参考线平滑设定

$$
x = f_i(t)
  = a_{i0} + a_{i1} * t + a_{i2} * t^2 + a_{i3} * t^3 + a_{i4} * t^4 + a_{i5} * t^5
$$

$$
y = g_i(t) = b_{i0} + b_{i1} * t + b_{i2} * t^2 + b_{i3} * t^3 + b_{i4} * t^4 + b_{i5} * t^5
$$

$$
cost = 
\sum_{i=1}^{n} 
\Big(
\int\limits_{0}^{t_i} (f_i''')^2(t) dt 
+ \int\limits_{0}^{t_i} (g_i''')^2(t) dt 
\Big)
$$

$$
\frac{1}{2} \cdot x^T \cdot H \cdot x + f^T \cdot x 
\\
s.t. LB \leq x \leq UB
\\
A_{eq}x = b_{eq}
\\
Ax \leq b
$$

$$
f_k(s_k) = f_{k+1} (s_0)
$$

$$
f'_k(s_k) = f'_{k+1} (s_0)
\\
f''_k(s_k) = f''_{k+1} (s_0)
\\
f'''_k(s_k) = f'''_{k+1} (s_0)
\\
g_k(s_k) = g_{k+1} (s_0)
\\
g'_k(s_k) = g'_{k+1} (s_0)
\\
g''_k(s_k) = g''_{k+1} (s_0)
\\
g'''_k(s_k) = g'''_{k+1} (s_0)
$$

$$
f_i(t_l) - x_l< boundary
\\
g_i(t_l) - y_l< boundary
$$