用四元数避免姿态奇异，让机器人跳跃更稳定
Robots with Attitude: Singularity-Free Quaternion-Based Model-Predictive Control for Agile Legged Robots
- 用单位四元数表示姿态，避开欧拉角的奇点问题
- 改进iLQR算法，实现快速稳定控制
- 在四足和人形机器人上验证了高效性
本文提出一种用于腿式机器人的模型预测控制（MPC）框架，通过使用无奇点的单位四元数参数化机器人姿态，避免了欧拉角在大角度旋转时出现的奇点问题。该方法对迭代线性二次调节器（iLQR）算法进行了修改，以处理由此带来的几何特性。算法推导仅依赖初等微积分与线性代数，刻意避免使用李群的抽象符号与记号。我们在四足和人形机器人上进行了多项实验，验证了该四元数MPC方法在性能与计算效率方面的优越性。
原文摘要 · Abstract (English)
We present a model-predictive control (MPC) framework for legged robots that avoids the singularities associated with common three-parameter attitude representations like Euler angles during large-angle rotations. Our method parameterizes the robot's attitude with singularity-free unit quaternions and makes modifications to the iterative linear-quadratic regulator (iLQR) algorithm to deal with the resulting geometry. The derivation of our algorithm requires only elementary calculus and linear algebra, deliberately avoiding the abstraction and notation of Lie groups. We demonstrate the performance and computational efficiency of quaternion MPC in several experiments on quadruped and humanoid robots.
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