In the field of robotics, bionic robots have garnered significant attention due to their ability to mimic biological organisms, offering enhanced adaptability and performance in complex environments. Among these, jumping robots stand out for their superior obstacle-crossing and evasion capabilities, making them ideal for applications such as exploration, search and rescue, and military operations. However, achieving high jumping heights and distances remains a challenge. Inspired by the remarkable jumping mechanics of jumping spiders, we have developed a novel composite jumping bionic robot that combines a body ejection mechanism with leg extension to maximize vertical and forward leap performance. This article details the design, analysis, and validation of this bionic robot, employing kinematic and dynamic modeling, energy-based spring design, and extensive simulation and experimental studies.
The jumping spider, a member of the Salticidae family, exhibits extraordinary jumping abilities, often leaping over ten times its body length. This is primarily attributed to its leg structure and hydraulic-driven extension mechanism. By studying this natural model, we identified key principles for our bionic robot: the use of multiple legs for coordinated motion and the accumulation of energy for rapid release. Our bionic robot incorporates three pairs of legs, each simplified into a four-link mechanism, and a central ejection device with an energy-storing spring. This composite approach allows for synergistic energy contribution from both leg extension and spring release, thereby enhancing overall jumping performance.
To understand the biomechanics behind our design, we first analyzed the jumping spider’s leg configuration. The spider’s legs consist of segments such as the coxa, femur, patella, tibia, metatarsus, and tarsus, with joints enabling flexion and extension. During a jump, the spider rapidly extends its legs, particularly the third and fourth pairs, utilizing hydraulic pressure from body fluids to propel itself. This process involves a preparatory crouch, explosive extension, and controlled landing. Our bionic robot emulates this by using servo motors to actuate leg joints and a spring-based ejection system to provide additional thrust. The robot’s legs are designed with linkages corresponding to the femur, tibia, and tarsus, with a damping spring integrated into the tarsal link to absorb impact during landing, ensuring stability.
The overall structure of our bionic robot was modeled using UG 3D software, comprising a main body, six legs, and the ejection device. The legs are arranged symmetrically, with each leg having four rotational joints: hip, thigh, knee, and ankle. The ejection device, positioned centrally, includes a ratchet and bevel gear transmission system to compress and release a spring. This design enables the bionic robot to perform both vertical and forward jumps by adjusting leg angles and timing the spring release. The composite jumping motion involves three phases: pre-jump posture adjustment, powered takeoff via leg extension and spring ejection, and stabilized landing with leg damping.
To optimize the bionic robot’s movement, we conducted kinematic analysis using the Modified Denavit-Hartenberg (MD-H) method. This involved defining coordinate frames for each leg segment and deriving transformation matrices. The position of the leg end-effector (tarsal link endpoint) relative to the base frame is given by:
$$^0_M\mathbf{T} = ^0_4\mathbf{T} \cdot ^4_M\mathbf{P} = \begin{bmatrix}
L_2 C_1 C_2 + L_3 C_1 C_{23} + L_4 C_1 C_{234} \\
L_2 S_1 C_2 + L_3 S_1 C_{23} + L_4 S_1 C_{234} \\
– L_2 S_2 – L_3 S_{23} – L_4 S_{234} \\
1
\end{bmatrix}$$
where \(C_i = \cos(\theta_i)\), \(S_i = \sin(\theta_i)\), \(C_{23} = C_2 C_3 – S_2 S_3\), \(S_{23} = C_2 S_3 + S_2 C_3\), \(C_{234} = C_2 C_{34} – S_2 S_{34}\), \(S_{234} = C_2 S_{34} + S_2 C_{34}\), and \(L_2, L_3, L_4\) are link lengths. The joint angles \(\theta_1, \theta_2, \theta_3, \theta_4\) correspond to hip, thigh, knee, and ankle rotations, respectively. The workspace of the leg was computed using MATLAB, considering both moving and fixed hip joints, to ensure sufficient range for jumping postures. The results, visualized in 3D plots, confirmed that the bionic robot’s legs can achieve the necessary configurations for takeoff and landing.
| Link | \(\alpha_{i-1}\) (deg) | \(a_{i-1}\) (mm) | \(\theta_i\) | \(d_i\) (mm) |
|---|---|---|---|---|
| 1 | 0 | 0 | \(\theta_1\) | 0 |
| 2 | -90 | 0 | \(\theta_2\) | 0 |
| 3 | 0 | \(L_2 = 100\) | \(\theta_3\) | 0 |
| 4 | 0 | \(L_3 = 104\) | \(\theta_4\) | 0 |
Dynamics analysis was performed using the Lagrangian method to determine the joint torques required for jumping. The kinetic and potential energies of each link were calculated, considering masses concentrated at link ends. The Lagrangian \(L = E_K – W_G\), where \(E_K\) is total kinetic energy and \(W_G\) is total potential energy, led to the following equations of motion:
$$\tau_i = \frac{d}{dt} \left( \frac{\partial L}{\partial \dot{\theta}_i} \right) – \frac{\partial L}{\partial \theta_i}$$
For the four-link leg, the joint torques are:
$$\tau_1 = (m_1 L_1^2 + m_2 L_2^2 C_2^2 + m_3 L_3^2 C_{23}^2 + m_4 L_4^2 C_{234}^2) \ddot{\theta}_1$$
$$\tau_2 = (m_2 L_2^2 + m_3 L_3^2 + m_4 L_4^2) \ddot{\theta}_2 + \left( \frac{1}{2} m_2 L_2^2 \sin(2\theta_2) + m_3 L_3^2 C_{23} S_{23} + m_4 L_4^2 C_{234} S_{234} \right) \dot{\theta}_1^2 + m_2 g L_2 C_2 + m_3 g (L_3 C_{23} + L_2 C_2) + m_4 g (L_4 C_{234} + L_3 C_{23} + L_2 C_2)$$
$$\tau_3 = (m_3 L_3^2 + m_4 L_4^2) \ddot{\theta}_3 + (m_3 L_3^2 C_{23} S_{23} + m_4 L_4^2 C_{234} S_{234}) \dot{\theta}_1^2 + m_3 g L_3 C_{23} + m_4 g (L_4 C_{234} + L_3 C_{23})$$
$$\tau_4 = m_4 L_4^2 \ddot{\theta}_4 + m_4 L_4^2 C_{234} S_{234} \dot{\theta}_1^2 + m_4 g L_4 C_{234}$$
Here, \(m_1, m_2, m_3, m_4\) are the masses of the hip, thigh, knee-tibia, and tarsal links, respectively, and \(g\) is gravity. These torques guide the selection of servo motors for the bionic robot, ensuring adequate force generation during jumps.
| Component | Length (mm) | Mass (g) |
|---|---|---|
| Hip Link | 44.2 | 29.72 |
| Thigh Link | 100 | 25.31 |
| Knee-Tibia Link | 104 | 34.44 |
| Tarsal Link | 140 | 40.03 |
| Base | 215 × 115 | 350.21 |
The ejection device is a critical innovation in our bionic robot, designed to store and release energy via a spring. The transmission system uses a ratchet and bevel gears (1:1:1 ratio) driven by a motor to compress the spring via a cable-wound rotating rod. Upon release, the spring’s elastic energy is transferred to the robot’s body, augmenting leg thrust. Based on energy conservation, the required initial kinetic energy for a 0.5 m vertical jump (robot mass 2.4 kg) is \(E_0 = mgh = 11.76 \, \text{J}\). Accounting for spring efficiency \(\eta_{\text{spring}} = 80\%\) and gear efficiency \(\eta_{\text{gear}} = 92.5\%\), the needed energy is:
$$E_1 = \frac{E_0}{\eta_{\text{spring}} \eta_{\text{gear}}^2} = 16.29 \, \text{J}$$
With a spring compression of \(\Delta x = 45 \, \text{mm}\), the theoretical stiffness is \(k_0 = 2E_1 / (\Delta x)^2 \approx 16.09 \, \text{N/mm}\). Two springs are used, each with stiffness \(k_1 = k_2 = 8.045 \, \text{N/mm}\). We selected non-standard springs with wire diameter \(d = 2 \, \text{mm}\), mean diameter \(D = 12 \, \text{mm}\), effective turns \(n = 11\), and free length 100 mm. The actual stiffness is given by:
$$k = \frac{G d^4}{8 D^3 n} = 8.312 \, \text{N/mm}$$
where \(G\) is the shear modulus. This meets the requirement, providing a force of \(F = k \Delta x = 360 \, \text{N}\) per spring. Simulation in ADAMS showed spring force, deformation, and velocity profiles aligning with theoretical predictions, validating the design for our bionic robot.
Control of the bionic robot is achieved through an Arduino-based system. An Arduino UNO R3 board sends signals to a PCA9685 16-channel servo driver, which actuates the leg servos for posture adjustment. An ultrasonic distance sensor (US-100) measures jump height. The control sequence includes pre-joint angle setting, synchronized spring release, and landing stabilization. This system ensures precise timing for composite jumping, crucial for maximizing performance.
We simulated the bionic robot’s jumps using ADAMS software. For vertical jumps, the leg joint angles were set as follows:
| Joint | Leg 1 | Leg 2 | Leg 3 | Leg 4 | Leg 5 | Leg 6 |
|---|---|---|---|---|---|---|
| Hip (deg) | 0 | 0 | 0 | 0 | 0 | 0 |
| Thigh (deg) | -60 | -60 | -60 | 60 | 60 | 60 |
| Knee (deg) | 60 | 60 | 60 | -60 | -60 | -60 |
| Ankle (deg) | 50 to -30 | 50 to -30 | 50 to 30 | -50 to 30 | -50 to 30 | -50 to 30 |
The simulation results showed a maximum centroid height of 734.1176 mm, exceeding the 500 mm target. The centroid velocity peaked during takeoff and decayed to zero at the apex, while acceleration spikes occurred due to spring release and landing damping. For forward jumps, joint angles were adjusted to tilt the body 10 degrees forward, with asymmetric leg configurations. The bionic robot achieved a maximum height of 425.9005 mm and a forward distance of 447.6417 mm. Displacement, velocity, and acceleration curves in both vertical (Z) and horizontal (Y) directions demonstrated stable motion, with brief oscillations upon landing attributable to the damping springs.
To validate the bionic robot design, we fabricated a scale model using 3D printing. The model had a height of 19.5 cm, extended length of 86.6 cm, and mass of 901.3 g. Experiments with the Arduino control system and ultrasonic sensor yielded jump heights and velocities comparable to simulations, though minor discrepancies arose due to spring stiffness tolerances and wiring interference. The overall trend confirmed the feasibility of composite jumping. The model’s postures during jump phases closely matched simulation frames, reinforcing the bio-inspired approach.
In conclusion, our composite jumping bionic robot successfully integrates leg extension and body ejection to enhance jumping performance. Kinematic and dynamic analyses provided a foundation for design optimization, while the spring-based ejection device offered substantial energy augmentation. Simulations and experiments validated the bionic robot’s ability to achieve high vertical and forward jumps, with maximum heights over 700 mm and distances near 450 mm. Future work may focus on improving energy efficiency, adding adaptive control for terrain variation, and miniaturizing the system for broader applications. This research underscores the potential of bionic robots in overcoming mobility challenges through biomimicry and innovative engineering.
The development of this bionic robot highlights the importance of interdisciplinary approaches, combining biology, mechanics, and control theory. By emulating the jumping spider, we have created a robust platform for exploration and disaster response. The composite jumping mechanism, with its synergy of leg and spring forces, sets a new benchmark for agile robotics. As bionic robots continue to evolve, they will undoubtedly play a pivotal role in advancing automation and interaction with complex environments.
Further analysis could involve optimizing the leg linkage proportions for greater workspace or incorporating smart materials for adaptive damping. The ejection system might be enhanced with variable stiffness springs for adjustable jump trajectories. Additionally, machine learning algorithms could be implemented to enable autonomous jump planning based on sensor feedback. These directions promise to make bionic robots even more versatile and efficient.
In summary, the bionic robot presented here represents a significant step forward in jumping robotics. Its design principles, rooted in natural observation, offer a blueprint for future innovations. We believe that continued exploration of biological systems will yield further breakthroughs, pushing the boundaries of what bionic robots can achieve. The composite jumping approach, in particular, demonstrates how hybrid strategies can outperform single-mechanism designs, paving the way for next-generation mobile robots.