提出新算法解决带非线性等式约束的最优控制问题
Line-Search Filter Differential Dynamic Programming for Optimal Control with Nonlinear Equality Constraints
- 用滤波器+线搜索处理等式约束，不依赖传统罚函数
- 采用拉格朗日量作为步长接受标准，提升稳定性
- 适用于机器人接触隐式轨迹优化，收敛快且鲁棒
我们提出FilterDDP，一种用于求解离散时间最优控制问题（OCPs）的微分动态规划算法，该问题包含非线性等式约束。与基于增广拉格朗日或目标函数的已有方法不同，FilterDDP结合线搜索与步长滤波器来处理等式约束。我们识别出两个关键设计选择以实现稳健的数值性能：1）在步长接受准则中使用拉格朗日量而非代价函数；2）在后向传播中扰动值函数的海森矩阵。后者通过严格的局部二次收敛性证明得到形式化支持。此外，我们还提供了针对同时含等式和不等式约束的OCPs的原对偶内点扩展。我们在三个机器人接触隐式轨迹优化问题上验证了FilterDDP的有效性。
原文摘要 · Abstract (English)
We present FilterDDP, a differential dynamic programming algorithm for solving discrete-time, optimal control problems (OCPs) with nonlinear equality constraints. Unlike prior methods based on merit functions or the augmented Lagrangian class of algorithms, FilterDDP uses a step filter in conjunction with a line search to handle equality constraints. We identify two important design choices for the step filter criteria which lead to robust numerical performance: 1) we use the Lagrangian instead of the cost in the step acceptance criterion and, 2) in the backward pass, we perturb the value function Hessian. Both choices are rigorously justified, for 2) in particular by a formal proof of local quadratic convergence. In addition to providing a primal-dual interior point extension for handling OCPs with both equality and inequality constraints, we validate FilterDDP on three contact implicit trajectory optimisation problems which arise in robotics.
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