This paper presents a novel approach using sensitivity analysis for generalizing Differential Dynamic Programming (DDP) to systems characterized by implicit dynamics, such as those modelled via inverse dynamics and variational or implicit integrators. It leads to a more general formulation of DDP, enabling for example the use of the faster recursive Newton-Euler inverse dynamics. We leverage the implicit formulation for precise and exact contact modelling in DDP, where we focus on two contributions: (1) Contact dynamics in acceleration level that enables high-order integration schemes; (2) Formulation using an invertible contact model in the forward pass and a closed form solution in the backward pass to improve the numerical resolution of contacts. The performance of the proposed framework is validated (1) by comparing implicit versus explicit DDP for the swing-up of a double pendulum, and (2) by planning motions for two tasks using a single leg model making multi-body contacts with the environment: standing up from ground, where a priori contact enumeration is challenging, and maintaining balance under an external perturbation.
翻译:本文介绍了一种新颖的方法,利用敏感性分析,将差异动态规划(DDP)普遍适用于具有隐含动态特征的系统,例如通过反动动态和变异或隐隐含整合器模拟的系统,从而将差异动态规划(DDP)普遍化为一种新颖的方法,从而更全面地拟订DDP,例如能够使用更快的递归式牛顿-欧勒反动态。我们利用隐含的公式,在DDP建立精确和精确的联系模型,我们侧重于两种贡献:(1) 加速级的接触动态,从而能够实现高度一体化计划;(2) 采用前方通道的不可忽略的接触模型和后方通道的封闭式解决方案来改进接触的数值分辨率。拟议框架的绩效得到验证:(1) 将隐含式和显性DDP对双弯曲进行对比,(2) 利用单一的腿模型规划两项任务的动议,使多体与环境接触:从地面站起,事先接触的查点具有挑战性,并在外部扰动下保持平衡。