论文标题
通过非convex最大耗散原理与接触的铰接体的隐式集成
Implicit Integration for Articulated Bodies with Contact via the Nonconvex Maximal Dissipation Principle
论文作者
论文摘要
我们提出了非凸最大耗散原理（NMDP），这是一种与同时接触的表达物体的时间集成方案。我们的方案通过最大耗散原理（MDP）解决了接触力。先前的MDP求解器通过凸编程来计算接触力，假设使用正向多步方案集成了线性化的动力学。取而代之的是，我们考虑使用向后集成方案进行时间集成到时间集成的非线性牛顿 - 欧拉动力学和MDP的耦合系统。我们表明，可以使用保证收敛的投影梯度方法有效地求解了方程式的耦合系统。我们通过预测四足机器人的几个运动轨迹来评估我们的方法。结果表明，我们的NMDP方案具有多种理想的属性，包括：（1）对新型接触模型的概括； （2）在较大的时间段尺寸下的出色稳定性； （3）在变化的时间步长下一致的轨迹产生。
We present non-convex maximal dissipation principle (NMDP), a time integration scheme for articulated bodies with simultaneous contacts. Our scheme resolves contact forces via the maximal dissipation principle (MDP). Prior MDP solvers compute contact forces via convex programming by assuming linearized dynamics integrated using the forward multistep scheme. Instead, we consider the coupled system of nonlinear Newton-Euler dynamics and MDP, which is time-integrated using the backward integration scheme. We show that the coupled system of equations can be solved efficiently using the projected gradient method with guaranteed convergence. We evaluate our method by predicting several locomotion trajectories for a quadruped robot. The results show that our NMDP scheme has several desirable properties including: (1) generalization to novel contact models; (2) superior stability under large timestep sizes; (3) consistent trajectory generation under varying timestep sizes.
