The idea is simple enough: given an initial guess at the input and state trajectory, make a linear approximation of the dynamics and a quadratic approximation of the cost function. Then compute and simulate the time-varying LQR controller to find a new input and state trajectory. Repeat until convergence.

原本 iLQR & SLQ 只支持无约束轨迹优化,为了处理约束条件,常采用 augmented-Lagrangian 或 relaxed barrier methods.