Differential dynamic programming with nonlinear constraints
Differential dynamic programming with nonlinear constraints
复制标题
具有非线性约束的微分动态规划
DOI：
--
复制
发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Kris K. Hauser
中科院分区：
文献类型：
--
作者：
Zhaoming Xie;C. K. Liu;Kris K. Hauser
微分动态规划(DDP)是解决非线性最优控制问题的一种广泛使用的轨迹优化技术，可以方便地处理非线性代价函数。但是，它既不处理状态约束，也不处理控制约束。本文提出了一种新的DDP公式，该公式能够适应状态和控制上的任意非线性不等式约束。标准DDP的主要观点是，值函数的二次近似可以使用递归后向传递来获得，然而递归公式只适用于无约束问题。该方法的主要技术贡献是在每个时间点识别了一组有效约束后，在存在非线性约束的情况下推导了递推二次逼近公式。这个公式被用在一种新的约束DDP(CDDP)算法中，该算法迭代地确定这些活动集，并保证收敛到局部最小值。在几个具有避障和控制约束的12维欠驱动最优控制问题上，CDDP被证明优于其他适应约束的方法。
Differential dynamic programming (DDP) is a widely used trajectory optimization technique that addresses nonlinear optimal control problems, and can readily handle nonlinear cost functions. However, it does not handle either state or control constraints. This paper presents a novel formulation of DDP that is able to accommodate arbitrary nonlinear inequality constraints on both state and control. The main insight in standard DDP is that a quadratic approximation of the value function can be derived using a recursive backward pass, however the recursive formulae are only valid for unconstrained problems. The main technical contribution of the presented method is a derivation of the recursive quadratic approximation formula in the presence of nonlinear constraints, after a set of active constraints has been identified at each point in time. This formula is used in a new Constrained-DDP (CDDP) algorithm that iteratively determines these active set and is guaranteed to converge toward a local minimum. CDDP is demonstrated on several underactuated optimal control problems up to 12D with obstacle avoidance and control constraints and is shown to outperform other methods for accommodating constraints.