
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%f:3x6,前一轴给后一轴的力，n:3x6,前一轴给后一轴的力矩
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dof_num = size(dthetalist,1);
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alpha = dh_list(:,1);
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a = dh_list(:,2);
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d = dh_list(:,3);
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theta = dh_list(:,4);
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m = mass_list;
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Pc = mass_center_list';
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Ic = inertia_tensor_list;
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Z=[0;0;1];
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%转换矩阵建立
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theta = theta + thetalist;
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T=zeros(4,4,dof_num);R=zeros(3,3,dof_num);P=zeros(3,dof_num);
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for i=1:dof_num
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T(:,:,i)=[cos(theta(i)) -sin(theta(i)) 0 a(i)
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sin(theta(i))*cos(alpha(i)) cos(theta(i))*cos(alpha(i)) -sin(alpha(i)) -d(i)*sin(alpha(i))
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sin(theta(i))*sin(alpha(i)) cos(theta(i))*sin(alpha(i)) cos(alpha(i)) d(i)*cos(alpha(i))
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0 0 0 1];
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R(:,:,i)=T(1:3,1:3,i);
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P(:,i)=T(1:3,4,i);
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end
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TT = eye(4,4);
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for i = 1:dof_num
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TT = TT*T(:,:,i);
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end
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%运动学正向递推
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w0 = zeros(3,1); dw0 = zeros(3,1);
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dv0 = [0;0;g];
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w = zeros(3,dof_num); dw = zeros(3,dof_num);
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dv = zeros(3,dof_num); dvc = zeros(3,dof_num);
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F = zeros(3,dof_num); N = zeros(3,dof_num);
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%i = 0
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w(:,1) = R(:,:,1)' * w0 + dthetalist(1) * Z;
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dw(:,1) = R(:,:,1)' * dw0 + cross(R(:,:,1)' * w0, dthetalist(1) * Z) + ddthetalist(1) * Z;
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dv(:,1) = R(:,:,1)' * (cross(dw0,P(:,1)) + cross(w0,cross(w0, P(:,1))) + dv0);
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dvc(:,1) = cross(dw(:,1), Pc(:,1))+cross(w(:,1), cross(w(:,1), Pc(:,1))) + dv(:,1);
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for i = 1:dof_num-1
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w(:,i+1) = R(:,:,i+1)' * w(:,i) + dthetalist(i+1) * Z ;
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dw(:,i+1) = R(:,:,i+1)' * dw(:,i) + cross(R(:,:,i+1)' * w(:,i), dthetalist(i+1) * Z)+ ddthetalist(i+1) * Z;
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dv(:,i+1) = R(:,:,i+1)' * (cross(dw(:,i), P(:,i+1)) + cross(w(:,i), cross(w(:,i), P(:,i+1))) + dv(:,i));
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dvc(:,i+1) = cross(dw(:,i+1), Pc(:,i+1)) + cross(w(:,i+1), cross(w(:,i+1), Pc(:,i+1))) + dv(:,i+1);
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end
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for i = 1:dof_num
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F(:,i)=m(i)*dvc(:,i) ;
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N(:,i)=Ic(:,:,i) * dw(:,i) + cross(w(:,i), Ic(:,:,i) * w(:,i));
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end
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%动力学逆向递推
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%先计算杆6的力和力矩
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taulist = zeros(dof_num,1);
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f=zeros(3,dof_num); n=zeros(3,dof_num);
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f(:,dof_num) = F(:,dof_num) + f_tip(1,:)';
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n(:,dof_num) = N(:,dof_num) + f_tip(2,:)' + cross(Pc(:,dof_num), F(:,dof_num));
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taulist(dof_num) = n(:,dof_num)' * Z;
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%再计算杆5到1的力和力矩
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for i=dof_num-1:-1:1
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f(:,i) = R(:,:,i+1) * f(:,i+1) + F(:,i);
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n(:,i) = N(:,i) + R(:,:,i+1) * n(:,i+1) + cross(Pc(:,i), F(:,i))...
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+ cross(P(:,i+1), R(:,:,i+1) * f(:,i+1));
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taulist(i) = n(:,i)' * Z;
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end
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end |