In recent years, the field of bionic robotics has seen significant advancements, with researchers drawing inspiration from biological systems to develop machines capable of performing complex tasks. Among these, bionic robots that mimic the locomotion of animals have gained attention for their ability to navigate challenging terrains. This article focuses on the design and analysis of a bionic robot inspired by the jumping spider, which exhibits remarkable jumping capabilities. The primary goal is to enhance the vertical and forward jumping performance of multi-legged robots by integrating a compound mechanism that combines leg extension with a body ejection system. The bionic robot leverages principles from biomechanics to achieve efficient energy storage and release, enabling it to overcome obstacles and adapt to various environments. Through kinematic and dynamic modeling, along with simulations and experimental validation, this study demonstrates the effectiveness of the proposed design in improving jumping height and distance, making it suitable for applications in exploration, rescue operations, and beyond.
The jumping spider, known for its agile movements, utilizes a hydraulic-like mechanism in its legs to propel itself into the air. By analyzing its leg structure and jumping behavior, we have designed a bionic robot that replicates this motion through a combination of mechanical linkages and an ejection device. The robot features six legs, each composed of multiple segments analogous to the spider’s hip, femur, knee-tibia, and tarsus, with integrated damping springs to absorb impact during landing. The ejection mechanism, positioned at the center of the body, stores energy in springs and releases it synchronously with leg movements to achieve compound jumping. This approach allows the bionic robot to generate greater thrust compared to traditional leg-driven systems, resulting in enhanced performance. The following sections detail the design process, mathematical modeling, control system implementation, and validation through simulations and physical experiments.
To understand the locomotion of the bionic robot, a kinematic analysis of the leg structure is essential. The leg is modeled as a series of linkages connected by rotational joints, and the Modified Denavit-Hartenberg (MD-H) method is employed to establish coordinate frames and derive transformation matrices. Each leg consists of four segments: the hip link, femur link, knee-tibia link, and tarsus link, with lengths denoted as $L_1$, $L_2$, $L_3$, and $L_4$, respectively. The D-H parameters for these segments are summarized in the table below, where $\alpha_{i-1}$ represents the twist angle, $a_{i-1}$ is the link length, $\theta_i$ is the joint angle, and $d_i$ is the offset.
| Link | $\alpha_{i-1}$ (°) | $a_{i-1}$ (mm) | $\theta_i$ (°) | $d_i$ (mm) |
|---|---|---|---|---|
| 1 | 0 | 0 | $\theta_1$ | 0 |
| 2 | -90 | 0 | $\theta_2$ | 0 |
| 3 | 0 | $L_2$ | $\theta_3$ | 0 |
| 4 | 0 | $L_3$ | $\theta_4$ | 0 |
The transformation matrix between consecutive frames is given by:
$$^{i-1}T_i = \begin{bmatrix}
\cos \theta_i & -\sin \theta_i & 0 & a_{i-1} \\
\cos \alpha_{i-1} \sin \theta_i & \cos \alpha_{i-1} \cos \theta_i & -\sin \alpha_{i-1} & -d_i \sin \alpha_{i-1} \\
\sin \alpha_{i-1} \sin \theta_i & \sin \alpha_{i-1} \cos \theta_i & \cos \alpha_{i-1} & d_i \cos \alpha_{i-1} \\
0 & 0 & 0 & 1
\end{bmatrix}$$
The position of the end-effector (tarsus tip) in the base coordinate frame is derived as:
$$^0M_P = \begin{bmatrix}
L_2 C_1 C_2 + L_3 C_1 C_{23} + L_4 C_1 C_{234} \\
L_2 S_1 C_2 + L_3 S_1 C_{23} + L_4 S_1 C_{234} \\
-L_2 S_2 – L_3 S_{23} – L_4 S_{234} \\
1
\end{bmatrix}$$
where $S_i = \sin \theta_i$, $C_i = \cos \theta_i$, $C_{23} = C_2 C_3 – S_2 S_3$, $S_{23} = C_2 S_3 + S_2 C_3$, $C_{234} = C_2 C_{34} – S_2 S_{34}$, and $S_{234} = C_2 S_{34} + S_2 C_{34}$. The workspace of the leg is analyzed using MATLAB, considering joint angle ranges of $(-\pi/2, \pi/2)$ for the hip and knee joints, and $(-3\pi/4, \pi/2)$ for the tarsus joint. This analysis ensures that the bionic robot can achieve sufficient reach and flexibility during jumping motions.
Dynamic modeling of the bionic robot’s leg is performed using the Lagrangian method to determine the torques required at each joint for jumping. The system’s kinetic energy $E_K$ and potential energy $W_G$ are considered, and the Lagrangian $L$ is defined as $L = E_K – W_G$. The torque $\tau_i$ for each joint is computed as:
$$\tau_i = \frac{d}{dt} \frac{\partial L}{\partial \dot{\theta}_i} – \frac{\partial L}{\partial \theta_i}$$
Assuming the center of mass for each link is at its end, the equations for the torques are derived as follows:
$$\tau_1 = (m_1 L_1^2 + m_2 L_2^2 C_2^2 + m_3 L_3^2 C_{23}^2 + m_4 L_4^2 C_{234}^2) \ddot{\theta}_1$$
$$\tau_2 = (m_2 L_2^2 + m_3 L_3^2 + m_4 L_4^2) \ddot{\theta}_2 + \left( \frac{1}{2} m_2 L_2^2 \sin(2\theta_2) + m_3 L_3^2 C_{23} S_{23} + m_4 L_4^2 C_{234} S_{234} \right) \dot{\theta}_1^2 + m_2 g L_2 C_2 + m_3 g (L_3 C_{23} + L_2 C_2) + m_4 g (L_4 C_{234} + L_3 C_{23} + L_2 C_2)$$
$$\tau_3 = (m_3 L_3^2 + m_4 L_4^2) \ddot{\theta}_3 + (m_3 L_3^2 C_{23} S_{23} + m_4 L_4^2 C_{234} S_{234}) \dot{\theta}_1^2 + m_3 g L_3 C_{23} + m_4 g (L_4 C_{234} + L_3 C_{23})$$
$$\tau_4 = m_4 L_4^2 \ddot{\theta}_3 + m_4 L_4^2 C_{234} S_{234} \dot{\theta}_1^2 + m_4 g L_4 C_{234}$$
Here, $m_1$, $m_2$, $m_3$, and $m_4$ represent the masses of the hip, femur, knee-tibia, and tarsus links, respectively, and $g$ is the acceleration due to gravity. These equations help in selecting appropriate actuators for the bionic robot to ensure efficient energy transfer during jumping.
The ejection mechanism is a critical component of the bionic robot, designed to store and release energy in coordination with leg movements. It employs a ratchet and bevel gear transmission system driven by a motor and reducer. The mechanism compresses springs via a rotating杆 connected to a soft steel cable, which pulls an ejection plate. When the plate contacts the frame, energy storage is complete, and the motor stops. The ratchet ensures unidirectional torque transmission, preventing energy feedback to the motor during release. The transmission ratio is 1:1:1 between the motor, ratchet, and bevel gears, allowing precise control over spring compression.
The energy storage springs are designed based on the conservation of energy and Hooke’s law. The target vertical jumping height is set to 0.5 m, and the robot’s mass is estimated at 2.4 kg. The required energy for jumping is calculated as:
$$E_0 = E_K = E_G = m g h = 2.4 \times 9.8 \times 0.5 = 11.76 \, \text{J}$$
Considering spring energy utilization efficiency $\eta_{\text{spring}} = 80\%$ and gear transmission efficiency $\eta_{\text{gear}} = 90\%$, the initial energy needed is:
$$E_1 = \frac{E_0}{\eta_{\text{spring}} \eta_{\text{gear}}^2} = \frac{11.76}{0.8 \times 0.9^2} = 16.29 \, \text{J}$$
With a spring compression length of 45 mm, the required spring stiffness $k_0$ is:
$$k_0 = \frac{2 E_1}{(0.045)^2} = \frac{2 \times 16.29}{0.002025} \approx 16.09 \, \text{N/mm}$$
Since two springs are used, each spring has a stiffness of $k_1 = k_2 = 8.045 \, \text{N/mm}$. The force exerted by each spring at full compression is:
$$F_{\text{spring}} = k_1 \times \Delta x = 8.045 \times 45 = 362.03 \, \text{N}$$
A non-standard spring with a mean diameter $D = 12 \, \text{mm}$, wire diameter $d = 2 \, \text{mm}$, and 11 active coils is selected. The stiffness of this spring is verified as:
$$k = \frac{G d^4}{8 D^3 n} = \frac{79 \times 10^9 \times (0.002)^4}{8 \times (0.012)^3 \times 11} \approx 8.312 \, \text{N/mm}$$
which meets the design requirements. Simulations in ADAMS show that the spring force, deformation, and velocity during jumping align with theoretical predictions, ensuring reliable performance of the bionic robot.
The control system for the bionic robot is implemented using an Arduino platform, which coordinates leg joint movements and ejection timing. The hardware includes an Arduino UNO R3 board, PCA9685 16-channel servo driver, servos for joint actuation, and ultrasonic sensors for distance measurement. The system adjusts pre-jump posture, mid-air balance, and landing stance by controlling servo angles and sequences. For example, during vertical jumping, the hip joints remain fixed, while leg, knee, and tarsus joints are set to specific angles. The table below summarizes the joint angle configurations for vertical and forward jumping.
| Jump Type | Joint | Leg 1 (°) | Leg 2 (°) | Leg 3 (°) | Leg 4 (°) | Leg 5 (°) | Leg 6 (°) |
|---|---|---|---|---|---|---|---|
| Vertical | Hip | 0 | 0 | 0 | 0 | 0 | 0 |
| Leg | -60 | -60 | -60 | 60 | 60 | 60 | |
| Knee | 60 | 60 | 60 | -60 | -60 | -60 | |
| Tarsus | 50/-30 | 50/-30 | 50/30 | -50/30 | -50/30 | -50/30 | |
| Forward | Hip | 0 | 0 | 0 | 0 | 0 | 0 |
| Leg | -29/29 | -35/-40/75 | -53.5/-40/93.5 | 29/-29 | -35/-40/-75 | -53.5/-40/93.5 | |
| Knee | 35/-35 | 25/40/-65 | 38.5/40/-78.5 | -35/35 | -25/-40/65 | -38.5/-40/78.5 | |
| Tarsus | 40/30/-70 | 9.9/40/-49.9 | 22/60/-82 | -40/-30/70 | -9.9/-40/49.9 | -22/-60/82 |
Simulations in ADAMS are conducted to validate the jumping performance of the bionic robot. For vertical jumping, the robot achieves a maximum height of 734.1176 mm, exceeding the target of 500 mm. The center of mass displacement, velocity, and acceleration curves indicate stable take-off and landing, with minor oscillations due to spring damping. In forward jumping, the robot reaches a maximum height of 425.9005 mm and a forward distance of 447.6417 mm. The acceleration profiles show peaks during take-off and landing, which are mitigated by the damping springs in the tarsus links. These results demonstrate the efficacy of the compound jumping mechanism in enhancing the mobility of the bionic robot.
Experimental validation is performed using a 3D-printed model of the bionic robot, with a total height of 19.5 cm and a mass of 901.3 g. The control system is implemented with Arduino, and ultrasonic sensors measure jumping height and velocity. The experimental data closely match the simulation results, with deviations attributed to slight differences in spring stiffness and environmental factors. The jumping postures observed in experiments align with the simulated sequences, confirming the feasibility of the compound jumping approach for bionic robots. This validation underscores the potential of bio-inspired designs in advancing robotic locomotion.
In conclusion, the bionic robot with a compound jumping mechanism effectively combines leg extension and body ejection to achieve significant improvements in vertical and forward jumping performance. The kinematic and dynamic analyses provide a foundation for optimizing leg movements and energy storage, while the ejection mechanism ensures synchronized energy release. Simulations and experiments validate the design, showing that the bionic robot can reach heights over 700 mm and distances near 450 mm. Future work may focus on refining the control system for adaptive terrain response and integrating sensors for autonomous navigation. This study highlights the importance of biomimicry in developing advanced bionic robots for real-world applications.