In physics‐based character animation, Proportional‐Derivative (PD) controllers are commonly used for tracking reference motions in motor control tasks. Stable PD (SPD) controllers significantly improve the numerical stability of traditional PD controllers and support large gains and large integration time steps during simulation [TLT11]. For an articulated rigid body system with n degrees of freedom, all SPD implementations to date, however, use an O(n3) dense matrix factorization based method. In this paper, we propose a linear time algorithm for SPD computation, which is based on Featherstone's forward dynamics formulation for articulated rigid body systems in generalized coordinates [Fea14]. We demonstrate the performance advantage of our algorithm by comparing with both the conventional dense matrix factorization based method and an alternative sparse matrix factorization based method. We show that the proposed algorithm provides superior stability when controlling complex models at large time steps. We further demonstrate that our algorithm can improve the learning speed and quality of a Deep Reinforcement Learning (DRL) system for physics‐based character animation.

中文翻译：

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用于基于物理的角色动画的线性时间稳定 PD 控制器

在基于物理的角色动画中，比例微分 (PD) 控制器通常用于跟踪电机控制任务中的参考运动。稳定 PD (SPD) 控制器显着提高了传统 PD 控制器的数值稳定性，并在仿真过程中支持大增益和大积分时间步长 [TLT11]。然而，对于具有 n 个自由度的铰接刚体系统，迄今为止的所有 SPD 实现都使用基于 O(n3) 密集矩阵分解的方法。在本文中，我们提出了一种用于 SPD 计算的线性时间算法，该算法基于 Featherstone 的广义坐标中铰接刚体系统的前向动力学公式 [Fea14]。我们通过与传统的基于密集矩阵分解的方法和基于稀疏矩阵分解的替代方法进行比较，证明了我们算法的性能优势。我们表明，所提出的算法在大时间步长控制复杂模型时提供了卓越的稳定性。我们进一步证明，我们的算法可以提高基于物理的角色动画的深度强化学习 (DRL) 系统的学习速度和质量。