matlab局部路径规划五次多项式实例

以下是一个MATLAB实现五次多项式的局部路径规划的示例：

% 定义起点和终点
start_point = [0, 0];
end_point = [10, 10];

% 定义起点和终点的速度和加速度
start_velocity = 0;
end_velocity = 0;
start_acceleration = 0;
end_acceleration = 0;

% 定义时间间隔和轨迹长度
dt = 0.1;
trajectory_length = 100;

% 计算五次多项式系数
[a0, a1, a2, a3, a4, a5] = quintic_poly_coefficients(start_point(1), end_point(1), start_velocity, end_velocity, start_acceleration, end_acceleration, trajectory_length);

% 生成轨迹
trajectory_x = zeros(1, trajectory_length/dt);
trajectory_y = zeros(1, trajectory_length/dt);
for t = 0:dt:trajectory_length-dt
    s = t / trajectory_length;
    x = a0 + a1*s + a2*s^2 + a3*s^3 + a4*s^4 + a5*s^5;
    y = a0 + a1*s + a2*s^2 + a3*s^3 + a4*s^4 + a5*s^5;
    trajectory_x(1 + t/dt) = x;
    trajectory_y(1 + t/dt) = y;
end

% 绘制轨迹
plot(trajectory_x, trajectory_y);

该代码段使用`quintic_poly_coefficients`函数计算五次多项式系数，并使用这些系数生成轨迹。 `quintic_poly_coefficients`函数如下所示：

function [a0, a1, a2, a3, a4, a5] = quintic_poly_coefficients(start_pos, end_pos, start_vel, end_vel, start_acc, end_acc, duration)
% 计算五次多项式系数
% 输入参数：
% start_pos - 起点位置
% end_pos - 终点位置
% start_vel - 起点速度
% end_vel - 终点速度
% start_acc - 起点加速度
% end_acc - 终点加速度
% duration - 轨迹时间
% 输出参数：
% a0, a1, a2, a3, a4, a5 - 五次多项式系数

t0 = 0;
t1 = duration;
v0 = start_vel;
v1 = end_vel;
a0 = start_pos;
a1 = v0;
a2 = 0.5*start_acc;
a3 = (20*end_pos - 20*start_pos - (8*end_vel + 12*start_vel)*duration - (3*start_acc - end_acc)*duration^2)/(2*duration^3);
a4 = (30*start_pos - 30*end_pos + (14*end_vel + 16*start_vel)*duration + (3*start_acc - 2*end_acc)*duration^2)/(2*duration^4);
a5 = (12*end_pos - 12*start_pos - (6*end_vel + 6*start_vel)*duration - (start_acc - end_acc)*duration^2)/(2*duration^5);
end

该函数使用给定的起点、终点、速度和加速度计算五次多项式的系数，并返回这些系数。