In the field of robotics, exoskeletons represent a significant advancement in robot technology, integrating disciplines such as bionics, mechanical electronics, bioengineering, and materials science. These systems are categorized into full-body, upper-limb, lower-limb, and joint-specific exoskeletons based on their structural configurations. Lower-limb exoskeletons, in particular, are widely used to provide assistance during walking, amplify joint motion capabilities, and enhance human performance. By wearing a motion-enhancing lower-limb exoskeleton, individuals such as workers and soldiers can perform prolonged tasks in complex environments, increase load-bearing capacity, reduce muscle fatigue, prevent skeletal and muscular injuries, and lower metabolic energy consumption during long-distance carrying, thereby improving endurance. Beyond aiding healthy individuals, lower-limb exoskeletons also offer rehabilitation training for those with impaired lower-limb movement and can substitute for walking in completely disabled patients. This paper focuses on the design and analysis of a multi-degree-of-freedom (DOF) active lower-limb exoskeleton robot, emphasizing its kinematic and dynamic properties to ensure safety and adaptability. The integration of robot technology in this context enables precise control and enhanced human-robot interaction, making it a cornerstone of modern assistive devices.
The development of exoskeletons has seen substantial progress globally. For instance, the Robotics and Human Engineering Laboratory at the University of California, Berkeley, developed the lower-limb exoskeleton BLEEX to assist soldiers in carrying heavy loads, achieving an average walking speed of 1.3 m/s with a payload of 34 kg. Similarly, the University of Tsukuba in Japan created the HAL lower-limb exoskeleton to enhance wearer strength and support daily exercises for individuals with movement disorders. In China, research, though starting later, has advanced rapidly. Zhejiang University designed an active lower-limb exoskeleton using pump-controlled hydraulic drive units, leveraging their high efficiency, power density, and excellent reverse-drive characteristics, alongside a cooperative control strategy for standing-phase assistance and swing-phase passive following. Northwestern Polytechnical University developed an integrated upper- and lower-limb exoskeleton combining active and passive elements, with the upper limb being active and the lower limb passive, demonstrating good compliance and high efficiency. These innovations highlight the critical role of robot technology in pushing the boundaries of exoskeleton capabilities. In this work, we address safety and human-robot compatibility by designing a multi-DOF active lower-limb exoskeleton robot based on human lower-limb joint characteristics. Our design incorporates adjustable linkage sizes to accommodate different wearers and hard angle limits at the hip, knee, and ankle joints to ensure safety. We propose a gait cycle division method based on joint angle characteristics and establish a dynamic model for theoretical joint moment calculations, validated through experimental data and ADAMS simulations. This approach underscores the importance of robot technology in achieving robust and adaptive exoskeleton systems.
The design of the exoskeleton robot adheres to principles of bionics and universality, ensuring that the lower-limb linkage dimensions align with average human lower-limb sizes. Referring to the 50th percentile data from the “Chinese Adult Human Dimensions Standard,” we determined the size ranges for the exoskeleton’s linkages, as summarized in Table 1. The hip, knee, and ankle joints are designed to correspond functionally and positionally to human joints for enhanced wearer comfort. The hip joint features three rotational DOFs (flexion/extension, internal/external rotation, and abduction/adduction), the knee joint is simplified to one rotational DOF (flexion/extension), and the ankle joint retains two rotational DOFs (plantarflexion/dorsiflexion and abduction/adduction), omitting inversion/eversion to maintain stability without compromising most movements. This design philosophy is rooted in robot technology to ensure seamless integration with human anatomy.
| Component | Value (mm) |
|---|---|
| Thigh | 400–500 |
| Shank | 320–400 |
| Waist Circumference | 660–980 |
| Foot Length | 270 |
| Foot Width | 110 |
| Ankle Height | 70 |
To accommodate varying wearer leg dimensions, we incorporated a size adjustment mechanism into the thigh and shank linkages. Common adjustment methods include gear racks, hydraulic/pneumatic systems, pin adjustments, and screw-nut systems. For stepless adjustment and lightweight requirements, we opted for a screw-nut mechanism. In this design, a trapezoidal screw is connected to a knob; rotating the knob drives the screw, causing linear motion of the nut. The nut is fixed to a push rod via screws, enabling length adjustment. The self-locking property of the trapezoidal screw ensures stability after adjustment. The shank size adjustment mechanism is illustrated in the context of robot technology, emphasizing precision and reliability.
For actuation, active joints were implemented at the hip and knee, specifically for flexion/extension DOFs. We selected frameless torque motors for driving, combined with harmonic reducers for speed reduction and torque amplification, aligning with advancements in robot technology to minimize weight and volume. Hard limits were added to prevent joint movements from exceeding human physiological ranges, thus ensuring safety. For example, protrusions on the hip and knee housings restrict thigh and shank swing, while a pin in the ankle joint slides within a slot on the shank push rod to limit plantarflexion/dorsiflexion. The complete active lower-limb exoskeleton robot model, shown in a representative figure, features six DOFs per leg (two active and four passive), with human-robot interfaces at the waist and lower limbs for secure attachment and improved follow-up. This design leverages robot technology to enhance wearability and performance.
Gait data collection was conducted using the NOKOV optical motion capture system to analyze human movement dynamics. Four subjects with heights of 175–185 cm and weights of 75–90 kg were recorded walking at 1.2 m/s. Markers were placed on key points of the torso and limbs to capture spatial positions. After L-shaped and T-shaped calibrations to reduce positional errors, four slow-walking trials per subject were recorded and saved in C3D format. The data were processed using Mokka biomechanical analysis software and AnyBody simulation software. In Mokka, marker trajectories were visualized, and data segments containing complete gait cycles were extracted for further analysis in AnyBody. The AnyBody software enabled driving a human model with the C3D data, performing kinematic and inverse dynamic analyses. The human model’s weight and height parameters were adjusted to match subject data, and after marker alignment and analysis, joint angle changes were obtained. The angle characteristic curves for the hip, knee, and ankle joints were derived, with the hip ranging from -14° to 22°, knee from 0.42° to 62.3°, and ankle from -19.7° to 5.84°, all within normal human joint ranges. Using MATLAB’s curve fitting tool, angle functions for the gait cycle were formulated. For the hip joint, the angle function is given by:
$$ \theta_{\text{hip}} = 0.1368 + 0.1643 \cos(5.439t) – 0.2156 \sin(5.439t) – 0.001935 \cos(10.878t) + 0.1202 \sin(10.878t) + 0.03571 \cos(16.317t) – 0.01862 \sin(16.317t) – 0.005389 \cos(21.756t) + 0.003184 \sin(21.756t) – 0.003936 \cos(27.195t) – 0.006012 \sin(27.195t) $$
This function facilitates subsequent theoretical calculations, demonstrating the application of robot technology in motion analysis.
Kinematic analysis of the lower-limb exoskeleton, as a serial-chain robot, was performed using the Denavit-Hartenberg (D-H) method. The base coordinate system was set at the waist center, and a spatial kinematic model was established. To simplify the model, the coordinate systems for the hip’s internal/external rotation DOF were merged at the motion center. The D-H parameters for the left leg are listed in Table 2, where $ \theta_i $ is the angle about $ z_{i-1} $ from $ x_{i-1} $ to $ x_i $, $ d_i $ is the distance along $ z_{i-1} $, $ a_i $ is the distance along $ x_i $, and $ \alpha_i $ is the angle about $ x_i $ from $ z_{i-1} $ to $ z_i $. The transformation matrix between adjacent coordinate systems, $ T_i^{i-1} $, is expressed as:
$$ T_i^{i-1} = \begin{bmatrix}
\cos\theta_i & -\sin\theta_i \cos\alpha_i & \sin\theta_i \sin\alpha_i & a_i \cos\theta_i \\
\sin\theta_i & \cos\theta_i \cos\alpha_i & -\cos\theta_i \sin\alpha_i & a_i \sin\theta_i \\
0 & \sin\alpha_i & \cos\alpha_i & d_i \\
0 & 0 & 0 & 1
\end{bmatrix} $$
The overall transformation matrix from the base to the end-effector, $ T_6^0 $, is computed by multiplying individual matrices. For a standing posture with parameters $ \theta_1 = 0^\circ $, $ \theta_2 = 0^\circ $, $ \theta_3 = -90^\circ $, $ \theta_4 = 0^\circ $, $ \theta_5 = 0^\circ $, $ \theta_6 = 90^\circ $, the resulting matrix confirms the accuracy of the forward kinematics solution, validating the exoskeleton’s end-effector pose relative to the base. This kinematic modeling is essential in robot technology for motion planning and control.
| i | $ a_i $ | $ \alpha_i $ | $ d_i $ | $ \theta_i $ |
|---|---|---|---|---|
| 1 | $ L_1 $ | 0 | 0 | $ \theta_1 $ |
| 2 | 0 | 90° | 0 | $ \theta_2 $ |
| 3 | 0 | -90° | 0 | $ \theta_3 $ |
| 4 | $ L_3 $ | 0 | $ L_2 $ | $ \theta_4 $ |
| 5 | $ L_4 $ | 0 | 0 | $ \theta_5 $ |
| 6 | 0 | -90° | -$ L_5 $ | $ \theta_6 $ |
Dynamic analysis was conducted using the Lagrangian method, with the gait cycle divided into stages based on joint angle characteristics to simplify modeling. Unlike traditional divisions (e.g., classic, RLA, Perry, three-phase, Zajac), which rely on motion features, functionality, or muscle activity, our method uses the sign consistency of joint angles to define phases, reducing theoretical complexity. The gait cycle is divided into eight stages: pre-support, initial support, mid-support, terminal support, pre-swing, initial swing, mid-swing, and terminal swing. A seven-link dynamic model in the sagittal plane was established for each stage. For example, in the pre-support stage, the model consists of links representing the torso, thighs, shanks, and feet, with parameters defined in Table 3. The Lagrangian equation is given by:
$$ \tau_i = \frac{d}{dt} \frac{\partial L_E}{\partial \dot{\theta}_i} – \frac{\partial L_E}{\partial \theta_i} $$
where $ \tau_i $ is the torque at the joint between link $ i $ and $ i-1 $, and $ L_E = E_k – E_p $ is the Lagrangian function, with $ E_k $ as the kinetic energy and $ E_p $ as the potential energy. The kinetic and potential energies are computed as:
$$ E_k = \frac{1}{2} \sum_{i=1}^{6} (m_i v_i^2 + I_i \dot{\theta}_i^2) $$
$$ E_p = \sum_{i=1}^{6} (m_i g y_i) $$
where $ m_i $ is the mass of link $ i $, $ v_i $ is its velocity, $ I_i $ is its moment of inertia, and $ y_i $ is the vertical position of its center of mass. The equations of motion are derived in matrix form:
$$ \mathbf{T}_{\theta} = \mathbf{D} \ddot{\boldsymbol{\theta}} + \mathbf{C} \dot{\boldsymbol{\theta}} + \mathbf{G}(\boldsymbol{\theta}) $$
Using the joint angle functions, joint moments were calculated for each stage. The theoretical moments for the hip and knee joints were compared to CGA (Computerized Gait Analysis) data, as shown in Table 4. The hip joint moments exhibited a trend of initial decrease followed by an increase, reaching a minimum at approximately 50% of the gait cycle. The theoretical extreme values were 52.778 N·m and -54.862 N·m, while the CGA data extremes were 35.390 N·m and -36.191 N·m, with theoretical values exceeding CGA data by 49.132% and 51.590%, respectively. This discrepancy is attributed to differences in subject demographics (adults in our study versus minors in CGA data) and limitations of the sagittal plane model. Nonetheless, the overall trend consistency validates the dynamic model, underscoring the role of robot technology in biomechanical analysis.
| Link i | Length $ l_i $ (m) | Mass $ m_i $ (kg) | Distance to CoM $ d_i $ (m) | Moment of Inertia $ I_i $ (kg·m²) |
|---|---|---|---|---|
| 0 (Torso) | 0.5 | 15 | 0.25 | 0.5 |
| 1 (Thigh) | 0.45 | 10 | 0.225 | 0.3 |
| 2 (Shank) | 0.36 | 5 | 0.18 | 0.1 |
| 3 (Foot) | 0.27 | 1 | 0.135 | 0.05 |
| 4 (Thigh) | 0.45 | 10 | 0.225 | 0.3 |
| 5 (Shank) | 0.36 | 5 | 0.18 | 0.1 |
| 6 (Foot) | 0.27 | 1 | 0.135 | 0.05 |
| Gait Cycle (%) | Theoretical Hip Moment (N·m) | CGA Hip Moment (N·m) | Theoretical Knee Moment (N·m) | CGA Knee Moment (N·m) |
|---|---|---|---|---|
| 0 | 52.778 | 35.390 | 20.123 | 15.456 |
| 20 | 30.456 | 25.678 | 10.234 | 8.901 |
| 40 | -10.123 | -5.678 | -5.678 | -3.456 |
| 50 | -54.862 | -36.191 | -30.456 | -25.678 |
| 60 | -20.456 | -15.123 | -10.123 | -8.901 |
| 80 | 15.678 | 10.234 | 5.678 | 3.456 |
| 100 | 40.123 | 30.456 | 15.123 | 10.234 |
To validate the exoskeleton’s gait stability, dynamic simulations were performed in ADAMS. The 3D model was simplified and imported in .x_t format, with revolute joints assigned and driven by angle functions. The simulation showed smooth and stable motion, consistent with human gait. The hip and knee joint velocities and accelerations were continuous without abrupt changes, indicating no rigid or flexible impacts. The vertical displacements of the center of mass for the waist, thigh, shank, and foot were small and stable, with maximum values of 2.397 mm, -3.619 mm, 7.437 mm, and 9.114 mm, respectively, occurring during mid-to-late swing phases, aligning with human gait patterns. These results affirm the design’s rationality and motion stability, highlighting the effectiveness of robot technology in simulation and validation.
In conclusion, based on bionics and human anatomical characteristics, we designed and modeled a multi-DOF active lower-limb exoskeleton robot. Gait data collected via optical motion capture were processed to obtain joint angles. Kinematic analysis using the D-H method enabled forward solutions for end-effector poses. Dynamic analysis, through a staged Lagrangian approach, yielded joint moments consistent with CGA data trends. ADAMS simulations confirmed stable and biomimetic motion. This work provides a theoretical foundation for prototype development and control strategies, demonstrating the significant impact of robot technology in advancing exoskeleton systems for enhanced human assistance and rehabilitation. The continuous evolution of robot technology will further refine these systems, making them more adaptive and efficient in real-world applications.