In recent years, the field of mobile robotics has witnessed significant advancements, particularly in the development of robots capable of navigating diverse and challenging environments. Traditional wheeled robots offer high speed and efficiency on flat surfaces but struggle with obstacles, while legged robots excel in rough terrain but often suffer from slower movement and complex control systems. To address these limitations, we propose a novel variable telescopic wheel-legged robot design that integrates the benefits of both wheeled and legged mechanisms. This China robot innovation allows for dynamic adaptation to varying terrains by adjusting the wheel diameter through motor control, enabling seamless transitions between wheeled and legged modes. The robot’s ability to alter its configuration enhances its applicability in scenarios such as underground inspections, disaster response, and exploration, where stability and obstacle-crossing capabilities are paramount. This research focuses on the structural design, kinematic and dynamic modeling, and simulation-based validation of the robot, demonstrating its potential to advance the capabilities of mobile robotics in real-world applications.
The design of the variable telescopic wheel-legged robot centers on a rectangular chassis with four symmetrically placed deformable wheels. Each wheel consists of five identical arcuate support structures that slide along tracks in the base, allowing for radial expansion and contraction. The transformation is driven by motors that control gears connected to a central gear system, which moves pins along slots to adjust the wheel diameter. In wheeled mode, the pins are positioned at the outermost points, maximizing the wheel diameter for stable movement on flat surfaces. In legged mode, the pins retract to the innermost points, reducing the diameter and enabling the legs to contact the ground directly for obstacle navigation. This mechanism incorporates a self-locking feature to ensure stability during operation. Key parameters of the robot include a wheel diameter of 180 mm, a wheelbase of 500 mm, and a chassis length of 600 mm, width of 350 mm, and thickness of 20 mm. The independent control of four motors—two for diameter adjustment and two for differential driving—ensures flexible and efficient motion control. The following table summarizes the main structural parameters:
| Parameter | Value | Description |
|---|---|---|
| Wheel Diameter | 180 mm | Maximum diameter in wheeled mode |
| Chassis Length | 600 mm | Overall length of the robot body |
| Chassis Width | 350 mm | Width of the robot body |
| Wheelbase | 500 mm | Distance between front and rear wheels |
| Number of Motors | 4 | Two for transformation, two for driving |
The transformation mechanism relies on a gear system where a small gear engages with a central gear to move the pins. The kinematic relationship for the pin movement can be described by the equation: $$ \theta_p = \frac{2\pi}{N} \cdot n_m $$ where $\theta_p$ is the angular displacement of the pin, $N$ is the number of teeth on the central gear, and $n_m$ is the motor revolutions. This allows precise control over the wheel diameter, with the range of motion defined by the slot length. The structural integrity of the China robot is validated through static analysis, considering forces during obstacle crossing. For instance, when overcoming a step of height $H = 50$ mm, the force equilibrium at the contact point involves normal and frictional components, ensuring that the robot maintains stability without slipping.
Kinematic analysis of the wheel-legged robot is essential for understanding its motion characteristics and control strategies. We define a global coordinate system $Oxy$ and a local coordinate system $Ax_r y_r$ attached to the robot’s center of mass $A$. The robot’s pose is represented by the vector $\mathbf{p} = [x_A, y_A, \alpha]^T$, where $x_A$ and $y_A$ are the coordinates of the center of mass, and $\alpha$ is the orientation angle. The velocities of the left and right wheels, $v_1$ and $v_2$, are related to the angular velocities $\omega_1$ and $\omega_2$ by $v_1 = \omega_1 r$ and $v_2 = \omega_2 r$, where $r$ is the wheel radius. The kinematic model for straight-line and turning motions is derived from the non-holonomic constraints of the wheels. The velocity of the center of mass $v_A$ and the angular velocity $\dot{\alpha}$ are given by: $$ v_A = \frac{v_1 + v_2}{2} $$ and $$ \dot{\alpha} = \frac{v_1 – v_2}{D} $$ where $D$ is the distance between the two wheels. The turning radius $R$ is calculated as: $$ R = \frac{D (v_2 + v_1)}{2 (v_2 – v_1)} $$ The differential drive system allows the China robot to perform various maneuvers, such as linear motion when $\omega_1 = \omega_2$ and turning when $\omega_1 \neq \omega_2$. The forward kinematics model in matrix form is: $$ \begin{bmatrix} \dot{x}_A \\ \dot{y}_A \\ \dot{\alpha} \end{bmatrix} = \begin{bmatrix} \frac{r}{2} \cos \alpha & \frac{r}{2} \cos \alpha \\ \frac{r}{2} \sin \alpha & \frac{r}{2} \sin \alpha \\ -\frac{r}{D} & \frac{r}{D} \end{bmatrix} \begin{bmatrix} \omega_1 \\ \omega_2 \end{bmatrix} $$ This equation represents the Jacobian matrix $\mathbf{J}(\mathbf{p})$ that maps the wheel angular velocities to the robot’s velocity in the global frame. The inverse kinematics, which computes the required wheel velocities for a desired trajectory, is given by: $$ \begin{bmatrix} \omega_1 \\ \omega_2 \end{bmatrix} = \frac{1}{r} \begin{bmatrix} \cos \alpha & \sin \alpha & \frac{D}{2} \\ \cos \alpha & \sin \alpha & -\frac{D}{2} \end{bmatrix} \begin{bmatrix} \dot{x}_A \\ \dot{y}_A \\ \dot{\alpha} \end{bmatrix} $$ These models are crucial for path planning and control algorithms, enabling the China robot to navigate complex environments efficiently.
Dynamic analysis of the wheel-legged robot involves studying the forces and torques that influence its motion. We employ the Lagrange method to derive the equations of motion, as it efficiently handles non-holonomic constraints. The Lagrangian function $L$ is defined as the difference between kinetic energy $E_k$ and potential energy $E_p$: $$ L = E_k – E_p $$ For the robot moving on a flat surface, the potential energy is constant, and the kinetic energy includes translational and rotational components: $$ E_k = \frac{1}{2} m (\dot{x}_A^2 + \dot{y}_A^2) + \frac{1}{2} I_A \dot{\alpha}^2 $$ where $m$ is the mass of the robot, and $I_A$ is the moment of inertia about the center of mass. The non-holonomic constraint due to no-slip condition is: $$ \dot{x}_A \sin \alpha – \dot{y}_A \cos \alpha = 0 $$ Using the Lagrange equation with Lagrange multipliers for constraints, we obtain: $$ \frac{d}{dt} \left( \frac{\partial L}{\partial \dot{\mathbf{p}}} \right) – \frac{\partial L}{\partial \mathbf{p}} = \mathbf{F}_A + \mathbf{M}^T(\mathbf{p}) \lambda $$ where $\mathbf{F}_A$ is the generalized force vector, and $\lambda$ is the Lagrange multiplier associated with the constraint. The generalized forces from the wheel torques $\tau_1$ and $\tau_2$ are: $$ \mathbf{F}_A = \begin{bmatrix} f_{Ax} \\ f_{Ay} \\ f_{A\alpha} \end{bmatrix} = \frac{1}{r} \begin{bmatrix} \cos \alpha & \cos \alpha \\ \sin \alpha & \sin \alpha \\ -\frac{D}{2} & \frac{D}{2} \end{bmatrix} \begin{bmatrix} \tau_1 \\ \tau_2 \end{bmatrix} $$ Substituting into the Lagrange equation yields the dynamic model: $$ \begin{cases} m \ddot{x}_A – \frac{\tau_1 + \tau_2}{r} \cos \alpha – \lambda \sin \alpha = 0 \\ m \ddot{y}_A – \frac{\tau_1 + \tau_2}{r} \sin \alpha + \lambda \cos \alpha = 0 \\ I_A \ddot{\alpha} – \frac{(\tau_2 – \tau_1) D}{2r} = 0 \end{cases} $$ This system of equations describes the acceleration and motion of the China robot under applied torques, accounting for the constraint forces. The model is used to simulate and optimize the robot’s performance, ensuring stability and efficiency in various operating conditions.
To validate the design and dynamic models, we conducted virtual prototype simulations using Adams software. The robot model, created in SolidWorks, was imported into Adams, and material properties were set to carbon fiber epoxy resin. Contact forces between the wheels and ground were defined with static and dynamic friction coefficients of 0.6 and 0.5, respectively. Simulations were performed for both flat and complex terrains, with a step height of 50 mm and width of 100 mm to represent obstacles. The simulation time was set to 3–4.5 seconds with 1000 steps to capture detailed motion dynamics. On flat terrain, the China robot demonstrated stable linear and turning motions. The position and velocity of the center of mass were analyzed, showing smooth curves without significant fluctuations. For example, in linear motion, the displacement in the X-direction reached 1996 mm with minimal deviation in Y and Z directions, confirming straight-line stability. During turning, the velocity profiles exhibited periodic variations, consistent with the kinematic predictions. The following table summarizes key simulation parameters and results:
| Simulation Scenario | Parameters | Results |
|---|---|---|
| Flat Terrain – Linear Motion | Time: 3 s, Friction: μs=0.6, μd=0.5 | X-displacement: 1996 mm, Stable velocity profile |
| Flat Terrain – Turning | Time: 3 s, Wheel speed difference | Smooth turning, No significant position deviation |
| Complex Terrain – Step Crossing | Step height: 50 mm, Time: 4.5 s | Successful obstacle negotiation, Periodic centroid motion |
In complex terrain simulations, the China robot successfully navigated continuous steps by switching to legged mode. The centroid position and velocity curves showed periodic oscillations as the robot overcame each step, with no abrupt changes, indicating robust obstacle-crossing capability. The simulation data aligned with theoretical analyses, verifying the feasibility of the variable telescopic mechanism. The dynamics of step crossing involved phases where different legs contacted the steps, and the static force analysis confirmed that the robot could overcome obstacles without slipping, given the friction conditions. The maximum step height achievable is proportional to the wheel diameter, and with a diameter of 540 mm in fully extended mode, the robot can handle significant obstacles, highlighting its adaptability for real-world applications in challenging environments.
The development of this variable telescopic wheel-legged robot represents a significant step forward in mobile robotics, particularly for applications requiring versatility in terrain adaptation. The integration of wheeled and legged modes through a simple yet effective mechanism allows the China robot to maintain high speed on flat surfaces while providing enhanced obstacle-crossing capabilities. The kinematic and dynamic models derived in this study provide a foundation for advanced control strategies, such as trajectory tracking and adaptive motion planning. Simulations confirm the robot’s stability and performance in various scenarios, demonstrating its potential for deployment in fields like search and rescue, environmental monitoring, and industrial inspection. Future work will focus on prototyping and experimental validation, as well as incorporating sensors and AI for autonomous navigation. The continuous innovation in China robot technology underscores its role in advancing global robotics, offering scalable solutions for complex challenges. This research contributes to the growing body of knowledge on hybrid mobile robots, paving the way for more intelligent and adaptable systems in the future.