刚体系统二阶微分动态规划的加速算法
Accelerating Second-Order Differential Dynamic Programming for Rigid-Body Systems
摘要：
本文提出了一种将二阶动力学灵敏度信息引入微分动态规划（DDP）轨迹优化算法的方法。DDP的方法开发的所有必要的衍生物计算具有相同的复杂性，在迭代线性二次调节器（iLQR）。与iLQR中使用的线性化模型相比，DDP更准确地表示局部动态，但由于动态的二阶导数是张量的且计算昂贵，因此不经常使用。这项工作展示了如何避免计算导数张量的需要，而是利用导数信息的反向模式累积来直接计算关键向量张量乘积。我们还展示了如何动态的结构可以用来进一步加速这些计算在刚体系统。多连杆机械手轨迹优化的基准测试表明，DDP的好处往往可以包括在不牺牲评估时间，可以在更少的迭代比iLQR。
英文摘要：
This letter presents a method to reduce the computational demands of including second-order dynamics sensitivity information into the Differential Dynamic Programming (DDP) trajectory optimization algorithm. An approach to DDP is developed where all the necessary derivatives are computed with the same complexity as in the iterative Linear Quadratic Regulator (iLQR). Compared to linearized models used in iLQR, DDP more accurately represents the dynamics locally, but it is not often used since the second-order derivatives of the dynamics are tensorial and expensive to compute. This work shows how to avoid the need for computing the derivative tensor by instead leveraging reverse-mode accumulation of derivative information to compute a key vector-tensor product directly. We also show how the structure of the dynamics can be used to further accelerate these computations in rigid-body systems. Benchmarks of this approach for trajectory optimization with multi-link manipulators show that the benefits of DDP can often be included without sacrificing evaluation time, and can be done in fewer iterations than iLQR.
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