The pursuit of enhancing the locomotion capabilities of multi-legged robots, particularly their ability to overcome obstacles and navigate complex terrains, has led to significant interest in bionic robot design. Inspired by the remarkable jumping prowess of arthropods like the jumping spider, this work focuses on the design and analysis of a novel bionic robot that employs a compound jumping strategy. The primary objective is to substantially improve both the vertical leap height and forward jumping distance compared to conventional designs. The proposed mechanism synergistically combines a body-ejection system with coordinated leg extension, mimicking the explosive launch observed in nature. This integrated approach allows for a more efficient conversion of stored energy into kinetic energy for propulsion.
Observing the jumping spider (Salticidae) provides critical biological inspiration. This arachnid possesses eight legs, but not all contribute equally to its signature jump. The first pair often serves for sensory perception and manipulation, while the rear two pairs, especially the third, are primarily responsible for generating the powerful thrust. The jump is executed not merely by muscle contraction but through a rapid hydraulic mechanism: the spider increases hemolymph pressure in its legs, causing them to extend swiftly and launch its body. This efficient conversion of internal fluid pressure into kinetic energy suggests a design paradigm where energy can be stored centrally and released rapidly through the limbs.
Our bionic robot design translates this principle into a mechanical system. The overall structure comprises a central body housing control electronics and a specialized ejection device, flanked by three pairs of articulated legs. This simplification from eight to six legs retains the core jumping functionality while reducing mechanical complexity. Each leg is modeled as a serial chain of four main links: the coxa (hip link), femur (thigh link), a combined tibia-patella (knee-shin link), and the tarsus (foot link). A passive spring-damper system is integrated into the tarsal link to absorb impact energy during landing, enhancing stability. The cornerstone of the compound jump is the ejection device mounted centrally within the body. It consists of an energy storage spring, a transmission system using a parallel configuration of a ratchet and bevel gears, and a launch plate. The spring is compressed via a motor-driven winding mechanism, storing elastic potential energy. Upon release, this energy is transferred almost instantaneously to the launch plate, which interacts with the ground to provide a primary thrust force. This thrust is precisely synchronized with the rapid extension of the robot’s legs, which provide additional ground reaction force and crucial attitude control during take-off, flight, and landing.
Kinematic and Dynamic Modeling of the Leg Mechanism
Precise control of leg posture is essential for optimizing the jump trajectory and ensuring stable landings. The kinematics of a single leg are analyzed using the Denavit-Hartenberg (D-H) convention to establish the relationship between joint angles and the foot-end position. The leg is treated as a 4-DOF serial manipulator with rotational joints at the hip, femur, knee, and tarsus. The coordinate frames and corresponding D-H parameters are established as follows:
The homogeneous transformation matrix between consecutive links, \( ^{i-1}_iT \), is given by:
$$ ^{i-1}_iT = \begin{bmatrix}
\cos\theta_i & -\sin\theta_i \cos\alpha_{i-1} & \sin\theta_i \sin\alpha_{i-1} & a_{i-1}\cos\theta_i \\
\sin\theta_i & \cos\theta_i \cos\alpha_{i-1} & -\cos\theta_i \sin\alpha_{i-1} & a_{i-1}\sin\theta_i \\
0 & \sin\alpha_{i-1} & \cos\alpha_{i-1} & d_i \\
0 & 0 & 0 & 1
\end{bmatrix} $$
Based on the leg’s geometry, the D-H parameters are summarized in the table below:
| Link (i) | \( \alpha_{i-1} \) | \( a_{i-1} \) | \( \theta_i \) | \( d_i \) |
|---|---|---|---|---|
| 1 | 0 | 0 | \( \theta_1 \) (Hip) | 0 |
| 2 | -90° | 0 | \( \theta_2 \) (Femur) | 0 |
| 3 | 0 | \( L_2 \) | \( \theta_3 \) (Knee) | 0 |
| 4 | 0 | \( L_3 \) | \( \theta_4 \) (Tarsus) | 0 |
The position of the foot endpoint \( \mathbf{P}_M = [X, Y, Z]^T \) in the base coordinate frame is derived by cascading the transformation matrices:
$$ ^0_4T = ^0_1T \cdot ^1_2T \cdot ^2_3T \cdot ^3_4T $$
This yields the forward kinematics equations:
$$ \begin{aligned}
X &= L_2 C_1 C_2 + L_3 C_1 C_{23} + L_4 C_1 C_{234} \\
Y &= L_2 S_1 C_2 + L_3 S_1 C_{23} + L_4 S_1 C_{234} \\
Z &= -L_2 S_2 – L_3 S_{23} – L_4 S_{234}
\end{aligned} $$
where \( C_1 = \cos\theta_1 \), \( S_{23} = \sin(\theta_2+\theta_3) \), \( C_{234} = \cos(\theta_2+\theta_3+\theta_4) \), etc., and \( L_2, L_3, L_4 \) are the lengths of the femur, tibia, and tarsus links, respectively. The working space of the leg, critical for planning viable take-off and landing poses, is visualized computationally by varying the joint angles within their mechanical limits \( (\theta_2, \theta_3 \in [-\pi/2, \pi/2]; \theta_4 \in [-3\pi/4, \pi/2]) \).
Dynamic analysis is performed using the Lagrangian method to estimate the joint torques required during the forceful leg extension phase of the jump. The Lagrangian \( \mathcal{L} \) is defined as the difference between the total kinetic energy \( K \) and potential energy \( P \) of the leg system:
$$ \mathcal{L} = K – P $$
The equation of motion for each joint \( i \) is then given by:
$$ \tau_i = \frac{d}{dt} \left( \frac{\partial \mathcal{L}}{\partial \dot{q}_i} \right) – \frac{\partial \mathcal{L}}{\partial q_i} $$
where \( \tau_i \) is the torque at joint \( i \), and \( q_i \) is the corresponding generalized coordinate (joint angle \( \theta_i \)). By formulating the kinetic and potential energies for each link (simplified with point masses at the distal end of each link), the torques for the femur (\( \tau_2 \)), knee (\( \tau_3 \)), and tarsus (\( \tau_4 \)) joints during the explosive extension can be derived. For instance, the simplified torque for the femur joint, considering contributions from subsequent links, takes a form similar to:
$$ \tau_2 = (m_2 L_2^2 + m_3 L_3^2 C_3^2 + m_4 L_4^2 C_{34}^2)\ddot{\theta}_2 + \text{(Coriolis, centrifugal, and gravitational terms)} $$
These calculations inform the selection of actuators (e.g., high-torque servos) capable of delivering the necessary forces for the leg-driven component of the compound jump in this bionic robot.
Design and Analysis of the Ejection System
The ejection system is the powerhouse of the compound jumping mechanism. Its design focuses on storing a significant amount of energy and releasing it rapidly and reliably. The chosen mechanism involves compressing a pair of helical spring via a motor-driven transmission. The transmission employs a parallel ratchet-and-bevel-gear system. A motor, coupled with a gear reducer, drives a shaft connected to both a ratchet mechanism and a set of bevel gears. The bevel gears ultimately rotate a spool that winds a cable, pulling the launch plate upwards and compressing the springs against the robot’s frame. The ratchet mechanism ensures that the energy stored in the compressed springs cannot drive the motor backwards, locking the energy in place until release. To initiate the jump, a separate release mechanism disengages the launch plate, allowing the springs to expand explosively. This design ensures that nearly all stored elastic energy is converted into kinetic energy for launch, with minimal losses back to the motor.
The heart of the system is the spring. Its parameters are determined based on the desired jumping performance of the bionic robot. For a target vertical leap height \( h \) for a robot of mass \( m \), the required potential energy at the peak is \( mgh \). Accounting for energy conversion efficiencies of the spring \( \eta_s \) (≈80%) and the transmission \( \eta_t \) (≈90%), the elastic potential energy \( E_s \) that must be stored is:
$$ E_s = \frac{m g h}{\eta_s \eta_t} $$
If the spring is designed to have a compression stroke \( \Delta x \), its required stiffness \( k \) (for two springs in parallel) can be found from the energy formula for a linear spring:
$$ E_s = \frac{1}{2} (2k) (\Delta x)^2 \quad \Rightarrow \quad k = \frac{m g h}{\eta_s \eta_t (\Delta x)^2} $$
For a prototype bionic robot with a target mass \( m = 2.4 \, \text{kg} \), target height \( h = 0.5 \, \text{m} \), and compression \( \Delta x = 0.045 \, \text{m} \), the calculated stiffness is approximately \( k \approx 8.0 \, \text{N/mm} \) per spring. The corresponding maximum force exerted by the two springs at full compression is \( F_{\text{max}} = 2k \Delta x \approx 720 \, \text{N} \). This substantial force is what enables the powerful body-ejection component of the compound jump. The spring force \( F \), deformation \( \Delta x \), and release velocity profiles over the jump cycle are critical outputs for system validation.
Control System Architecture
Coordinating the compound jump requires a precise and synchronized control system. The hardware architecture for this bionic robot is built around a central microcontroller (e.g., Arduino-based board). This board generates control signals for the numerous actuators involved: servo motors for each of the leg’s joints (hip, femur, knee, tarsus) and the motor responsible for winding the ejection spring.
A multi-channel servo driver board (e.g., PCA9685) is employed to manage the pulse-width modulation (PWM) signals for all servos simultaneously. The control logic sequences the jump into distinct phases:
- Pre-jump Pose Adjustment: The leg servos are commanded to move to a predefined crouched configuration. This pose optimizes the leg’s geometry for applying force to the ground upon extension.
- Energy Loading: The ejection system motor is activated to wind the cable and compress the spring, locking energy via the ratchet.
- Jump Execution: On command, the release mechanism is triggered. Concurrently, a precisely timed sequence commands the leg servos to extend maximally and rapidly. The synchronization between spring release and leg extension is crucial for maximizing the resultant ground reaction force.
- Flight Phase Attitude Adjustment: During the aerial phase, the leg servos can be adjusted to orient the body for a stable descent or to prepare for a specific landing angle.
- Landing and Stabilization: Upon detecting impact (via inertial measurement units or contact sensors), the control system commands the legs into a shock-absorbing posture, utilizing the passive tarsal springs and active servo compliance to dampen oscillations and achieve stability.
Sensors such as an ultrasonic range finder or an IMU can provide feedback on jump height, distance, and body orientation, allowing for closed-loop adjustment of control parameters in future iterations of this bionic robot.
Motion Simulation and Performance Analysis
To validate the design and analyze the performance of the compound jumping strategy, a dynamic simulation model was constructed using ADAMS software. The full 3D CAD model of the bionic robot, including the articulated legs, body, and detailed ejection mechanism, was imported. Material properties (mass, inertia) were assigned, and appropriate joints (revolute, translational) and contacts (foot-ground, launch plate-ground) were defined.
Two primary jumping maneuvers were simulated: a vertical jump and a forward jump. For each, the joint angle trajectories for the leg servos were prescribed as functions of time, and the ejection spring force was applied as an instantaneous release from its pre-compressed state.
1. Vertical Jump Simulation: The pre-jump pose had the body horizontal, with all femur joints at 60° and knee joints at 20° relative to the horizontal. The simulated motion showed a powerful launch. The key performance metric, the vertical displacement of the robot’s center of mass, reached a maximum of 734.1 mm, significantly exceeding the initial 500 mm target. The velocity profile showed a sharp acceleration during take-off, reaching zero at the apex, and a controlled deceleration upon landing aided by the foot dampers. The coordination between spring force release and leg extension was evident in the smooth, high-acceleration launch phase.
2. Forward Jump Simulation: To achieve forward motion, the pre-jump pose was modified to tilt the body forward by 10° and set asymmetric angles for the front, middle, and rear legs to both propel and pitch the body. The table below summarizes one example of the take-off joint configuration for a forward leap:
| Leg Pair | Femur Angle (°) | Knee Angle (°) | Tarsus Angle (°) |
|---|---|---|---|
| Front | -29 | 35 | 40 |
| Middle | -35 | 25 | 9.9 |
| Rear | -53.5 | 38.5 | 22 |
The simulation results for the forward jump showed a parabolic trajectory. The center of mass reached a maximum height of approximately 425.9 mm and a horizontal displacement of 447.6 mm. The velocity and acceleration profiles in both vertical (Z) and horizontal (Y) directions confirmed a coordinated thrust phase followed by ballistic flight and a stabilized landing.
Energy Contribution Analysis: A pivotal outcome of the simulation was the ability to analyze the energy contribution of each component. By examining the work done by the ground reaction forces generated by the leg extension versus that generated by the ejection plate, the energy ratio was found to be approximately 1:2 (legs:ejection system). This quantifies the “compound” nature of the jump, demonstrating that the body-ejection mechanism provides the majority of the impulse, while the leg extension provides a critical supplement and, more importantly, enables precise attitude control throughout the jump cycle of this advanced bionic robot.
Prototype Fabrication and Experimental Validation
To substantiate the simulation findings and test the practical feasibility of the mechanism, a partial physical prototype of the bionic robot was fabricated. Key components, including the leg assemblies with integrated servo mounts and the ejection mechanism frame, were manufactured using 3D printing technology. This prototype, with a total mass of approximately 900 grams, was used to conduct preliminary vertical jump tests.
The control system was implemented using an Arduino Uno and a servo driver board to sequence the leg movement and trigger the mechanical release of the ejection spring. An ultrasonic distance sensor (US-100) was positioned above the robot to measure the height of the jump. While the absolute height achieved in initial tests was lower than the simulated value due to prototype-specific factors like friction, spring non-ideality, and assembly tolerances, the measured jump profile was qualitatively consistent.
The experimental vertical displacement and velocity-over-time curves followed the same general trend as the simulation data: a rapid ascent, a peak, and a descent. The synchronized extension of the legs with the spring release was visually confirmed, resulting in a clear and powerful jump that distinguished it from a mere leg-push or a plain spring launch. This experimental validation, despite quantitative discrepancies, strongly supports the core premise that a compound jumping strategy, effectively merging body ejection with leg propulsion, is a viable and powerful design principle for enhancing the performance of bionic robots intended for agile locomotion.
Conclusion
This work presented the comprehensive design, analysis, and preliminary validation of a novel bionic robot employing a compound jumping strategy inspired by the jumping spider. The key innovation lies in the synergistic integration of a high-power body-ejection system, driven by a ratchet-latched spring mechanism, with a multi-legged articulated chassis capable of dynamic posture control. Through detailed kinematic and dynamic modeling of the leg mechanism, a systematic design of the energy storage and release system, and the development of a synchronized control architecture, the foundation for effective compound jumping was established.
Dynamic simulations demonstrated the significant performance gains offered by this approach, with the robot achieving a vertical leap of over 730 mm and a forward jump exceeding 440 mm. The analysis revealed that the ejection system contributed roughly twice the energy of the leg extension, highlighting its role as the primary impulse generator. The leg system’s role proved indispensable not just for adding thrust, but crucially for achieving stable and controllable take-off, flight, and landing attitudes.
Experimental tests with a 3D-printed partial prototype confirmed the fundamental viability and correct operation of the compound jumping sequence. While further refinement is needed to bridge the gap between simulation and physical performance—optimizing spring characteristics, reducing transmission losses, and implementing more advanced feedback control—the results unequivocally show that the proposed compound jumping motion is a highly effective method for dramatically improving the jumping height and distance of multi-legged bionic robots. This design paradigm opens promising avenues for developing agile robots capable of navigating complex, obstacle-rich environments for applications in exploration, search and rescue, and beyond.