A Novel Hybrid PID-LQR Controller for Sit-To-Stand Assistance Using a CAD-Integrated Simscape Multibody Lower Limb Exoskeleton

Abstract

Precise control of lower limb exoskeletons during sit-to-stand (STS) transitions remains a central challenge in rehabilitation robotics owing to the highly nonlinear, time-varying dynamics of the human-exoskeleton system and the stringent trajectory tracking requirements imposed by clinical safety. This paper presents the systematic design, simulation, and comparative evaluation of three control strategies: a classical Proportional-Integral-Derivative (PID) controller, a Linear Quadratic Regulator (LQR), and a novel Hybrid PID-LQR controller applied to a bilateral lower limb exoskeleton performing the sit-to-stand transition. A high-fidelity, physics-based dynamic model of the exoskeleton is constructed by importing a SolidWorks CAD assembly directly into the MATLAB/Simulink Simscape Multibody environment, preserving accurate geometric and inertial properties of all links. Physiologically representative reference joint trajectories for the hip, knee, and ankle joints are generated using OpenSim musculoskeletal simulation and decomposed into three biomechanical phases: flexion-momentum (0-33%), momentum-transfer (34-66%), and extension (67-100%). The proposed Hybrid PID-LQR controller combines the optimal transient response of LQR with the integral disturbance rejection of PID through a tuned blending coefficient alpha = 0.65. Simulation results demonstrate that the Hybrid PID-LQR achieves RMSE reductions of 72.3% and 70.4% over PID at the hip and knee joints, respectively, reduces settling time by over 90% relative to PID across all joints, and limits overshoot to 2.39%-6.10%, confirming its superiority over both baseline strategies across all evaluated performance metrics and demonstrating strong translational potential for clinical assistive exoskeleton deployment.

Figures (7)

• Figure 1: Overall simulation framework for the exoskeleton control system. The mechanical model is designed in SolidWorks and imported into MATLAB/Simulink via Simscape Multibody, while joint reference trajectories ($q$, $\dot{q}$, $\ddot{q}$) are derived from OpenSim Moco gait data. The controller receives reference trajectories alongside feedback states ($q$, $\dot{q}$) from the Simscape model and computes the required joint torques ($\tau$) to drive the human-exoskeleton system through the STS transition.
• Figure 2: CAD-to-Simulink Simscape Multibody workflow for the bilateral lower limb exoskeleton. (Left) SolidWorks CAD assembly showing the bilateral kinematic chain with labeled rigid links L1--L9 and annotated revolute joints at the hip, knee, and ankle. (Center) Simscape Multibody Link toolbox import interface. (Right) Auto-generated Simscape Multibody block diagram with the Mechanics Explorer 3-D rendering inset.
• Figure 3: Sit-to-stand (STS) gait generation. (Left) Simscape Multibody simulation showing sequential postural configurations of the human-exoskeleton system from seated to full upright stance in the sagittal plane. (Right) Reference joint angle trajectories for the hip, knee, and ankle joints over normalised motion time (0--100%, total duration 3.0 s), with dashed vertical lines demarcating the three biomechanical phases: flexion-momentum (0--33%), momentum-transfer (34--66%), and extension (67--100%).
• Figure 4: Joint angle tracking (left column) and tracking error (right column) for the hip, knee, and ankle joints. The Hybrid PID-LQR controller (dotted green) most closely follows the OpenSim reference trajectory (solid black) across all three biomechanical phases, with the smallest tracking error throughout the STS motion cycle.
• Figure 5: Tracking accuracy comparison: (a) Root Mean Square Error (RMSE) and (b) Mean Absolute Error (MAE) per joint for PID, LQR, and Hybrid PID-LQR controllers. The Hybrid PID-LQR achieves the lowest values at all three joints, with improvements of up to 72.3% over PID at the hip joint.