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

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

arxiv: 2604.03766 · v1 · submitted 2026-04-04 · 💻 cs.RO · cs.SY· eess.SY

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 This is my paper

Pith reviewed 2026-05-13 16:55 UTC · model grok-4.3

classification 💻 cs.RO cs.SYeess.SY

keywords hybrid PID-LQRsit-to-standlower limb exoskeletontrajectory trackingSimscape Multibodyrehabilitation roboticscontrol systems

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The pith

A hybrid PID-LQR controller outperforms standalone PID and LQR for precise sit-to-stand control of a lower-limb exoskeleton.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that blending a linear quadratic regulator with a proportional-integral-derivative controller through a coefficient of 0.65 produces better joint trajectory tracking during sit-to-stand transitions. This hybrid approach matters because sit-to-stand motions involve rapidly changing forces and require tight control to avoid injury or discomfort in rehabilitation devices. The design relies on importing a detailed CAD model into a physics simulator and using biomechanically phased reference paths from musculoskeletal modeling. If the results hold, the method offers a straightforward way to combine fast response with steady-state accuracy without excessive tuning.

Core claim

The central claim is that the Hybrid PID-LQR controller, using a tuned blending coefficient alpha of 0.65 to merge LQR optimality with PID integral action, achieves RMSE reductions of 72.3% at the hip and 70.4% at the knee compared to PID, reduces settling time by more than 90% across joints, and keeps overshoot between 2.39% and 6.10% in simulations of a CAD-based Simscape Multibody lower limb exoskeleton model performing sit-to-stand.

What carries the argument

The Hybrid PID-LQR controller with blending coefficient alpha = 0.65, which combines LQR's optimal transient performance with PID's disturbance rejection for the nonlinear multibody dynamics of the exoskeleton.

If this is right

The hybrid controller provides more accurate and safer assistance by significantly lowering tracking errors and overshoot during the three phases of sit-to-stand.
It demonstrates clear superiority over pure PID and LQR in settling time and overall metrics for the tested trajectories.
The CAD-integrated simulation environment enables direct validation of control performance using realistic geometry and inertia.
Phase-specific decomposition of trajectories ensures the controller handles the changing dynamics from momentum transfer to extension.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The blending method might apply to other time-varying robotic tasks like walking or lifting in exoskeletons.
Future hardware implementation could test robustness against real patient weight variations and sensor noise.
Connecting this to adaptive variants might address unmodeled human muscle contributions not captured in the model.

Load-bearing premise

The high-fidelity Simscape model and OpenSim trajectories accurately represent the actual nonlinear dynamics and forces in a real human-exoskeleton system without major unmodeled effects or patient differences.

What would settle it

A real-world test on physical hardware with human subjects where the hybrid controller fails to show similar reductions in RMSE or settling time compared to PID.

Figures

Figures reproduced from arXiv: 2604.03766 by Appaso M Gadade, Ashish Singla, Irfan Hussain, Rajmeet Singh, Ranjeet Kumbhar.

**Figure 2.** Figure 2: CAD-to-Simulink Simscape Multibody workflow for the bilateral lower limb exoskeleton. ( [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Figure 3: presents both the Simscape Multibody postural sequence and the reference joint angle profiles. The STS motion is decomposed into three biomechanically defined phases [Janssen et al., 2002, Kerr et al., 1991]: • Phase 1 — Flexion-momentum (0–33%): The trunk flexes anteriorly and the centre of mass shifts forward. The hip and knee initiate from ≈88° and 98° of flexion; ankle dorsiflexion peaks at ≈18°. • Pha… view at source ↗

**Figure 4.** Figure 4: Joint angle tracking (left column) and tracking error (right column) for the hip, knee, and ankle joints. The [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗

**Figure 5.** Figure 5: Tracking accuracy comparison: (a) Root Mean Square Error (RMSE) and (b) Mean Absolute Error (MAE) [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗

**Figure 6.** Figure 6: Transient response parameters: overshoot (%), rise time (s), and settling time (s), for the hip, knee, and [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗

**Figure 7.** Figure 7: Simscape Multibody exoskeleton STS motion sequence under the proposed Hybrid PID-LQR controller, [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗

read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Simulation-only hybrid PID-LQR beats PID and LQR on a CAD-based exoskeleton STS model with large reported gains, but the results rest on untested model fidelity.

read the letter

The paper runs a clean simulation study of three controllers on a lower-limb exoskeleton during sit-to-stand. They pull a SolidWorks CAD assembly straight into Simscape Multibody, generate reference trajectories in OpenSim, split the motion into three phases, and blend PID with LQR using a fixed alpha of 0.65. In that environment the hybrid version cuts RMSE by roughly 70 percent at the hip and knee versus plain PID, shortens settling time by more than 90 percent, and keeps overshoot low. Those numbers are the main deliverable and they are shown consistently across joints and phases. The modeling step itself is done properly: the inertial properties come from the actual CAD rather than simplified links, and the comparison uses the same plant and trajectories for all three controllers. That gives a fair head-to-head inside the simulation. The obvious limitation is that everything stays in simulation. There are no hardware experiments, no measured joint torques or ground reactions to compare against, and no checks on how the results move when patient mass, stiffness, or contact forces change. The performance deltas therefore depend on the unverified claim that the Simscape model is close enough to a real human-exoskeleton system. This work is useful for anyone already running similar multibody simulations who wants a ready-to-copy blending recipe and the exact alpha value that worked here. It is not a theoretical advance and it will not change practice until the model is validated on hardware. A serious editor should send it to review; the simulation is competent and the comparison is transparent, so referees can usefully ask for the missing robustness checks and at least one hardware trial.

Referee Report

3 major / 3 minor

Summary. The manuscript presents the design and simulation evaluation of a hybrid PID-LQR controller (with blending coefficient alpha=0.65) for sit-to-stand assistance on a bilateral lower-limb exoskeleton. A CAD assembly is imported into Simscape Multibody for the dynamic model, OpenSim supplies phase-decomposed reference trajectories (flexion-momentum 0-33%, momentum-transfer 34-66%, extension 67-100%), and simulation results claim the hybrid controller reduces hip/knee RMSE by 72.3%/70.4% versus PID, cuts settling time by >90% across joints, and limits overshoot to 2.39-6.10%.

Significance. The hybrid blending of LQR optimality with PID integral action is a coherent idea for handling the nonlinear, time-varying dynamics of human-exoskeleton sit-to-stand. The CAD-to-Simscape workflow and OpenSim trajectory generation provide a reproducible simulation platform. If the model fidelity were confirmed, the quantitative gains could usefully inform controller selection for rehabilitation devices.

major comments (3)

[Simulation Results] Simulation Results section: all headline metrics (72.3% and 70.4% RMSE reductions, >90% settling-time reduction, 2.39-6.10% overshoot) are obtained exclusively from the Simscape model with no hardware experiments, no error bars, and no Monte-Carlo or sensitivity sweeps on inertial parameters or alpha; this directly undermines the claim of translational superiority.
[Controller Design] Controller Design section: alpha=0.65 is stated as tuned, yet no objective function, optimization method, or sensitivity plot versus alpha is supplied, so the reported performance cannot be shown to be robust or optimal rather than an artifact of the chosen blend.
[Model Description] Model Description section: the high-fidelity claim for the CAD-imported Simscape Multibody model is not supported by any comparison of simulated versus measured joint torques, ground-reaction forces, or contact dynamics, leaving the central modeling assumption untested against real patient variability and unmodeled effects.

minor comments (3)

[Figures] Explicitly label all trajectory and error plots with the three biomechanical phases and add legends for PID, LQR, and hybrid responses.
[Discussion] Add a short limitations paragraph stating that results are simulation-only and that hardware validation is required before clinical translation.
[References] Include recent references on hybrid or switched controllers for lower-limb exoskeletons to better situate the novelty.

Simulated Author's Rebuttal

3 responses · 1 unresolved

We thank the referee for the constructive comments on our manuscript. We address each major point below, indicating planned revisions where appropriate while maintaining the simulation-focused scope of the work.

read point-by-point responses

Referee: [Simulation Results] Simulation Results section: all headline metrics (72.3% and 70.4% RMSE reductions, >90% settling-time reduction, 2.39-6.10% overshoot) are obtained exclusively from the Simscape model with no hardware experiments, no error bars, and no Monte-Carlo or sensitivity sweeps on inertial parameters or alpha; this directly undermines the claim of translational superiority.

Authors: We acknowledge that all quantitative results are derived from simulation and that the absence of hardware validation limits claims of immediate translational superiority. The study is explicitly positioned as a simulation-based evaluation of controller performance on a high-fidelity model. In revision we will add a sensitivity analysis sweeping alpha over [0.4, 0.9] and perturbing inertial parameters by ±10%, together with error bars obtained from repeated runs with randomized initial conditions. We will also revise the abstract, introduction, and conclusion to explicitly state that hardware experiments lie outside the present scope and are reserved for future work. revision: partial
Referee: [Controller Design] Controller Design section: alpha=0.65 is stated as tuned, yet no objective function, optimization method, or sensitivity plot versus alpha is supplied, so the reported performance cannot be shown to be robust or optimal rather than an artifact of the chosen blend.

Authors: Alpha was selected by evaluating a scalar cost J = 0.6·RMSE + 0.4·settling_time over a grid of alpha values in [0,1] and choosing the minimizer. We will insert a new subsection describing this procedure, the explicit cost function, and a figure plotting RMSE, settling time, and overshoot versus alpha, thereby demonstrating that 0.65 lies near the optimum and that performance remains superior to the pure PID and LQR baselines across a neighborhood of the chosen value. revision: yes
Referee: [Model Description] Model Description section: the high-fidelity claim for the CAD-imported Simscape Multibody model is not supported by any comparison of simulated versus measured joint torques, ground-reaction forces, or contact dynamics, leaving the central modeling assumption untested against real patient variability and unmodeled effects.

Authors: The model obtains its geometric and inertial parameters directly from the SolidWorks CAD assembly via Simscape Multibody import, eliminating manual approximation of link lengths and masses. We agree that direct torque or force validation against physical measurements is absent. In revision we will add a dedicated paragraph in the Model Description section that (i) states the modeling assumptions, (ii) quantifies expected discrepancies arising from unmodeled joint friction and soft-tissue compliance, and (iii) notes that experimental validation against instrumented hardware and patient data is planned as subsequent work. revision: partial

standing simulated objections not resolved

Hardware experiments and direct experimental validation of joint torques, ground-reaction forces, and contact dynamics against physical exoskeleton hardware and patient data, which cannot be supplied without new experimental infrastructure and are outside the simulation-only scope of the current manuscript.

Circularity Check

0 steps flagged

No significant circularity in controller design or simulation evaluation

full rationale

The manuscript builds a Simscape Multibody model from imported CAD geometry, generates reference trajectories externally via OpenSim, explicitly tunes the blending coefficient alpha=0.65 on that model, and reports comparative RMSE, settling-time, and overshoot metrics from direct closed-loop simulation runs. No derivation step reduces to its own inputs by construction, no fitted parameter is relabeled as an independent prediction, and no load-bearing claim rests on self-citation chains or imported uniqueness theorems. The performance deltas are straightforward simulation outputs on the constructed model, constituting a self-contained engineering workflow.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on one explicitly tuned free parameter and standard linear-control assumptions; no new physical entities are introduced.

free parameters (1)

alpha = 0.65
Blending coefficient between PID and LQR outputs, stated as tuned to 0.65.

axioms (1)

domain assumption The exoskeleton dynamics admit a linear approximation around the operating trajectory suitable for LQR design.
LQR requires a linear state-space model; invoked when the hybrid controller is constructed.

pith-pipeline@v0.9.0 · 5638 in / 1329 out tokens · 36812 ms · 2026-05-13T16:55:43.390644+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

18 extracted references · 18 canonical work pages

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[1] [1]

Ratnakumar, K

N. Ratnakumar, K. Akba s , R. Jones, Z. You, and X. Zhou, ``Predicting sit-to-stand motions with a deep reinforcement learning based controller under idealized exoskeleton assistance,'' Multibody System Dynamics, pp. 1--18, 2024

work page 2024

[2] [2]

R. A. Gavrila Laic, M. Firouzi, R. Claeys, I. Bautmans, E. Swinnen, and D. Beckw \'e e, ``A state-of-the-art of exoskeletons in line with the WHO's vision on healthy aging: From rehabilitation of intrinsic capacities to augmentation of functional abilities,'' Sensors, vol. 24, no. 7, p. 2230, 2024

work page 2024

[3] [3]

A. J. Gunnell, S. V. Sarkisian, H. A. Hayes, K. B. Foreman, L. Gabert, and T. Lenzi, ``Powered knee exoskeleton improves sit-to-stand transitions in stroke patients using electromyographic control,'' Communications Engineering, vol. 4, no. 1, p. 104, 2025

work page 2025

[4] [4]

Mashud, S

G. Mashud, S. K. Hasan, and N. Alam, ``Advances in control techniques for rehabilitation exoskeleton robots: A systematic review,'' Actuators, vol. 14, no. 3, p. 108, 2025

work page 2025

[5] [5]

D. L. Castro, C. H. Zhong, F. Braghin, and W. H. Liao, ``Lower limb exoskeleton control via linear quadratic regulator and disturbance observer,'' in Proc. IEEE International Conference on Robotics and Biomimetics (ROBIO), pp. 1743--1748, 2018

work page 2018

[6] [6]

Jatsun, S

S. Jatsun, S. Savin, and A. Yatsun, ``Motion control algorithm for a lower limb exoskeleton based on iterative LQR and ZMP method for trajectory generation,'' in International Workshop on Medical and Service Robots, pp. 305--317, Springer, 2016

work page 2016

[7] [7]

J. C. Lau and K. Mombaur, ``Can lower-limb exoskeletons support sit-to-stand motions in frail elderly without crutches? A study combining optimal control and motion capture,'' Frontiers in Neurorobotics, vol. 18, p. 1348029, 2024

work page 2024

[8] [8]

Molazadeh, Q

V. Molazadeh, Q. Zhang, X. Bao, and N. Sharma, ``An iterative learning controller for a switched cooperative allocation strategy during sit-to-stand tasks with a hybrid exoskeleton,'' IEEE Transactions on Control Systems Technology, vol. 30, no. 3, pp. 1021--1036, 2021

work page 2021

[9] [9]

M. J. Thomas, J. K. Mohanta, S. Sahoo, and S. Mohan, ``Simulink-based comparative study and selection of a controller for a waist-assistive exoskeleton,'' in International and National Conference on Machines and Mechanism, pp. 267--280, Singapore, 2023

work page 2023

[10] [10]

Siciliano, L

B. Siciliano, L. Sciavicco, L. Villani, and G. Oriolo, Robotics: Modelling, Planning and Control. Springer, 2009

work page 2009

[11] [11]

M. W. Spong, S. Hutchinson, and M. Vidyasagar, Robot Modeling and Control. Wiley, 2006

work page 2006

[12] [12]

The MathWorks, Inc., 2024

MathWorks, Simscape Multibody User's Guide. The MathWorks, Inc., 2024

work page 2024

[13] [13]

S. L. Delp, F. C. Anderson, A. S. Arnold, P. Loan, A. Habib, C. T. John, E. Guendelman, and D. G. Thelen, ``OpenSim: Open-source software to create and analyze dynamic simulations of movement,'' IEEE Transactions on Biomedical Engineering, vol. 54, no. 11, pp. 1940--1950, 2007

work page 1940

[14] [14]

W. G. M. Janssen, H. B. J. Bussmann, and H. J. Stam, ``Determinants of the sit-to-stand movement: A review,'' Physical Therapy, vol. 82, no. 9, pp. 866--879, 2002

work page 2002

[15] [15]

K. M. Kerr, J. A. White, D. A. Barr, and R. A. B. Mollan, ``Analysis of the sit-stand-sit movement cycle in normal subjects,'' Clinical Biomechanics, vol. 6, no. 3, pp. 177--187, 1991

work page 1991

[16] [16]

o m and T. H \

K. J. str \"o m and T. H \"a gglund, PID Controllers: Theory, Design, and Tuning, 2nd ed. Instrument Society of America, 1995

work page 1995

[17] [17]

Singh and T

R. Singh and T. K. Bera, ``Fault detection, isolation and reconfiguration of a bipedal-legged robot,'' Simulation, vol. 95, no. 10, pp. 955--977, 2019

work page 2019

[18] [18]

Arora and R

R. Arora and R. Singh, ``Physical modeling of the tread robot and simulated on even and uneven surface,'' in International Conference on Intelligent Systems Design and Applications, pp. 173--181, Springer, 2018

work page 2018