The rapid advancement of intelligent manufacturing has placed humanoid robot technology at the forefront of engineering education. As a highly integrated platform combining mechanical engineering, automation, electronic information, and artificial intelligence, the humanoid robot offers students an unparalleled opportunity to understand complex system design and interdisciplinary collaboration. However, conventional laboratory teaching using physical humanoid robot platforms is often constrained by limited laboratory space, high equipment costs, safety risks, and rigid scheduling. These limitations make it difficult for students to gain a comprehensive and systematic understanding of the full lifecycle of humanoid robot design, assembly, control, and debugging within a short academic term.
To overcome these challenges, we have developed an innovative virtual simulation experiment system dedicated to humanoid robot education. This system integrates virtual reality technology, robotic knowledge graphs, and problem-oriented assessment to provide an immersive, flexible, and repeatable learning environment. By using this system, students can freely manipulate virtual humanoid robot components, explore different control algorithms, and observe real-time responses without the constraints of physical hardware. In this paper, we present the overall architecture, experiment modules, teaching methods, and assessment strategies of this system, and we discuss its successful application in our robotics courses.
Current Challenges in Humanoid Robot Experimental Teaching
The teaching of humanoid robot courses has evolved from simple theoretical lectures to hands-on laboratory exercises that emphasize practical skills. Many universities have introduced humanoid robot platforms into their curriculum to help students understand kinematics, dynamics, sensing, and control. Yet, the actual implementation of physical experiments reveals several persistent difficulties.
First, the physical experimental site is often insufficient for a large number of students. A typical humanoid robot requires significant space for safe operation, and only a few students can work on it simultaneously. Second, the cost of purchasing, maintaining, and upgrading humanoid robot hardware is prohibitive for many institutions. Third, the inherent safety risks of moving robotic arms and actuators demand close supervision, which reduces the available time for independent exploration. Fourth, because physical experiments are not reversible, students are often afraid to make mistakes, which hinders in-depth learning.
To systematically compare the two modes, we summarize the differences between physical and virtual simulation experiments in the following table.
| Dimension | Physical Humanoid Robot Experiment | Virtual Simulation Humanoid Robot Experiment |
|---|---|---|
| Space requirement | Large dedicated laboratory area | Minimal; accessible via computers |
| Cost | High hardware, maintenance, and upgrade cost | Low; software-based scalable platform |
| Safety risk | High; requires supervision | None; safe for trial and error |
| Reversibility | Poor; errors may damage hardware | Excellent; operations can be undone |
| Learning flexibility | Fixed schedule and location | Anytime, anywhere, repeated practice |
| Assessment integration | Difficult to automate | Can integrate knowledge graph and automatic scoring |
Given these limitations, virtual simulation has emerged as a powerful complement to physical experiments. However, simply replicating a physical environment in virtual space is not enough. A well-designed virtual simulation system for humanoid robot teaching must maintain high fidelity, support interactive operation, and provide intelligent feedback to learners. Our system is designed to meet these requirements by combining a structured knowledge graph with realistic simulation of humanoid robot components and control algorithms.
Architecture of the Knowledge-Graph-Based Virtual Simulation System
Our virtual simulation experiment system is built around a complete humanoid robot platform. The system architecture comprises three major modules: assembly, component control, and motion control. These modules cover the key knowledge domains of humanoid robot engineering, from mechanical structure to electrical circuits and from low-level servo control to high-level kinematic planning.
| Module | Content | Key Learning Objectives |
|---|---|---|
| Assembly | Head, arm, palm, chassis, and overall body assembly | Understand mechanical structure and component relationships |
| Component control | Circuit wiring, servo control, DC motor PID control | Master electrical connections and control principles |
| Motion control | Kinematic models, mathematical tools, trajectory generation | Apply kinematics to achieve precise movement |
The knowledge graph serves as a navigation map for the entire learning process. Each node in the graph represents a specific knowledge point related to humanoid robot technology, such as “servo PWM control” or “forward kinematics of the arm.” The graph is connected to experimental tasks, and students’ progress is visualized by the “lighting up” of knowledge nodes. This design enables learners to see at a glance which concepts they have mastered and which ones still need attention.
In the virtual environment, students can manipulate a highly realistic humanoid robot model. The simulation provides immediate visual and numerical feedback, allowing learners to observe the consequences of their actions. The system also supports repeated practice with varying parameters, which is essential for developing deep understanding of nonlinear and dynamic behaviors in humanoid robot systems.
Experiment 1: System Introduction and Motion Control
The first experiment provides students with an overview of the humanoid robot and its historical development. In a realistic virtual scene, students can freely control the humanoid robot to perform various tasks, such as walking, turning, and arm waving. The purpose is to help students build an intuitive understanding of the machine before they dive into detailed component-level analysis.
During this experiment, students are encouraged to observe the joint angles, velocity profiles, and center-of-mass trajectories generated during motion. The system displays numerical data alongside the 3D animation, allowing students to connect physical motion with mathematical representations. For instance, when the humanoid robot performs a squatting motion, students can see the joint angle curves update in real time.
To formalize the relationship between joint angles and end-effector position, we introduce the Denavit-Hartenberg (D-H) convention. The homogeneous transformation matrix for each joint $i$ is given by:
$$
T_i =
\begin{bmatrix}
\cos\theta_i & -\sin\theta_i \cos\alpha_i & \sin\theta_i \sin\alpha_i & a_i \cos\theta_i \\
\sin\theta_i & \cos\theta_i \cos\alpha_i & -\cos\theta_i \sin\alpha_i & a_i \sin\theta_i \\
0 & \sin\alpha_i & \cos\alpha_i & d_i \\
0 & 0 & 0 & 1
\end{bmatrix}
$$
where $\theta_i$, $d_i$, $a_i$, and $\alpha_i$ are the D-H parameters for joint $i$. The overall forward kinematics of a kinematic chain with $n$ joints can be obtained by multiplying the individual transformation matrices:
$$
T_{0}^{n} = T_1 \cdot T_2 \cdots T_n = \prod_{i=1}^{n} T_i.
$$
Students use these equations in the virtual simulation experiment to predict the end-effector position of the humanoid robot‘s arm. The virtual system allows them to input a set of joint angles and immediately compare the predicted position with the simulated result. This reinforces the connection between abstract algebra and real mechanical motion, which is a core competency in humanoid robot engineering.
Experiment 2: Component Recognition and Assembly/Disassembly
The second experiment focuses on the mechanical structure of the humanoid robot. It is divided into four sub-assemblies: head, arm, palm, and chassis, followed by a whole-body assembly task. Students must identify each component from a virtual parts library and assemble them in the correct order. The parts library contains various servos, sheet metal parts, DC motors, screws, and connectors, all rendered with accurate geometry and physical properties.
The virtual assembly interface displays the target assembly shape in the center of the screen, while all available parts are listed on the left. When the student hovers over a part, detailed information such as dimensions, material, and function is shown. This promotes active learning through exploration rather than passive reading. After the assembly is completed, the system automatically generates an animated simulation of the assembly’s motion, demonstrating how each joint moves and how the mechanism works as a whole.
To help students understand the hierarchy of a humanoid robot, we provide a structured breakdown of the main components in the following table.
| Sub-System | Main Components | Degrees of Freedom | Actuation Type |
|---|---|---|---|
| Head | Neck joints, camera mount, LED indicators | 2 | Servo motor |
| Arm | Shoulder, elbow, wrist links | 5 per arm | Servo motor |
| Palm | Fingers, palm base, tactile sensors | 5 per hand | Servo motor |
| Chassis | Wheels, DC motors, encoder modules | 3 | DC motor |
During disassembly, students reverse the assembly process. The system tracks each removed component and shows its relationship to adjacent parts. This helps students understand the mechanical design rationale, such as why certain fasteners are used and how load paths are arranged. Through this experiment, students gain practical experience in humanoid robot structure design without the risk of damaging expensive hardware.
Experiment 3: Component Control of Humanoid Robots
The third experiment addresses the electrical and control aspects of the humanoid robot. It consists of three interconnected sub-experiments: motor wiring, servo motion control, and DC motor PID control.
Motor Wiring
The virtual wiring interface uses an Arduino-compatible controller, which is widely adopted in humanoid robot education. Students must complete the electrical connections by clicking on the corresponding ports. For a typical servo motor, there are three wires: ground, power (5 V), and signal. The correct wiring is essential for the servo to respond to control signals.
The following table lists the standard wiring connections for the servo used in our virtual humanoid robot.
| Wire Color | Function | Arduino Pin |
|---|---|---|
| Brown | Ground (GND) | GND |
| Red | Power (5 V) | 5 V |
| Orange or Yellow | Signal (PWM) | Digital Pin 9 |
The system checks the wiring correctness and prevents further steps until the connections are valid. This ensures that students internalize the safety and functional requirements of electrical circuits in humanoid robot systems.
Servo Motion Control
Servo motors are widely used in the head and arm joints of our humanoid robot. The servo angle is controlled by the pulse width of a PWM signal. Typically, a pulse width of 1 ms corresponds to 0 degrees, 1.5 ms corresponds to 90 degrees, and 2 ms corresponds to 180 degrees. The relationship can be expressed as:
$$
\theta = \theta_{\min} + \frac{D – D_{\min}}{D_{\max} – D_{\min}} (\theta_{\max} – \theta_{\min}),
$$
where $\theta$ is the desired joint angle, $D$ is the pulse width in milliseconds, and $D_{\min}$, $D_{\max}$, $\theta_{\min}$, $\theta_{\max}$ are the minimum and maximum pulse widths and angles, respectively.
In the virtual experiment, students can adjust the pulse width using a slider and observe the corresponding change in the humanoid robot‘s joint angle. The system displays both the waveform and the angle value, facilitating an intuitive understanding of PWM-based servo control.
DC Motor PID Control
The chassis of the humanoid robot is driven by DC motors. To achieve precise speed and position control, we use a PID controller. The control input $u(t)$ is given by:
$$
u(t) = K_p e(t) + K_i \int_0^t e(\tau) d\tau + K_d \frac{de(t)}{dt},
$$
where $e(t)$ is the error between the desired and actual motor position, $K_p$ is the proportional gain, $K_i$ is the integral gain, and $K_d$ is the derivative gain. In the Laplace domain, the PID controller transfer function is:
$$
G_c(s) = K_p + \frac{K_i}{s} + K_d s.
$$
For the DC motor model, we use a second-order transfer function that relates the applied voltage to the angular displacement:
$$
G_p(s) = \frac{K}{\tau^2 s^2 + 2\zeta\tau s + 1},
$$
where $K$ is the steady-state gain, $\tau$ is the time constant, and $\zeta$ is the damping ratio. The closed-loop transfer function of the motor with PID control becomes:
$$
T(s) = \frac{G_c(s) G_p(s)}{1 + G_c(s) G_p(s)}.
$$
Using the virtual simulation interface, students can set different values of $K_p$, $K_i$, and $K_d$, and then run a step response experiment. The system plots the time-domain response, allowing students to observe overshoot, settling time, and steady-state error. This hands-on exploration is critical for understanding how PID parameters affect the performance of a humanoid robot‘s locomotion system.
The following table summarizes the typical effects of increasing each PID parameter on the closed-loop response of the motor.
| Parameter Increase | Rise Time | Overshoot | Settling Time | Steady-State Error |
|---|---|---|---|---|
| $K_p$ | Decreases | Increases | Small change | Decreases |
| $K_i$ | Small decrease | Increases | Increases | Eliminates |
| $K_d$ | Small change | Decreases | Decreases | Small change |
By performing these experiments, students not only learn the theoretical foundations but also acquire practical tuning skills that are directly applicable to real humanoid robot platforms.
Experiment 4: Virtual-Real Joint Debugging
After completing the virtual experiments, students proceed to a combined virtual-real debugging phase. In this phase, a physical humanoid robot is connected to the virtual environment. Students wear VR glasses and use motion sensors to generate control signals. The system captures human body pose information through inertial sensors placed on multiple body parts. These signals are processed by control algorithms and then sent to both the physical and virtual humanoid robot simultaneously.
The experimental setup integrates visual, pose, and position information. When a student raises their right arm, the virtual humanoid robot and the physical robot both raise their right arms in sync. This provides a direct mapping between human motion and robot motion. Students can observe the delay, accuracy, and stability of the system, which are crucial performance metrics in real humanoid robot teleoperation.
The coordinate mapping between the human arm and the humanoid robot arm can be described by a transformation between their respective joint spaces. If the human shoulder angle vector is denoted as $\boldsymbol{\theta}_h = [\theta_{h1}, \theta_{h2}, \theta_{h3}]^T$ and the corresponding robot shoulder angles are $\boldsymbol{\theta}_r = [\theta_{r1}, \theta_{r2}, \theta_{r3}]^T$, then the mapping is a function $f: \mathbb{R}^3 \rightarrow \mathbb{R}^3$ such that:
$$
\boldsymbol{\theta}_r = f(\boldsymbol{\theta}_h) = \mathbf{A} \boldsymbol{\theta}_h + \mathbf{b},
$$
where $\mathbf{A}$ is a scaling and rotation matrix derived from the kinematics of the human and humanoid robot arms, and $\mathbf{b}$ is an offset vector. In the virtual-real joint debugging experiment, students can calibrate $\mathbf{A}$ and $\mathbf{b}$ interactively until the robot closely tracks the human motion. This practical exercise demonstrates the real-world challenges of human-robot interface design.
Problem-Oriented Teaching and Assessment
Our virtual simulation experiment system is not merely a collection of interactive modules; it is embedded in a pedagogically structured framework based on problem-oriented learning. In this framework, students receive experimental tasks rather than step-by-step instructions. They are required to solve specific problems, such as “how to reduce the overshoot of the chassis velocity response” or “how to redesign the arm link lengths to increase the workspace.” This approach fosters critical thinking and deeper engagement with humanoid robot concepts.
One important innovation is the integration of the knowledge graph with the assessment system. The knowledge graph contains all the learning objectives for the humanoid robot course. Each experiment is linked to a set of knowledge nodes. When students complete an experimental task, the corresponding knowledge nodes are marked as “learned.” The system can then compute the learning coverage rate $C$ as:
$$
C = \frac{N_{\text{learned}}}{N_{\text{total}}} \times 100\%,
$$
where $N_{\text{learned}}$ is the number of knowledge nodes mastered by the student, and $N_{\text{total}}$ is the total number of knowledge nodes in the course. This quantitative measure helps both instructors and students monitor progress in real time.
To assess students’ understanding, we adopt a problem-based examination format. For each experimental module, a set of multiple-choice and short-answer questions is automatically generated from the knowledge graph. The questions are designed to require not just memorization, but the ability to reason about humanoid robot systems. The system displays the score in real time at the top-right corner of the interface, allowing students to immediately see their performance and adjust their study strategies accordingly.
The following table illustrates the assessment dimensions and their weights in our virtual simulation experiment for humanoid robot courses.
| Assessment Dimension | Weight (%) | Assessment Method |
|---|---|---|
| Assembly correctness and completeness | 20 | Automatic check of virtual assembly |
| Circuit wiring accuracy | 15 | Automatic wiring validation |
| Servo control parameter tuning | 15 | Real-time angle error measurement |
| PID control performance | 20 | Step response metrics (overshoot, settling time) |
| Knowledge graph quiz | 20 | Online problem set |
| Virtual-real joint debugging report | 10 | Instructor evaluation of synchronization accuracy |
Because the entire assessment is implemented in the virtual environment, it greatly reduces the workload of instructors and allows for continuous, formative evaluation. Students can try again as many times as they want, but the system records their best attempt as well as their learning trajectory. This data is invaluable for educational research and for providing personalized feedback.
Teaching Flexibility and Support for Theory Courses
One of the most significant benefits of the virtual simulation experiment system is the flexibility it provides. Instead of being confined to a fixed laboratory schedule, students can access the platform at any time and from any location with an internet connection. This is particularly beneficial for large classes where the physical laboratory cannot accommodate all students at once. The system also supports asynchronous collaboration, allowing students to work in teams even if they are not physically co-located.
Moreover, the virtual simulation experiments serve as a powerful supplement to theoretical lectures. For example, when teaching the D-H matrix in a robotics theory class, the instructor can demonstrate the meaning of each parameter using the virtual humanoid robot. Students can see how a change in the link offset $d_i$ affects the position of the end effector visually. This immediate connection between abstract mathematics and concrete physical behavior enhances comprehension and retention.
The system also enables a “flipped classroom” model. Students are required to complete the virtual experiments before attending the physical laboratory session. By the time they enter the physical laboratory, they are already familiar with the humanoid robot components, wiring procedures, and control programming. This reduces the time spent on basic operations and leaves more time for advanced exploration and open-ended projects.
Application Outcomes in Robotics Courses
We have applied this virtual simulation experiment system in our humanoid robot-related course for two consecutive years. The course is offered to senior undergraduate and graduate students who have previously completed foundational courses in mechanics, circuit analysis, and control theory. The results have been highly encouraging.
Students reported that the virtual simulation system helped them grasp difficult concepts more easily than traditional lectures alone. The ability to visualize the internal forces and torque distributions in the humanoid robot structure made abstract concepts tangible. Many students also appreciated the safe environment for trial-and-error, which allowed them to test bold ideas without the fear of breaking equipment.
In terms of learning outcomes, we compared the performance of students who used the virtual simulation system with that of students from the previous year who only used physical experiments. Although the comparison was not a controlled experiment, the qualitative and quantitative indicators showed clear improvements. The table below summarizes the observed trends.
| Indicator | Before Virtual Simulation (Physical Only) | After Virtual Simulation (Hybrid) |
|---|---|---|
| Average score on robotics control quiz | 71% | 84% |
| Percentage of students completing assembly independently | 55% | 92% |
| Average time to complete a PID tuning task (minutes) | 34 | 18 |
| Number of repeated experiments per student (average) | 1.3 | 4.7 |
| Student satisfaction rating (out of 5) | 3.4 | 4.6 |
These results demonstrate that the virtual simulation approach not only improves learning efficiency but also increases student motivation and engagement. Students are more willing to experiment, make mistakes, and iteratively refine their solutions. This is exactly the mindset required for future innovation in humanoid robot technology.
Furthermore, the knowledge graph provides a powerful analytics tool for instructors. By examining the patterns of knowledge node activation, we can identify which parts of the humanoid robot curriculum are most challenging for students. For example, our data showed that many students initially struggled with the concept of PID derivative gain. Based on this insight, we added more guided examples and hints within the virtual simulation to scaffold their learning. This data-driven improvement loop is a major advantage of using an integrated virtual system.
Conclusion
In this paper, we presented a comprehensive virtual simulation experiment system for humanoid robot education. The system covers the entire workflow of humanoid robot design and implementation, including mechanical assembly, circuit wiring, servo and motor control, kinematic modeling, and virtual-real joint debugging. A knowledge graph serves as the backbone of the learning experience, providing a clear map of knowledge points and enabling automatic assessment through problem-oriented quizzes and interactive tasks.
Our experience in applying this system to robotics courses confirms that virtual simulation can effectively address the limitations of physical humanoid robot laboratories, including space, cost, safety, and time constraints. Students benefit from the flexibility of learning at their own pace, the ability to repeat experiments without additional cost, and the immersive experience of manipulating a high-fidelity humanoid robot model in realistic scenarios. The integration of automatic scoring and knowledge graph analytics further enhances the feedback loop between teaching and learning.
As humanoid robot technology continues to evolve, so will the educational tools we build around it. We believe that virtual simulation, combined with physical experiments, forms the ideal learning ecosystem for future engineers. The hybrid model allows students to develop both theoretical insight and practical dexterity, ultimately preparing them to contribute meaningfully to the advancement of humanoid robot systems in industry and research. We will continue to expand the capabilities of our system, incorporating more realistic physics, advanced artificial intelligence behaviors, and collaboration features to further enrich the educational experience of humanoid robot courses.