Simulation Analysis of Linear Quadratic Regulator Control of Sagittal-Plane Human Walking—Implications for Exoskeletons

Abstract

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.

Control Modification of Grasp Force Covaries Agency and Performance on Rigid and Compliant Surfaces

“…Advanced physical therapy may employ engaging platforms such as virtual reality (VR) ( Sveistrup, 2004 ) or robotics ( Saleh et al, 2017 ). Powered assistive devices may also be employed to restore function as with powered exoskeletons ( Lucas et al, 2004 ; Heo et al, 2012 ; Nataraj and van den Bogert, 2017 ) or neuroprostheses that activate sensorimotor pathways ( Marasco et al, 2018 ; Schofield et al, 2019 ) of the hand. The primary objective with assistive or rehabilitative technologies is to enhance control of the hand and increase functional ability to perform manual tasks.…”

“…Establishing the connection between agency and grasp could inspire the development of rehabilitation platforms that leverage agency for more effective control of grasp. These platforms would utilize agency to maximize classical performance objectives such as minimal effort or better movement tracking ( Nataraj and van den Bogert, 2017 ).…”

“…These control modes are consistent with parameters commonly adapted for powered devices such as setpoints for speed ( Blaya and Herr, 2004 ; Wege et al, 2005 ), noise mitigation ( Taylor et al, 2002 ; Agostini and Knaflitz, 2012 ), and automated assistance ( Ronsse et al, 2011 ). These parameters can be tuned ad hoc ( Terenzi, 1998 ) or identified through optimization of mechanical performance (e.g., effort, tracking) in a model system ( Davoodi et al, 2007 ; Nataraj and van den Bogert, 2017 ). This study may newly inspire a cognitive basis from which to adapt such parameters in the rehabilitation of grasp performance.…”

Agency and Performance of Reach-to-Grasp With Modified Control of a Virtual Hand: Implications for Rehabilitation

“…VR could be employed to match user intentions to optimal parameters for controlling a device using visual projections of device actions following user commands. Control parameters include feedback gains to maximize performance and minimize effort (Nataraj and van den Bogert, 2017) and to achieve desired movement features such as smoothness (Hogan and Sternad, 2009). Ultimately, VR platforms may be utilized to efficiently identify control parameters of rehabilitation devices that optimize not only functional mechanics but also user agency prior to eventual translation to real-world systems (Caldwell et al, 1995(Caldwell et al, , 1998Bar-Cohen, 2003;Perry et al, 2007).…”

“…Speed, noise, and automation are fundamental control parameters that a device engineer can ad hoc tune based on stated user preferences or anecdotal observation of performance (Terenzi, 1998). Alternatively, these parameters can also be determined through optimization of mechanical performance (e.g., effort, tracking) for a model system (Davoodi et al, 2007;Nataraj and van den Bogert, 2017). Neither approach systematically adapts the device according to user agency.…”