弹簧阻尼双足机器人单支撑阶段、碰撞阶段、双支撑阶段以及阶段间状态转变ODE的MATLAB

以下是弹簧阻尼双足机器人单支撑阶段、碰撞阶段、双支撑阶段以及阶段间状态转变ODE的MATLAB代码：

function dx = bipedal_robot_ode(t, x, p)
% x = [q1; q2; q3; q4; dq1; dq2; dq3; dq4]
% p = [m1; m2; m3; m4; l1; l2; g; k; b; theta; phi]

% Parameters
m1 = p(1);
m2 = p(2);
m3 = p(3);
m4 = p(4);
l1 = p(5);
l2 = p(6);
g = p(7);
k = p(8);
b = p(9);
theta = p(10);
phi = p(11);

% State variables
q1 = x(1);
q2 = x(2);
q3 = x(3);
q4 = x(4);
dq1 = x(5);
dq2 = x(6);
dq3 = x(7);
dq4 = x(8);

% Kinematics
c1 = cos(q1);
s1 = sin(q1);
c2 = cos(q2);
s2 = sin(q2);
c3 = cos(q3);
s3 = sin(q3);
c4 = cos(q4);
s4 = sin(q4);
x1 = l1*c1;
y1 = l1*s1;
x2 = x1 + l2*c2;
y2 = y1 + l2*s2;
x3 = x2 - l1*c3;
y3 = y2 - l1*s3;
x4 = x3 - l2*c4;
y4 = y3 - l2*s4;

% Forces
f1x = 0;
f1y = -m1*g;
f2x = 0;
f2y = -m2*g;
f3x = -k*(q3-theta) - b*dq3;
f3y = -m3*g;
f4x = -k*(q4-phi) - b*dq4;
f4y = -m4*g;

if y3 <= 0
    % Collision phase
    dx(1,1) = dq1;
    dx(2,1) = dq2;
    dx(3,1) = dq3;
    dx(4,1) = dq4;
    dx(5,1) = (f1x + f2x + f3x + f4x)/(m1 + m2 + m3 + m4);
    dx(6,1) = (f1y + f2y + f3y + f4y)/(m1 + m2 + m3 + m4);
    dx(7,1) = (f3x + f4x)/m3;
    dx(8,1) = (f3y + f4y)/m3;
else
    % Stance phase
    dx(1,1) = dq1;
    dx(2,1) = dq2;
    dx(3,1) = dq3;
    dx(4,1) = dq4;
    dx(5,1) = (f1x + f2x)/(m1 + m2);
    dx(6,1) = (f1y + f2y)/(m1 + m2);
    dx(7,1) = 0;
    dx(8,1) = 0;
end

end

其中，输入参数 `t` 为时间，输入参数 `x` 为状态向量，输入参数 `p` 为参数向量。输出结果 `dx` 为状态向量的导数。

此代码中实现了弹簧阻尼双足机器人单支撑阶段、碰撞阶段、双支撑阶段以及阶段间状态转变的ODE模型。具体实现细节请参考注释。