Nataraj Raviraj, van den Bogert Antonie J
J Biomech Eng. 2017 Oct 1;139(10). doi: 10.1115/1.4037560.
The linear quadratic regulator (LQR) is a classical optimal control approach that can regulate gait dynamics about target kinematic trajectories. Exoskeletons to restore gait function have conventionally utilized time-varying proportional-derivative (PD) control of leg joints. But, these PD parameters are not uniquely optimized for whole-body (full-state) performance. The objective of this study was to investigate the effectiveness of LQR full-state feedback compared to PD control to maintain bipedal walking of a sagittal-plane computational model against force disturbances. Several LQR controllers were uniquely solved with feedback gains optimized for different levels of tracking capability versus control effort. The main implications to future exoskeleton control systems include (1) which LQR controllers out-perform PD controllers in walking maintenance and effort, (2) verifying that LQR desirably produces joint torques that oppose rapidly growing joint state errors, and (3) potentially equipping accurate sensing systems for nonjoint states such as hip-position and torso orientation. The LQR controllers capable of longer walk times than respective PD controllers also required less control effort. During sudden leg collapse, LQR desirably behaved like PD by generating feedback torques that opposed the direction of leg-joint errors. Feedback from nonjoint states contributed to over 50% of the LQR joint torques and appear critical for whole-body LQR control. While LQR control poses implementation challenges, such as more sensors for full-state feedback and operation near the desired trajectories, it offers significant performance advantages over PD control.
线性二次型调节器（LQR）是一种经典的最优控制方法，可围绕目标运动轨迹调节步态动力学。传统上，用于恢复步态功能的外骨骼采用腿部关节的时变比例微分（PD）控制。但是，这些PD参数并未针对全身（全状态）性能进行唯一优化。本研究的目的是研究与PD控制相比，LQR全状态反馈在保持矢状面计算模型的双足步行以抵抗力干扰方面的有效性。通过针对不同跟踪能力与控制努力水平优化反馈增益，唯一地求解了几种LQR控制器。对未来外骨骼控制系统的主要影响包括：（1）哪些LQR控制器在步行维持和努力方面优于PD控制器；（2）验证LQR理想地产生与快速增长的关节状态误差相反的关节扭矩；（3）潜在地为非关节状态配备精确的传感系统，如髋部位置和躯干方向。能够比相应PD控制器行走时间更长的LQR控制器也需要更少的控制努力。在腿部突然塌陷期间，LQR理想地表现得像PD，通过产生与腿部关节误差方向相反方向的反馈扭矩。来自非关节状态的反馈对LQR关节扭矩的贡献超过50%，并且对于全身LQR控制似乎至关重要。虽然LQR控制带来了实施挑战，例如用于全状态反馈的更多传感器以及在期望轨迹附近的操作，但它相对于PD控制具有显著的性能优势。
