Enhanced terminal sliding mode control for gait exoskeleton device: experimental investigation and validation

Abstract

The design of pediatric lower-limb exoskeleton devices demands advanced control strategies that ensure safe, stable, and accurate real-time gait tracking despite model uncertainties and external disturbances. This study introduces an improved fast terminal sliding mode (IFTSM) control framework incorporating an adjustable exponential reaching law to enhance the reaching-phase dynamics of conventional terminal sliding mode schemes. The proposed formulation accelerates attraction to the sliding surface for large tracking errors while ensuring smoother finite-time convergence near equilibrium. Lyapunov-based analysis establishes finite-time stability and bounded tracking performance of the coupled subject-exoskeleton system. The controller is implemented on an existing pediatric lower-limb exoskeleton and evaluated under passive-assist operation with one healthy child (12 years, 40 kg, 132 cm) and one child with spastic cerebral palsy (12 years, 35 kg, 131 cm). Comparative experiments with multiple classical and advanced control schemes demonstrate superior real-time tracking behavior of the proposed IFTSM, with tracking error deviations relative to IFTSM on the order of 40–65% for conventional controllers and about 5–20% for advanced sliding-mode variants across the lower-limb joints, together with improved convergence characteristics and reduced cumulative control effort for the healthy child. Over a 25-day experimental protocol, consistent within-subject reductions in tracking error were observed for the CP-affected subject (37.54% hip, 49.47% knee, and 16.29% ankle), together with modest within-subject changes in joint kinematics and 10% increased alignment toward a healthy reference. These pilot-level results demonstrate the technical feasibility, robustness, and stable real-time performance of the proposed IFTSM framework for pediatric exoskeleton gait tracking, while broader statistical validation and functional outcome assessment remain topics for future investigation.

Introduction

As the global population grows, there is a noticeable increase in cardiovascular and neurological conditions, such as stroke, spinal cord injury (SCI), and cerebral palsy (CP). Pediatric stroke, occurring at a rate of 2.5 to 13 cases per 100,000 individuals annually, underscores the prevalence of neurological challenges in younger demographics¹. In developing countries, CP has an estimated prevalence of 2.95 cases per 1000 individuals². Individuals with neurological conditions often experience lower limb dyskinesia due to partial or complete paralysis, necessitating feasible gait training measures. Previous studies^3,4 show that repetitive therapeutic sessions by physical therapists can significantly improve lower limb motor function. Booth et al.⁵ reported promising outcomes of functional gait training for CP-affected individuals. Nevertheless, standard assessment protocols are labor-intensive, requiring repeated, consistent gait cycles, close control of movement parameters (such as speed and amplitude), and separate measurements of training outcomes for each subtask⁶. Traditional approaches also rely heavily on skilled labor, which raises concerns about sustainability. To address these concerns, researchers have proposed single- and multi-joint gait exoskeleton robots for motion assistance^7–9.

Despite remarkable progress in lower-limb exoskeleton technology, its predominant focus has been on addressing the needs of the elderly population, leaving a noticeable gap in solutions tailored for pediatric users¹⁰. Notable advancements in this area include a knee exoskeleton designed to improve knee extension for the pediatric population with crouch gait, as proposed by¹¹. Additionally, the introduction of the P-REX knee exoskeleton, developed to assist children with cerebral palsy, demonstrates the growing recognition of the importance of catering to pediatric orthopedic needs^12,13. By expanding the scope to ankle exoskeletons, Orekhov et al.¹⁴ made a notable contribution with a lightweight, bilateral, bidirectional ankle exoskeleton. This design, featuring motors at the waist, is crafted to meet the unique needs of children affected by CP. However, the limitations of single-joint exoskeletons become apparent in critical conditions that affect multiple limb segments. Recognizing this challenge, the CPWalker platform was introduced in 2016, representing a comprehensive robotic solution that combines an orthosis with a smart walker. This innovative approach was specifically developed to expedite the therapy benefits for CP-affected individuals following surgical interventions¹⁵. Building on this concept, the ExoRoboWalker, presented in 2019 by¹⁶, took a step further by incorporating a device with six degrees of freedom (6-DOFs). This design aims to enhance mobility in the lower limb joints, offering a more versatile solution for individuals diagnosed with CP. For gait rehabilitation of pediatric subjects, Marsi-Bionics contributed to the design of the ATLAS exoskeleton, available as ATLAS 2020 and ATLAS 2030. These versions specifically target the gait rehabilitation process for children of 3–14 years age suffering from conditions like Spinal Muscular Atrophy (SMA) and CP^17,18. Sarajchi et al.¹⁹ a novel size-adjustable lower-limb exoskeleton (LLE) for children aged 8–12, integrating six active joints with BLDC actuation and Harmonic Drives, and rigorously analyzing forward and inverse kinematics using algebraic-geometric methods. Furthermore, the models are validated in MATLAB/Simulink and Simscape, and extended with dynamic interaction assessments to suggest the device’s potential to support standard gait patterns, thereby addressing the relative underdevelopment of pediatric exoskeletons²⁰. However, the studies rely on model-based simulation and virtual validation without extensive physical prototyping or experimental trials with real pediatric users, which may constrain the comfort conclusions in clinical or real-world settings. Despite these translational gaps, the diversified applications of these exoskeletons underscore the importance of tailoring solutions to various pediatric orthopedic conditions.

In the early phases of therapeutic intervention, ensuring precise position control is pivotal for exoskeleton robots to adhere to the desired gait pattern. Feedback devices that process actual movement data play a crucial role in achieving this goal^21,22. However, trajectory control encounters challenges stemming from parametric variations, unknown noise, and disturbances, leading to deviations from the intended exoskeleton trajectory^21,23. These uncertainties arise from intricate mechanical configurations, unintentional user reflexes, and pathological conditions of the limb. Traditional control methods are unable to manage such uncertain environments, underscoring the necessity of robust control strategies. Consequently, there has been a growing interest in robust control frameworks, particularly applicable to exoskeletons for elderly populations and their unique gait patterns^24–29. An innovative approach was suggested by²⁴, who introduced a time-delay-aided neural-PID control scheme for a simulated 5-DOFs gait exoskeleton with uncertain parameters and external interferences. However, the necessary selection of initial hyperparameters in this approach requires an iterative and laborious process for effective model identification. Jin et al.²⁵ developed a model predictive control (MPC) approach using an Extended State Observer that can estimate total system disturbances, improving control accuracy by over 34% compared to conventional MPC and fuzzy PID controllers. However, results are presented to show the performance of the developed controller at the simulation level.²⁶ proposed a model-based adaptive control approach, utilizing a nonlinear observer, for a knee-joint assistance device and exhibited enhanced robustness and superior trajectory tracking abilities compared to traditional approaches. While the proposed method showed promising simulation results with better tracking and estimation errors, real-world experimental validation remains a critical next step to confirm its practical effectiveness. Further contributions to robust control in exoskeletons include the work of Espinosa-Espejel et al.²⁷ who designed controllers using Artificial Neural Networks for active disturbance rejection, specifically addressing model uncertainties and external disturbances from patient-exoskeleton interaction. A closed-loop iterative learning control approach has been developed by Huang et al.²⁸ to achieve consistent tracking in lower-limb therapy systems, effectively addressing challenges posed by initial-state deviations. Meanwhile, Lu et al.²⁹ implemented model-based fuzzy control for lower-limb exoskeleton robots to address uncertainties and disturbances, including gravity variation, gait variation, and strap connection disparities. Using this explicit model, experiments were conducted with both able-bodied individuals and patients. While promising, these approaches still face challenges in universally handling patient variability, requiring continued refinement of control algorithms to achieve consistent, personalized rehabilitation outcomes. In the context of pediatric exoskeleton devices, it is noteworthy that PID-like controllers have commonly been employed at the actuator level for walking control^15,17,20.

Over the past two decades, sliding mode control has gained popularity due to its robustness in managing uncertain and complex nonlinear dynamics^30,31. The extension of conventional sliding mode control to achieve convergence in measurable time, known as terminal sliding mode (TSM) control, was introduced in the late 90s³¹. TSM control ensures the convergence of system states within a measurable time, asymptotic to the origin along the sliding manifold^31,32. However, TSM control may underperform when the system starts far from equilibrium, often leading to chattering phenomena. To address this limitation, the concept of fast terminal sliding mode (FTSM) control was proposed to guarantee rapid and finite-time convergence along the sliding manifold³³. Despite its merits, conventional FTSM control schemes often employ an exponential reaching law (ERL), resulting in slow convergence of system states to the sliding manifold and increased chattering. In this direction, recent works have extended SMC frameworks by proposing an adaptive RBFNN-based fixed-time nonsingular TSM control to achieve fast, initial-condition-independent convergence for robotic trajectory tracking³⁴, with validation restricted mainly to rigid manipulators and not explicitly addressing real-time constrained interaction scenarios. Building on earlier efforts to mitigate chattering and improve reaching dynamics, Brahmi et al.³⁵ proposed a quasi-time-delay-estimation-aided high-order TSM controller with an adaptive reaching law for uncertain manipulators, demonstrating improved robustness and reduced chattering, yet leaving scope for faster convergence and scalability to more complex systems. More recently, a robust ultralocal model predictive control with cascaded EKF–LESO was proposed for sensorless IPMSM drives, enabling strong disturbance rejection and accurate state estimation without precise models³⁶, with potential sensitivity to severe noise and computational constraints. In parallel, integrating adaptive learning and time-guaranteed convergence, a predefined-time non-singular TSM control with prescribed performance and neural-network compensation is developed to handle actuator faults and uncertainties in manipulators, guaranteeing bounded errors and user-defined convergence time³⁷, though at the cost of higher structural and tuning complexity.

Several studies have explored various forms of sliding mode control for elderly exoskeletons, including adaptive sliding mode control by³⁸, periodic event-triggered sliding mode by³⁹, disturbance rejection with FTSM control by¹², and sliding mode control with a chattering attenuator by⁴⁰. Although TSM and FTSM controllers have been widely used in robotic and exoskeleton systems, challenges persist when these methods are transferred to coupled pediatric human–exoskeleton applications. Classical TSM ensures finite-time convergence but often exhibits slow reaching dynamics³², while conventional FTSM improves sliding behavior yet relies on a fixed exponential reaching law that may lead to slower attraction and residual chattering³³. More recent sliding-mode variants enhance robustness but introduce increased computational burden and tuning complexity^34,35,37,41, which can be restrictive for real-time pediatric platforms. Moreover, variable power and exponential reaching laws have been previously investigated within the sliding mode control literature, particularly for robotic manipulators and simulation-based studies^34,42,43. However, their direct applicability to pediatric lower-limb exoskeletons remains non-trivial, owing to the coupled human–robot dynamics, safety-critical motion constraints, and the need for smooth finite-time convergence during passive-assist gait modulation, particularly in the presence of uncertain dynamics and disturbances.

Notably, none of the existing works have addressed the improvement of sliding surface convergence during the approaching phase, a crucial aspect for coupled pediatric exoskeleton systems. Improving sliding surface convergence during the reaching phase is crucial for coupled pediatric exoskeleton systems, as it ensures smoother transitions and faster error correction, both of which are vital for maintaining natural gait patterns and avoiding abrupt movements that could compromise patient safety. To address this research gap, the present study presents an experimentally validated IFTSM-based control framework for a pediatric gait exoskeleton, aimed at providing safe motion assistance and demonstrating measurable kinematic improvements during passive-assist gait training in both typically developing children and a child with spastic cerebral palsy. The main technical and experimental contributions of this study can be outlined as follows:

• To design and experimentally validate an IFTSM-based control framework implemented on a pediatric lower-limb exoskeleton for safe and smooth gait assistance.

• To demonstrate Lyapunov-based stability analysis, finite-time convergence, and bounded tracking behavior of the coupled subject–exoskeleton system.

• To evaluate comparative experimental outcomes of IFTSM against conventional and advanced TSM controllers on a healthy pediatric subject, highlighting improved tracking accuracy and control efficiency.

• To investigate pilot-level experiments of passive-assist gait training using the IFTSM-controlled exoskeleton in a child with spastic cerebral palsy over twenty-five days, showing measurable kinematic improvements.

System description

Exoskeleton system

It is crucial to consider an exoskeleton’s capacity to sustain various static and dynamic loads while guaranteeing the wearer’s safety. To fulfill the design specifications, the exoskeleton should also include the necessary degrees of freedom (DOFs). To help children in the sagittal plane, Narayan et al.⁴⁴ proposed a walker-supported exoskeleton system called LLESv2 with six degreees-of-freedom (6 DOFs). Children between the ages of 8 and 12 who weigh between 25 and 40 and have a height of are the target audience for the LLESv2. Figs.The model of LLESv2’s limbs, walker, and LLESv2 attached to a child mannequin is shown in Fig. 1a–c. The following permissible ranges-of-motion (ROM) have been established for various joints in order to ensure the subject’s safety: Hip flexion/extension is , knee flexion/extension is , and ankle dorsiflexion/plantarflexion is .

Fig. 1.

CAD: (a) LLESv2 (Components: 1. Thigh frame, 2. Shin frame, 3. Footplate support, 4. Geared stepper, 5. Screw-driven actuator, 6. Outer shin link, 7. Lead screw, 8. Less-rated stepper, 9. Viscoelastic clamps 10. Joint connectors (b) Walker (1. Assembly and 2. Supporting wheels) and (c) LLESv2 attached to the limbs of a child mannequin⁴⁴.

The real-time control system for the coupled subject exoskeleton involves various hardware components, as displayed in Fig. 2a. The control strategy, implemented in MATLAB/Simulink using the Arduino Hardware Support Package, uses electronic drivers to control hip and ankle actuators (stepper motors) via an Arduino Mega2560. Actuator positions and velocities are measured using feedback units (a multiturn potentiometer for the hip and knee, a single-turn potentiometer for the ankle) and fed back to the control framework via the microcontroller. More details on hardware components can be found in⁴⁴. The actuation and sensing hardware introduce practical non-idealities, including backlash of approximately 1.5 at the hip joint, 0.3–1.0 mm at the lead-screw transmission at the knee joint, control and measurement delays of about 10–25 ms arising from driver response and sampling, bandwidth limitations below roughly 10–20 Hz restricting rapid motion tracking, and potentiometer sensor noise of approximately ±0.5–1.5% of full-scale output with an effective resolution of about 0.2–0.5. These effects were not explicitly modeled and were instead treated as bounded uncertainties and disturbances within the robust control framework, and the reported performance therefore reflects real-time operation under practical hardware conditions.

Fig. 2.

(a) Developed LLESv2⁴⁴ and (b) healthy subject (left) Spastic CP-affected subject (right) with LLESv2.

Participant details

In this work, a 12-year-old typically-developed male (body mass: 40 kg, body height: 132 cm) and a 12-year-old CP-affected male (body mass: 35 g, body height: 131 cm) are recruited for the passive-assist gait training, as shown in Fig. 2b. The CP-affected subject, exhibiting diplegic topography with a crouch gait pattern, has post-effects of spastic CP with no sign of pain and discomfort and has an FMA ordinal score of 1. As per the institute hospital, the subject’s record was maintained under the GMFCS-III with flexion deformities of 3.75 hip, 6.92 knee, and 0.85 of the ankles. Although the subject can walk short distances without any assistance; however, can not apply significant force from his side which is required for the experiments in the passive-assist mode. Informed consent was obtained from both participants and/or their parents/legal guardians prior to participation in the study. Specific written consent was obtained from the parents/legal guardians for the publication of any information or images that could potentially identify the participant in an online open-access publication. Table 1 details limb parameters for subjects and the exoskeleton. The gait trajectory for pediatric subjects was computed using a Kinect-LabVIEW-based motion capture system, as described in⁴⁵. The stride length and cycle time for the healthy subject were observed to be 92 cm and 0.9 s, respectively, while for the CP-affected subject, these parameters were recorded as 76 cm and 1.2 s. The healthy and CP-affected gait trajectory is visually depicted in Fig. 3, respectively. Considering the hardware constraints, a gait cycle duration of 2 s (time-normalized) was adopted for the coupled human–exoskeleton system during the control experiments. The healthy mean ROM (over 10 gait cycles) for a 12-year-old child is recorded as 22.23 to (hip), 58.21 to 1.15 (knee), and 7.18 to (ankle), respectively. The respective CP-affected mean ROM for 12-year-old child is recorded as 18.59 to (hip), 51.41 to 0.53 (knee), and 6.75 to (ankle), respectively.

Table 1.

Parameters of LLES v2, Healthy Pediatric Subject, and CP-Affected Pediatric Subject.

Category	Part	Mass (kg)	Length (m)	COM (m)
LLESv2	Thigh link
	Shank link
	Foot link
Healthy subject (40 kg, 132 cm)	Thigh
	Shank
	Foot
CP-affected subject (35 kg, 131 cm)	Thigh
	Shank
	Foot

Fig. 3.

Healthy and CP-affected (time-normalized) (a) hip (b) knee, and (c) ankle joint trajectory.

Dynamic modeling

To facilitate natural gait training and ensure the subject’s mobility, the actuators within the subject-exoskeleton model must generate adequate torques. Consequently, conducting a dynamic analysis of the gait exoskeleton becomes crucial as it provides valuable insights into the joint torques. These torques are influenced by both the geometric specifications of the exoskeleton links and the anthropometric measurements of the human leg. This section is dedicated to the dynamic modeling of the integrated human-exoskeleton system, specifically focusing on a simplified 3-DOFs coupled system illustrated in Fig. 4. The dynamic model is formulated using the Euler-Lagrange principle through the following second-order nonlinear differential equation:

1

where the various variables and matrices presented in this dynamic model (Eq. 1) are described as so:

2

The M(q) denotes a symmetric positive definite inertial matrix, represents Coriolis effects, and G(q) denotes gravity effects. Referring to Table 1, these matrices include the following parameters: and denote the aggregate of thigh, calf and ankle-foot masses; and denote the aggregate of thigh, calf, and ankle-foot measurements; and signify the center of mass position for the respective measurements. These matrices are presented in their expanded form in Narayan et al.⁴⁶. The overall torque is , the joint actuator torque is , and the disturbances to the system is . The joint position and higher-order derivatives (velocity and acceleration) are denoted by , and . In Eq. (2), the notations ‘’ and ‘’ are employed for the brevity of the term exoskeleton ‘robot’ and the ‘human’. It is noted that under passive-assist operation, the exoskeleton guides the limb motion without active torque contribution from the subject. Under this mode, rigid kinematic coupling between the human limb and exoskeleton joints is commonly assumed through mechanical interfaces to ensure synchronized and safe motion. Accordingly, considering a rigid structure (), the interactive torques, denoted as from the robot to the human and from the human to the robot, become negligible in the passive-assistance. Any residual human–robot interaction effects arising from involuntary muscle activity, pathological gait patterns, or modeling inaccuracies are treated as lumped uncertainties and external disturbances, which are explicitly compensated by the robust control design.

Fig. 4.

Proposed IFTSM control architecture.

Remark 1

It is assumed that the subject can generate the ground reaction force independently^24,28,29; therefore, to maintain the model’s analytical tractability and avoid unnecessary complexity, both the swing and stance phases are represented in a unified dynamic framework. This assumption is clinically guided and applicable to the selected pediatric participants, who were ambulatory and capable of independent stance and weight-bearing, as confirmed by the supervising therapist.

Design of improved FTSM control scheme

This section presents a new FTSM control scheme for the uncertain coupled subject-exoskeleton system, emphasizing quick convergence in both approaching and sliding phases. It includes a problem definition using a sliding manifold and a control law, along with a Lyapunov stability proof for fast-converging error states.

Problem definition

In real-world implementations, system behavior often diverges from its mathematical model because of payload fluctuations and structural uncertainties. Accordingly, Eq. (1) is modified to account for these variations:

3

The matrices , , and indicate the nominal model parameter, i.e., the ideal characteristics, usually decided in the robot’s design phase, while signifies the perturbation parameter. The symbol represents frictional effects based on Coulomb friction and viscous friction from⁴⁶.

4

where denotes joint velocity in Nm/rad, and sgn is the signum function.

Reformulating Eq.  (3),

5

with

6

The above Eq. (5) can be represented in a second-order nonlinear form as below.

7

8

where is the nominal exoskeleton model free from uncertain parameters and interferences, and denotes the lumped form of uncertain parameters and interferences.

Assuming no prior knowledge of dynamic parameter limits, the following criterion can be used.

9

where signifies a positive constant.

Fast terminal sliding mode with variable power reaching law

The proposed fast terminal sliding mode controller, incorporating an expedited reaching law (Fig. 4), is initiated by defining a rapid terminal sliding manifold. This manifold ensures the rapid convergence of gait error states to equilibrium, maintaining stability along the surface, as discussed in³³. It is defined as follows.

10

where represents the angular error in gait tracking, where (equal to ) represents the intended gait trajectory for a healthy subject, and (equal to q) represents the observed gait trajectory of the subject-exoskeleton. , , and are involved also involved positive constants.

If , the expression leads to the attainment of within a finite time, , when an appropriate value of is chosen as specified below.

11

Now, building on the work of Kang et al.⁴² and Zhang et al.⁴³, a fast-reaching law with variable exponent power terms is employed to dynamically adjust the convergence speed of system states as they transition from distant positions to closer proximity to the sliding manifold. This is done to reduce the chattering while reducing the speed of converging error states towards the sliding manifold.

12

where the values of and are

13

where . Adding a variable exponential power term allows the reaching law to adapt dynamically to the system state, enabling a faster convergence rate as the system moves towards the sliding manifold. Notably, when , the reaching law simplifies to a fast power reaching law, which achieves even quicker convergence. Furthermore, as the system state approaches zero ( or ), the velocity becomes zero, ensuring a smooth transition onto the sliding surface. This smooth approach significantly reduces sliding mode chattering, enhancing the stability and control of the exoskeleton system.

Lemma 1

Provided the model in Eqs. (7)–(8) with state vectors , the manifold variables s and move towards the equilibrium (0, 0) via variable power reaching law given in Eq. (12).

Proof

From Eq. (12), it follows that when , , and when , . Based on this analysis, only when . This satisfies the conditions for the existence and reachability of the reaching law, ensuring that the system state variable reaches the sliding mode surface under the influence of the variable power reaching law.

Theorem 2

Considering the dynamic model described by equations Eqs. (7), (8) and the sliding manifold denoted as (s) in Eq. (10) , along with the variable power reaching law expressed by in Eq. (12), the choice of the control scheme can be made as

14

with

15

16

where denotes a fixed positive value, and the introduction of the term is intended to counterbalance parametric uncertainties and external interferences, then the gait tracking deviation rapidly approaches the sliding manifold and achieves convergence to the origin position within a finite timeframe.

Proof

Taking derivative of the sliding manifold in Eq. (10) and utilizing Eqs. (7) and (8) to obtain,

17

Applying the control input from Eq. (14) to the aforementioned equation,

18

The subsequent Lyapunov function is examined to validate the Theorem 2:

19

Now, assessing the rate of change of the Lyapunov function

20

From the aforementioned expression, it is evident that exhibits negative definiteness. As a result, the error variables in gait tracking will rapidly converge towards the origin over a finite duration along the sliding manifold, validating the above theorem. Accordingly, the stability guarantees provided by the proposed IFTSM controller remain valid in the presence of unmodeled interaction forces and pathological gait-induced disturbances, provided these effects remain bounded.

Remark 2

Selection procedure of sliding manifold parameters , , and : The coefficient governs the linear error dissipation and determines the overall approaching speed; increasing accelerates transient response but may raise control effort. The parameter weights the nonlinear terminal term and enhances finite-time convergence as |e| decreases; larger strengthens terminal attraction but may increase sensitivity to noise if excessively large. The exponent shapes the terminal convergence profile and must satisfy the finite-time stability condition; in practice, choosing yields finite-time convergence while maintaining smooth behavior near the equilibrium.

Remark 3

Selection procedure of reaching-law parameters , , and : The gains and regulate the attraction speed to the sliding manifold and the robustness of the reaching phase. Higher values result in faster reaching from large initial errors, but may increase control activity and induce oscillations. Hence, moderate initial values are recommended and should be gradually increased until satisfactory convergence is achieved without noticeable chattering. The exponent shapes the near-surface behavior of the variable-power reaching law; smaller accelerates convergence close to the manifold, whereas values closer to unity provide smoother behavior with reduced switching.

Remark 4

Selection procedure of robustness parameters and : The term represents an upper bound on lumped uncertainties and disturbances and should be conservatively estimated from modeling errors, friction variations, and expected external perturbations. The positive margin is introduced to ensure strict dominance of the robust term over unmodeled effects. Increasing enhances robustness against disturbances but may also increase control effort and chattering. In practice, should be selected as the smallest value that eliminates steady-state tracking bias and ensures consistent reaching under the worst observed disturbance conditions.

Experimental protocol

The experimental procedure for exoskeleton-assisted gait training encompasses various components, including the desired gait trajectory, exoskeleton system, training sessions, and outcome assessments. The comprehensive framework is delineated as follows:

Gait Trajectory To commence, a physiotherapist affiliated with the institute hospital is engaged to meticulously establish the walking parameters for the participant throughout the motion capture experiment. The used motion capture system is based on the Kinect-LabVIEW-based framework, as detailed by⁴⁵. The therapist takes the responsibility of curating and validating the participant information sheet to ensure the accuracy and reliability of the motion capture setup results.

Exoskeleton System The lower-extremity exoskeleton (LLESv2) is configured within a controlled environment, guaranteeing the secure and functional attachment of its mechanical components. Bracing straps connect the lower limb segments of the subject to the corresponding links of the exoskeleton. The study was reviewed and approved by the Institute Human Ethics Committee, Indian Institute of Technology Guwahati. All trials involving human experiments were conducted in accordance with the ethical approval granted by the committee on February 28, 2020. Human participants were recruited in full compliance with relevant institutional guidelines and regulations, and all procedures adhered to the principles of the Declaration of Helsinki. Written informed consent was secured from both participants and/or their parents or legal guardians before enrollment in the study. Additional written consent was obtained from the parents/legal guardians for the dissemination of potentially identifiable information or images in an open-access publication.

Training Sessions for healthy Subject: In a controlled experimental setup, a single-day session is conducted for the healthy subject using a pediatric exoskeleton equipped with the proposed IFTSM control as illustrated in Fig. 5. The session involves 5 trials, with each trial consisting of 10 gait cycles. The duration of each gait cycle for the healthy subject is fixed at 2 s. A 10-minute gap is maintained between consecutive trials to ensure optimal participant readiness.

Fig. 5.

Experiment protocol for exoskeleton-assisted gait training of healthy and Spastic-CP affected pediatric subjects. Note: Outcomes are assessed at the twenty-fifth trial for each day.

Training Sessions for CP-affected Subject Following the evaluation of the proposed IFTSM control with the healthy subject, gait training experiments are extended to the subject affected by cerebral palsy (CP). Over six months, 25 sessions are conducted over 25 days as illustrated in Fig. 5. Each session comprises 5 trials, with 10 gait cycles per trial, utilizing the coupled subject-exoskeleton system. An additional trial of 10 gait cycles on the 25th day is performed without the exoskeleton to investigate the kinematic and spatiotemporal retentions. A 10-minute preparation gap is allowed between trials. Due to ethical, logistical, and participant burden considerations in pediatric trials, the extended protocol was conducted using a single control framework and did not include controller switching, washout phases, or repeated baseline measurements.

Outcomes Assessment Desired healthy gait data is processed by the hardware architecture, implementing the proposed IFTSM control in MATLAB/Simulink, alongside FTSM and TSM control schemes. The exoskeleton guides the pediatric participant’s lower limbs, facilitating motion assistance through effective trajectory tracking. Real-time control performance is monitored by collecting data on tracking errors and control signals, utilizing statistical measures such as root mean square error and root mean square voltage. Following validation of the proposed IFTSM control scheme, the same hardware processes healthy gait data to guide the exoskeleton for assisting the CP-affected subject. Continuous monitoring of real-time control performance and data collection occur across sessions. The study evaluates the percentage improvement after 25 days of exoskeleton-assisted training and explores the correlation between healthy and CP-affected gait patterns before and after intervention. These percentage values represent within-subject descriptive changes relative to baseline performance and are reported to illustrate trends in tracking behavior rather than statistically significant improvements.

Remark 5

This study is intended as a pilot-level experimental investigation aimed at demonstrating the feasibility and real-time performance of the proposed control framework. Owing to the limited number of participants, the reported results are not intended to establish statistical effectiveness or generalizable outcomes. Moreover, all reported metrics are used to characterize controller behavior under passive-assist operation and are not intended as clinical or functional outcome measures.

Experimental results: pilot-level observations

In this section, we present a comprehensive discussion of the experimental results obtained from implementing the IFTSM control scheme. Following numerical iterations as per the Remarks 2-4, the sliding manifold and control parameters for the IFTSM scheme are selected as , , , , , , , and . Numerical iterations refers to iterative adjustment within physically bounded parameter ranges informed by stability conditions and experimental constraints, rather than arbitrary trial-and-error tuning. The scheme was tested with specific input parameters, namely the healthy gait trajectory, as well as limb lengths and masses, across two distinct groups: healthy pediatric subjects and those affected by CP (Table 1). Given the schematic representation of the proposed control in Fig. 4. The healthy gait trajectory serves as a baseline, representing the normative walking pattern for individuals without any pathological conditions. The aim is to assess the scheme’s efficacy in accommodating and adapting to the unique gait characteristics of individuals with CP, as compared to the baseline established by the gait trajectories of healthy individuals. Furthermore, notable trends and deviations observed during the experimental sessions are discussed to highlight the scheme’s robustness and adaptability for pediatric gait control using the lower-limb exoskeleton.

Gait tracking with healthy subject

The effectiveness of the suggested IFTSM is evaluated in comparison to two alternative control strategies, i.e., TSM control by³² and FTSM control by³³. All controllers were tuned under identical trajectory inputs and operating constraints, with stability and bounded tracking ensured prior to comparison. The assessment metrics, such as root mean square error (RMSE), percentage tracking performance (PTP), root mean square voltage (RMSV), and percentage voltage performance (PVP) are considered as follows:

21

22

where p denotes the performance value such that if p: joint tracking error (e), then RMS(P) denotes the root mean square error (RMSE); if p: control voltage (U), then RMS(P) refers to the root mean square volatge (RMSV); N represents the total number of data points.

This section presents the results of the healthy trajectory tracking with proposed and contrast control schemes for 10 gait cycles. Figures 6a, 7a, and 8a illustrate the monitoring of a normal walking path, which includes the hip, knee, and ankle movements. Examining Figure 6b, the average maximum absolute deviation for the hip trajectory () is found to be 2.56, 1.54, and 1.13 with TSM, FTSM, and IFTSM control, respectively, around the mid-stance phase. Referring Fig. 7b), the corresponding absolute deviation values for the knee trajectory () are computed as 11.67 (TSM), 6.86 (FTSM), and 4.51 (IFTSM) during the early swing phase. For the ankle trajectory, as illustrated in Fig. 8b, the corresponding deviations () with the proposed and alternative control schemes are 2.24 (TSM), 1.21 (FTSM), and 0.79 (IFTSM) in the mid-swing phase.

Fig. 6.

Hip trajectory (a) tracking, (b) tracking error, and (c) tracking RMSE with contrast and proposed control schemes for the healthy subject.

Fig. 7.

Knee trajectory (a) tracking, (b) tracking error, and (c) tracking RMSE with contrast and proposed control schemes for healthy subject.

Fig. 8.

Ankle trajectory (a) tracking, (b) tracking error, and (c) tracking RMSE with contrast and proposed control schemes for healthy subject.

Moreover, the RMSE values for the proposed IFTSM control and contrast FTSM and TSM are illustrated in Figs. 6c, 7c, 8c. For hip joint tracking, as indicated in Fig. 6c and Table 2, the IFTSM control demonstrated a noteworthy 10.64% improvement in tracking compared to FTSM and an even more substantial improvement of 40.05% when contrasted with TSM control. Similarly, the advantages of IFTSM control extended to knee joint tracking (Fig. 7c and Table 2), where it outperformed FTSM and TSM control schemes by 17.24% and an impressive 53.97%, respectively, reflecting its robust capabilities in minimizing tracking errors. In the case of ankle joint tracking (Fig. 8c and Table 2), the IFTSM control exhibited a notable superiority, achieving an improvement of 14.12% compared to FTSM and an even more substantial 44.79% enhancement compared to TSM control. These outcomes strongly suggest that the IFTSM control strategy not only demonstrates remarkable accuracy but also holds substantial promise for improving the overall feasibility of gait trajectory tracking within the domain of subject-exoskeleton systems.

Table 2.

Tracking performance comparison for contrast and proposed control schemes.

	RMSE, (TSM)	RMSE, (FTSM)	RMSE, (IFTSM)	PTP (%) (TSM, IFTSM)	PTP (%) (FTSM, IFTSM)
Hip	0.88	0.59	0.52	40.05	10.64
Knee	3.65	2.03	1.68	53.97	17.24
Ankle	0.67	0.43	0.36	44.79	14.12

The sliding surfaces corresponding to each lower-limb joint are visually presented in Fig. 9a–c. The zoomed-in-views display the sliding surface for a gait cycle. In the context of the hip joint, the sliding surface associated with the proposed IFTSM control scheme initiates convergence towards equilibrium at the onset of a gait cycle , demonstrating a notable advantage over the contrast control schemes, namely FTSM and TSM control. Similarly, for the knee joint, the sliding surface is observed to be consistently converging from under IFTSMC, whereas FTSM and TSM control exhibit convergence at and , respectively. Regarding the ankle joint, the sliding surface under IFTSM control commences convergence from the initiation of the gait cycle , contrasting with FTSM and TSM control, where convergence is identified at and , respectively. Additionally, a noteworthy observation from Fig. 9 indicates that the proposed control approach results in significantly reduced chattering compared to the contrast control schemes. The comprehensive analysis of the sliding surfaces underscores the superior performance of the IFTSM control methodology, particularly in achieving minimal convergence times for gait-tracking errors compared to the contrast control schemes.

Fig. 9.

Sliding surface for (a) hip joint (b) knee joint, and (c) ankle joint tracking with contrast and proposed control schemes for healthy subject.

The evolution of control signals is presented in Fig. 10. Examining the hip trajectory in Fig. 10a, the average maximum absolute control voltage () is determined as 20.59V, 19.1V, and 9.87V for TSM, FTSM, and IFTSM control, respectively. To comprehensively assess the technical effectiveness, the root mean square voltage (RMSV) is calculated for the hip trajectory, resulting in values of 1.96 V (TSM), 1.74 V (FTSM), and 1.53 V (IFTSM). For the knee trajectory in Fig. 10b, the maximum absolute control voltage () is identified as 2.25V, 2.74V, and 2.21V for TSM, FTSM, and IFTSM control, respectively. The corresponding RMSV is computed as 0.38V, 0.49V, and 0.34V. In the case of the ankle trajectory (Fig. 10c), the maximum absolute peak values () are determined as 0.49V (TSM), 0.43V (FTSM), and 0.23V (IFTSM), with corresponding RMSV values calculated as 0.056V, 0.046V, and 0.031V. The performance index, summarized in Table 3, highlights that the proposed IFTSM control requires a lower input voltage to effectively track the subject’s healthy walking, demonstrating its efficiency in achieving control objectives with reduced power requirements.

Fig. 10.

Control evolution and RMSV for (a) hip joint (b) knee joint, and (c) ankle joint tracking with contrast and proposed control schemes for an healthy subject.

Table 3.

Voltage consumption performance comparison for contrast and proposed control schemes.

	RMSV, V (TSM)	RMSV, V (FTSM)	RMSV, V (IFTSM)	PVP (%) (TSM, IFTSM)	PVP (%) (FTSM, IFTSM)
Hip	1.96	1.74	1.53	21.93	12.07
Knee	2.25	2.74	2.21	1.77	19.34
Ankle	0.056	0.046	0.031	44.64	32.61

In addition, time-, energy-, and smoothness-weighted performance indices are evaluated as

23

24

25

where e(t) denotes the joint tracking error, U(t) represents the applied control input (actuator voltage), is the discrete-time rate of change of the control input at the sampling instant, and T denotes the total number of samples.

The ITAE index emphasizes late-stage tracking performance and convergence quality by penalizing sustained errors, while ISU reflects the cumulative actuation effort and energy utilization. The chattering index (CI) quantifies the smoothness of the control action, where lower values indicate reduced chattering and improved actuator comfort. As observed in Table 4, the proposed IFTSM controller achieves consistently lower ITAE values compared with TSM and FTSM across all joints. For instance, at the hip joint, ITAE is reduced from 112.98 (TSM) and 90.01 (FTSM) to 80.86 with IFTSM, and at the knee joint from 493.13 (TSM) and 290.68 (FTSM) to 248.81. Similarly, the ankle ITAE decreases to 61.54 under IFTSM. In terms of control effort, the ISU index is also reduced under the proposed scheme; for example, at the hip joint, ISU decreases from 77.25 (TSM) to 46.84 (IFTSM), at the knee joint from 3.035 (TSM) to 1.056 (IFTSM), and at the ankle joint from 0.063 (TSM) to 0.020 (IFTSM). Furthermore, the chattering index (CI) demonstrates a significant reduction, indicating smoother actuator commands; at the hip joint CI decreases from 850.85 (TSM) and 723.97 (FTSM) to 403.67 with IFTSM, at the knee joint from 167.30 and 84.56 to 59.49, and at the ankle joint from 24.25 and 19.12 to 8.20. These results confirm that the proposed controller achieves faster error attenuation, reduced control effort, and substantially smoother control action compared with conventional sliding mode approaches.

Table 4.

Integral performance and chattering indices comparison for contrast and proposed control schemes.

	ITAE, (TSM)	ITAE, (FTSM)	ITAE, (IFTSM)	ISU, V (TSM)	ISU, V (FTSM)	ISU, V (IFTSM)	CI, V (TSM)	CI, V (FTSM)	CI, V (IFTSM)
Hip	112.98	90.01	80.86	77.25	60.21	46.84	850.85	723.97	403.67
Knee	493.13	290.68	248.81	3.035	2.63	1.056	167.30	84.56	59.49
Ankle	102.21	71.10	61.54	0.063	0.043	0.020	24.25	19.12	8.20

To further validate the performance effectiveness of the proposed IFTSM controller, Fig. 11 presents a joint-wise comparison of percentage tracking performance (PTP) and percentage peak value performance (PVP), as defined in Eq. (22), for different contrast controllers. These indices quantify the RMS-based percentage deviation of each controller relative to IFTSM, with positive values indicating degraded performance and negative values indicating improvement. In Fig. 11a, the classical computed torque controller (CTC)²⁰ exhibits the largest degradation in tracking performance, with PTP values ranging from approximately 52.4% to 65.2% across the hip, knee, and ankle joints. The TSM³² mitigates this degradation, yet exhibits high positive deviations, with PTP values ranging from 40.05% to 53.97%. The FTSM³³ further improves tracking accuracy, yielding smaller positive PTP values between approximately 10.64% and 17.24%. The adaptive terminal sliding mode (ATSM) controller achieves comparable performance, with PTP values remaining below 12% for all joints⁴¹. The fixed-time nonsingular terminal sliding mode (FTNTSM) controller³⁴ shows a negative PTP of at the hip joint, indicating a 3.6% improvement over IFTSM, while exhibiting positive deviations of 5.4% and 6.8% at the knee and ankle joints, respectively. Overall, the proposed IFTSM yields the smallest RMS tracking error across all joints, except at the hip, where FTNTSM marginally outperforms it.

Fig. 11.

Comparison of joint-wise tracking performance with respect to the proposed IFTSM controller. (a) Percentage Tracking Performance (PTP, %) and (b) Percentage Voltage Performance (PVP, %) for the hip, knee, and ankle joints. The shaded regions illustrate the relative deviation envelopes of the CTC, TSM, FTSM, ATSM, and FTNTSM controllers compared to the proposed IFTSM controller.

A similar interpretation applies to the PVP results shown in Fig. 11b. CTC produces the largest RMS voltage deviations, with PVP values ranging from approximately 24.8% to 54.3% across the joints²⁰. TSM reduces the RMS voltage deviation but retains pronounced variability, with PVP values in the range of about 1.77–44.64%³². FTSM further decreases the deviation, yielding PVP values between approximately 12.07 and 32.61%³³. ATSM achieves additional suppression, with PVP values remaining below approximately 18% for all joints⁴¹. FTNTSM further limits the deviation to 6.8%, 2.6, and 12.3% at the hip, knee, and ankle joints, respectively³⁴. The proposed IFTSM consistently produces the lowest RMS voltage response across all joints, confirming its superior transient regulation and robustness characteristics.

Further comparison of tuning complexity reveals a clear trade-off between controller performance and parameterization burden. The classical CTC²⁰ and TSM controller³² require only 2 and 4 tuning parameters, respectively; however, their low tuning effort is accompanied by poor PTP and PVP. To overcome these limitations, more advanced sliding mode variants introduce additional design parameters. In particular, FTSM controller³³ and ATSM controller⁴¹ increase the number of tunable parameters to 9 and 5, respectively, enabling faster convergence and enhanced robustness, which is reflected in improved PTP and PVP characteristics. The FTNTSM controller³⁴ further enhances the controller structure by employing 13 tuning parameters, resulting in additional performance gains at the expense of substantially increased tuning effort. In contrast, the proposed IFTSM requires 8 tuning parameters, positioning it between classical and higher-order schemes. These results indicate that while a certain increase in tuning complexity is necessary to achieve high tracking accuracy and effective voltage regulation, the proposed IFTSM provides a favorable compromise, delivering substantial improvements in joint-wise PTP and PVP without incurring the excessive parameter burden associated with more complex controllers.

Gait tracking with CP-affected subject

After validating the technical feasibility of the proposed IFTSM control, exoskeleton training is carried out to track a healthy gait trajectory by the CP-affected pediatric subject. The extended 25-day protocol involving the CP-affected subject is designed to evaluate the stability, repeatability, and feasibility of the proposed IFTSM-based control framework under prolonged passive-assist operation. Unlike the short-term experiments conducted for controller comparison, this protocol is not intended as a long-term comparative study across multiple control schemes. Accordingly, the observations reported in this subsection reflect within-subject kinematic trends under sustained use rather than isolated controller-induced effects. In this case, the RMSE and related percentage improvement (PI) are considered between tracking outcomes from the first day and the twenty-fifth day. The definitions of RMSE and PI are as follows.

26

27

where (e) denotes the tracking error and N denotes the number of data points.

The trajectory tracking for each lower-limb joint is visually represented in Figs. 12a, 13a, and 14a, capturing the progression from the initial to the final day of training. Detailed insights into the tracking variations during this period are provided through zoomed-in views. Analyzing Fig. 12b, the average maximum absolute deviations for the hip trajectory () is determined to be 2.04 on the first day and shows a reduction to 1.88 by the twenty-fifth day, specifically around the late-swing phase. For the knee trajectory (Fig. 13b), the corresponding absolute deviations () are computed as 15.71 on the first day and exhibit improvement to 8.26 on the twenty-fifth day, focusing on the mid-stance phase. For ankle trajectory, as depicted in Fig. 14b, the corresponding deviations () are 0.86 on the first day and demonstrate a reduction to 0.76 by the twenty-fifth day, specifically in the late-swing phase of the gait cycle. These comprehensive tracking assessments provide a dynamic view of the evolving trajectory-tracking performance during exoskeleton training, revealing encouraging reductions in tracking errors at the hip, knee, and ankle joints throughout the intervention.

Fig. 12.

Hip trajectory (a) tracking, and (b) tracking error (deviation from healthy) with proposed control scheme at day 1 and day 25 for CP-affected subject.

Fig. 13.

Knee trajectory (a) tracking, and (b) tracking error (deviation from healthy) with proposed control scheme at day 1 and day 25 for CP-affected subject.

Fig. 14.

Ankle trajectory (a) tracking, and (b) tracking error (deviation from healthy) with proposed control scheme at day 1 and day 25 for CP-affected subject.

The RMSE values for hip, knee, and ankle tracking are illustrated in Fig. 15a–c, depicting the tracking performance on the first day and twenty-fifth day. Analyzing the hip trajectory, there is a notable enhancement in tracking accuracy from the first day (: 0.903) to the twenty-fifth day (: 0.564), marking a significant PI of 37.54% improvement. Similarly, the knee trajectory exhibits a substantial boost in tracking performance, showcasing a PI of 49.47% when comparing the RMSE values of the first day (: 4.924) with those of the twenty-fifth day (: 2.488). This indicates a considerable refinement in the accuracy of knee joint tracking over the course of the twenty-five-day training period. In the case of ankle joint tracking, a discernible PI of 16.29% is observed when contrasting the RMSE values of the first day (: 0.399) with those of the twenty-fifth day (: 0.344).

Fig. 15.

RMS of (a) hip tracking error, (b) knee tracking error, (c) ankle tracking error with proposed control over twenty-five days for CP-affected subject.

Pre- and post-intervention assessment

The assessment of positive outcomes stemming from gait training with proposed control is crucial, particularly when evaluating the impact of the intervention without the exoskeleton after the training day. Moreover, the tracking progress is evaluated over the healthy trajectory, using the root mean square deviation (RMSD) and related percentage enhancement (PE) before and after the intervention. The definitions of RMSD and PE are as follows.

28

where

Here, denotes the trajectory deviation between the CP-affected trajectory before intervention and the healthy trajectory, represents the trajectory deviation between the CP-affected trajectory after intervention and the healthy trajectory, and N represents the total number of data points.

The comparisons of hip, knee, and ankle trajectories before (Spastic-CP) and after (corrected) the intervention, in relation to the healthy trajectory, are depicted in Fig. 16a–c. To quantify the efficacy of the intervention, based on the RMSD values, the percentage enhancement (PE) in hip, knee, and ankle trajectories toward the healthy trajectory is determined as 14.01%, 10.30%, and 13.38%, respectively. These observations indicate relatively larger within-subject changes in hip and ankle joint trajectories over the course of the training sessions when compared to the knee joint, which may reflect differences in joint-level kinematic variability and spatiotemporal demands rather than differential responsiveness to the intervention. Given the single-subject design, such joint-specific trends are reported descriptively to characterize observed gait kinematics within this pilot evaluation.

Fig. 16.

Comparison of joint trajectories for the CP-affected pediatric subject relative to the healthy reference: (a) hip, (b) knee, and (c) ankle joint trajectories before training and after twenty-five days of passive-assist gait training. Panel (d) illustrates the relative within-subject percentage change in trajectory deviation with respect to the healthy reference, reported as a descriptive metric for this pilot-level evaluation.

Furthermore, Table 5 presents a descriptive comparison of the mean ROM for the hip, knee, and ankle joints in a healthy pediatric subject and a child with spastic CP before and after the 25-day passive-assist training period. Stride time and gait cycle time are also reported to provide additional descriptive spatiotemporal context for the observed gait patterns during passive-assist operation. Following the training period of the spastic CP subject, modest within-subject changes in joint excursion were observed, particularly at the hip and knee, illustrating kinematic trends across repeated sessions within the scope of this pilot-level evaluation.

Table 5.

Mean ROM (in degrees) and spatiotemporal parameter comparison for healthy and spastic CP subjects before and after intervention.

Condition Parameter	Healthy	Spastic CP (Pre-intervention)	Spastic CP (Post-intervention)
Hip ROM (deg)	22.23–(− 10.93)	18.59–(− 9.58)	19.22–(− 9.88)
Knee ROM (deg)	58.21–(1.15)	51.41–(0.53)	51.99–(0.57)
Ankle ROM (deg)	7.18–(− 8.96)	6.75–(− 7.78)	7.05–(− 8.09)
Stride Length (cm)	92	76	82
Cycle Time (s)	0.9	1.2	1.1

The kinematic and spatiotemporal results presented in this section are intended to characterize the real-time control behavior and tracking performance of the proposed framework under passive-assist operation. Reductions in trajectory-tracking error and observed alignment of joint kinematics with a healthy reference are reported as descriptive, within-subject observations reflecting controller stability and convergence. These measures do not provide information regarding neuromuscular engagement, voluntary effort, or functional motor recovery, which would require additional physiological measurements and standardized clinical outcome assessments. Furthermore, in the absence of a control condition or crossover design during the extended protocol, the observed trends cannot be attributed solely to the control strategy and may reflect training-related factors such as familiarisation or repeated task exposure.

Conclusions and future works

This work addresses the challenges of real-time tracking of the desired gait trajectory for a pediatric exoskeleton, accounting for parametric uncertainties and external disturbances. An IFTSM-based control framework was implemented and experimentally evaluated on an existing pediatric lower-limb exoskeleton to address real-time gait tracking under model uncertainties and external disturbances. The control strategy enables smooth finite-time convergence and accurate trajectory tracking, supporting safe motion assistance during passive-assist gait training. The proposed framework was evaluated through experimental trials involving a typically developing pediatric subject and a child with spastic cerebral palsy. In this pilot evaluation, the IFTSM control exhibited consistently lower tracking error than the CTC, TSM, FTSM, ATSM, and FTNTSM schemes for the healthy pediatric subject. In particular, relative RMS tracking error deviations with respect to IFTSM were approximately 52–65% for CTC, 40–54% for TSM, and 10–17% for FTSM across the hip, knee, and ankle joints. The ATSM controller showed comparable but still inferior performance, with PTP values remaining below approximately 12% across all joints. The FTNTSM scheme marginally outperformed IFTSM at the hip joint (about 3.6%), while exhibiting degraded tracking at the knee and ankle (about 5–7%). In addition, reduced ITAE, ISU, CI indices were observed under the proposed controller, indicating improved convergence characteristics, lower cumulative control effort, and smoothness behavior. To examine the stability and repeatability of the control framework, exoskeleton training with the proposed control was conducted for the CP-affected subject over twenty-five days. Consistent within-subject trends in hip, knee, and ankle trajectory tracking were observed across repeated sessions, indicating stable controller behavior during prolonged passive-assist operation. Additionally, a comparison of CP-affected trajectories before and after training, relative to a healthy reference, revealed modest within-subject changes in joint ROM, particularly at the hip and ankle, with post-training alignment improvements on the order of approximately 10–15%. Overall, the experimental results demonstrate the technical feasibility and stable real-time performance of the proposed control framework in a pediatric exoskeleton setting.

Despite demonstrating technical feasibility and measurable within-subject kinematic trends, this study has certain limitations. The experimental validation was conducted on a single healthy pediatric subject and one child with spastic cerebral palsy, which precludes statistical analysis, inter-subject variability assessment, and hypothesis testing. Additionally, potential effects of learning, adaptation, or fatigue across sessions were not independently controlled. Looking ahead, future studies will involve larger cohorts and controlled protocols to enable statistically grounded evaluation. While the modeling assumptions were appropriate for passive-assist operation, future work will extend the framework to incorporate compliant coupling and interaction torque estimation for active or human-in-the-loop assistance modes, and to integrate advanced sensing modalities and data-driven methods to capture neuromuscular activity, effort-related variables, and task-level responses for interpretation beyond kinematic tracking. In addition, while short-term experiments isolate controller-level performance through direct comparison with TSM and FTSM schemes, the extended training protocol does not permit separating controller effects from training-related influences, such as familiarization, repetition, or natural variability. Moreover, controlled crossover or multi-arm study designs could also be explored to establish such causal relationships in future work.

Author contributions

J.N. conceived and designed the study framework; J.N. and M.A. performed the experimental implementation, data acquisition, data processing, and quantitative analysis; P.R. and K.K.P. contributed to technical validation and manuscript writing and refinement; S.K.D. contributed to result interpretation, supervision, and project administration. All authors reviewed the manuscript.

Funding

Open access funding provided by Manipal University Jaipur.

Data availability

The datasets generated and analyzed during the current study are not publicly available due to institutional data-protection policies but are available from the corresponding author upon reasonable request.

Declarations

Competing interests

The authors declare no competing interests.

Ethical approval

The study was reviewed and approved by the Institute Human Ethics Committee, Indian Institute of Technology Guwahati. Ethical clearance was granted for the project titled “Design and Development of Powered Lower Limb Exoskeleton System for Elderly Health Care” during the committee meeting held on 28 February 2020. Human participants were recruited in full compliance with relevant institutional guidelines and regulations, and all procedures adhered to the principles of the Declaration of Helsinki.

Informed consent

Informed consent was obtained from all participants and/or their legal guardians prior to their involvement in the study. All participants received detailed information about the study’s objectives, procedures, potential risks, and their right to withdraw at any time without consequences. Written informed consent for publication of any potentially identifiable data or images was secured from the parents/legal guardians prior to submission to an online open-access publication.