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

Ranjeet Kumbhar; Rajmeet Singh; Appaso M Gadade; Ashish Singla; Irfan Hussain

cs.ROApr 4, 2026

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

Authors: Ranjeet Kumbhar, Rajmeet Singh, Appaso M Gadade, Ashish Singla, Irfan Hussain

Organizations: Department of Mechanical Engineering Thapar Institute of Engineering and Technology Patiala, India · Khalifa University Center for Autonomous Robotic Systems (KUCARS) Khalifa University Abu Dhabi, UAE

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 & tables

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.

Link	Segment	L (mm)	m (kg)	CoM [x,y,z] (m)
L1	Backboard	380	0.358	$[0,\ 0.010,\ 0.086]$
L2	Hip rot. bracket	—	0.182	$[0,\ 0.059,\ 0]$
L3	Hip flex connector	—	0.054	$[0.003,\ 0.011,\ 0.003]$
L4	Hip joint conn.	—	0.068	$[0.003,\ 0.030,\ 0.007]$
L5	Thigh link	395	0.459	$[0,\ 0.148,\ 0]$
L6	Knee joint conn.	—	0.068	$[0.003,\ 0.030,\ 0.007]$

Table 1: Physical parameters of the lower limb exoskeleton links extracted from the CAD-integrated Simscape Multibody model (Al 6061-T6,

\rho=2700

kg/m 3 ).

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%).

Controller	Parameter	Hip	Knee	Ankle
PID	$K_{p}$ (Proportional)	120.0	150.0	80.0
	$K_{i}$ (Integral)	8.50	10.20	5.40
	$K_{d}$ (Derivative)	18.0	22.0	12.0
LQR	$Q_{11}$ (position weight)	200.0	280.0	120.0
	$Q_{22}$ (velocity weight)	10.0	14.0	6.0
	$R$ (control weight)	0.10	0.08	0.15

Table 2: Tuned control parameters of PID, LQR, and Hybrid PID-LQR controllers for sit-to-stand exoskeleton assistance.

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.

Figure 6: Transient response parameters: overshoot (%), rise time (s), and settling time (s), for the hip, knee, and ankle joints across all three controllers. Star markers indicate best-performing values per joint. The Hybrid PID-LQR achieves the lowest overshoot and settling time at all three joints, while maintaining comparable rise times.

Parameter	Joint	PID	LQR	Hybrid PID-LQR
Overshoot (%)	Hip	9.73	6.73	2.72
	Knee	12.85	8.94	2.39
	Ankle	20.32	14.47	6.10
Rise time (s)	Hip	0.843	0.863	0.883
	Knee	0.923	0.943	0.943
	Ankle	1.706	1.666	1.645

Table 3: Transient response parameters of PID, LQR, and Hybrid PID-LQR controllers for the sit-to-stand operation. Bold values indicate the best performance per joint per metric.

Figure 7: Simscape Multibody exoskeleton STS motion sequence under the proposed Hybrid PID-LQR controller, presenting five key postural configurations along the normalised motion timeline (0–100%): Seated, Push-Up, Mid-Stand, Stand, and Final Stand. The smooth and progressive transitions confirm stable postural evolution and accurate joint trajectory tracking throughout the full STS cycle.

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Sit-to-stand (STS) transitions impose significant joint-loading demands on elderly individuals, making them a primary target for lower-limb exoskeleton assistance. However, accurate trajectory tracking during STS is challenging due to complex, time-varying human exoskeleton interaction dynamics and inter-subject variability that render model-based control approaches difficult to apply in practice. This paper presents an intelligent model free adaptive backstepping control strategy for a bilateral lower-limb exoskeleton during STS motion. The proposed controller design uses an ultra-local second-order model to avoid explicit system identification, while a Gaussian radial basis function (RBF) neural network estimates the unknown lumped dynamics online. To further improve phase-aware tracking performance, a Twin Delayed Deep Deterministic Policy Gradient (TD3) reinforcement learning agent is integrated as a supervisory gain scheduler that adaptively adjusts controller gains across the distinct phases of STS motion. The proposed controller is evaluated through co-simulation in MATLAB/Simulink and Simscape Multibody using OpenSim-derived reference trajectories and benchmarked against state-of-the-art controllers. Results demonstrate that the proposed controller achieves the lowest average RMSE of 0.078 degree across all joints, representing improvements of 60.2%, 54.4%, 48.7%, and 42.6% over proportional integral derivative (PID), model-free adaptive control (MFAC), linear quadratic regulator (LQR), and sliding-mode control (SMC), respectively. TD3 integration further reduces tracking error by 35%, 33%, and 79% at the hip, knee, and ankle joints compared to the standalone RBF-MFAC baseline. These results demonstrate the effectiveness and robustness of the proposed controller design for assistive exoskeleton control during STS transitions.

Abstract

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