collocation method for trajectory optimization

Overview

• Direct collocation
• Trapezoidal Collocation
• Hermite–Simpson Collocation
• Orthogonal collocation

同时离散控制量和状态量,把状态方程当作等式约束

$$\begin{aligned}\min_{u^0 \cdots u^t, x^0 \cdots x^t}&\quad \sum(J(x^t)) \\ s.t. & \quad x^{t+1} = f(x^t, u^t)\end{aligned}$$

Trapezoidal Collocation

Hermite–Simpson Collocation

Orthogonal collocation

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