如何在 MATLAB 中正确使用 ode45 函数用于差动驱动机器人？

Question

我正在尝试使用 ode45 确定差动驱动机器人的位姿 (x,y,theta)。我下面的代码解决了 x 位置，但我遇到了初始条件的问题。我将它设置为 0，因为在时间 0 机器人被假定在原点，但我得到一个错误。如何设置 ode45 的初始条件以获得预期的输出？

我试图通过将初始条件设置为 41x1 零矩阵来制作与 dxdt 长度相同的初始条件向量，但我不理解输出，我不相信我做得正确。

% Given conditions for a differential drive robot:
B = 20; % (cm) distance along axle between centers of two wheels
r = 10; % (cm) diameter of both wheels
w_l = 5*sin(3*t); % (rad/s) angular rate of left wheel
w_r = 5*sin(3*t); % (rad/s) angular rate of right wheel
v_l = r*w_l; % (cm/s) velocity of left wheel
v_r = r*w_r; % (cm/s) velocity of right wheel
v = (v_r+v_l)/B; % (cm/s) velocity of robot
theta = 90; % constant orientation of robot since trajectory is straight

% Solve differential equation for x:
dxdt = v*cos(theta); % diff equaition for x
tspan = [0 20]; % time period to integrate over
x0 = 0; % initial condition since robot begins at origin
[t,x] = ode45(@(t,y) dxdt, tspan, x0);

我想在初始条件为0 的情况下求解0 到20 秒的微分方程dxdt。我希望输出给我一个从0 到20 的时间向量和一个x 的数组。我认为问题在于初始条件。 MATLAB 在实时编辑器中给我一个错误，告诉我“@(t,y)dxdt returns a vector of length 69, but the length of initial conditions vector is 1. The vector returned by @(t,y)dxdt and the initial conditions vector must have the same number of elements.”

Answer 1

问题不是初始条件。您需要将dxdt 定义为函数，即

% Define differential equation
function derivative = dxdt(t,y)

% Given conditions for a differential drive robot:
B = 20; % (cm) distance along axle between centers of two wheels
r = 10; % (cm) diameter of both wheels
w_l = 5*sin(3*t); % (rad/s) angular rate of left wheel
w_r = 5*sin(3*t); % (rad/s) angular rate of right wheel
v_l = r*w_l; % (cm/s) velocity of left wheel
v_r = r*w_r; % (cm/s) velocity of right wheel
v = (v_r+v_l)/B; % (cm/s) velocity of robot
theta = 90; % constant orientation of robot since trajectory is straight

derivative = v*cos(theta); % diff equation for x

end

那么当你使用ode45 时，你应该告诉它把t 和y 变量作为参数传递给dxdt 之类的

[t,x] = ode45(@(t,y) dxdt(t,y), tspan, x0);

这应该可以工作。在这种情况下，dxdt 只接受默认参数，你也可以这样写

[t,x] = ode45(@dxdt, tspan, x0);

你得到的错误表明你在某个时候将dxdt 变成了一个长度为 69 的向量，而当 MATLAB 将一个 t 和一个 y 传递给你的dxdt'功能'。每当你遇到这样的错误时，我建议把

clear all

`clearvars` % better than clear all - see am304's comment below

在脚本的顶部，以避免先前定义的变量污染您的工作区。