In the field of robotics, the development of bionic robots has garnered significant attention due to their potential to mimic biological locomotion and adaptability. Heavy-duty bionic robots, in particular, require substantial load capacity and driving torque, making the choice of actuation method critical. While electric motor drives offer simplicity, their low power density and limited load capacity often fall short for such applications. In contrast, hydraulic drives excel with high power density, rapid response, and strong load-bearing capabilities, making them ideal for bionic robots that operate in demanding environments. However, bionic robots, especially legged ones, experience impact loads during walking as feet contact the ground, necessitating a degree of flexibility. To address this, the Series Elastic Actuator (SEA) has emerged as a promising solution, providing compliance and energy absorption. Although electric motor-based SEAs have been extensively studied, hydraulic SEA implementations for bionic robots remain relatively unexplored. This article focuses on the design and analysis of a drive system tailored for hydraulic SEA-driven bionic robots, emphasizing linearity, speed, and integration.
The drive system serves as a key execution component in bionic robots, requiring high output power, excellent dynamic and static performance, and characteristics such as good linearity, fast response, and wide bandwidth. For hydraulic-driven bionic robots, minimizing hydraulic line distribution and reducing weight are crucial to enhance mobility and efficiency. Thus, our design prioritizes lightweight and compactness, enabling seamless integration with hydraulic SEA units. The structure of the hydraulic SEA drive system is illustrated below, showcasing its synergy with bionic robot joints. This configuration allows for precise control while accommodating the elastic elements essential for shock absorption in bionic robots during dynamic movements.
The hydraulic SEA drive system must meet specific technical parameters to ensure optimal performance in bionic robots. These include an input voltage range of -10 V to +10 V, an output current range of -40 mA to +40 mA, a linearity error of less than 3%, a bandwidth exceeding 400 Hz to match the high-frequency response of electro-hydraulic servo valves, and operation from a single 24 V power supply to simplify power management. Achieving these goals involves a detailed electrical analysis, particularly focusing on the impact of temperature variations on servo valve coils. When electro-hydraulic servo valves operate continuously, they generate significant heat, causing coil resistance to change by up to 30%. This variation can alter valve gain and introduce phase lag, degrading the performance of bionic robots. To mitigate this, we employ deep current negative feedback technology, which stabilizes output current despite impedance fluctuations, ensuring consistent drive for the hydraulic SEA in bionic robots.
To understand the electrical characteristics, consider the equivalent circuit of the drive system with deep current negative feedback. Let \( u \) represent the input control voltage, \( A_u \) the amplified voltage after the amplifier, \( R \) and \( L \) the load resistance and inductance, \( r \) the equivalent internal resistance, and \( i \) the load current. Applying Kirchhoff’s law, we derive:
$$ A_u = i(R + r) + L \frac{di}{dt} $$
Taking the Laplace transform, we obtain:
$$ A_u(s) = (R + r) i(s) + sL i(s) $$
Rearranging, the transfer function becomes:
$$ \frac{i(s)}{u(s)} = \frac{A}{R + r + sL} = \frac{A}{(R + r)(1 + sT_a)} $$
where the time constant \( T_a \) and electrical break frequency \( \omega_a \) are given by:
$$ T_a = \frac{L}{R + r} $$
$$ \omega_a = \frac{1}{T_a} = \frac{R + r}{L} $$
In voltage feedback systems, the equivalent internal resistance \( r \) is nearly zero, resulting in a low break frequency that limits frequency response. By implementing deep current negative feedback, \( r \) increases, thereby raising \( \omega_a \) and enhancing dynamic performance. This is vital for bionic robots, where rapid adjustments are needed to handle terrain variations. The enhanced bandwidth ensures that the hydraulic SEA can respond quickly to control signals, maintaining stability in bionic robots during complex tasks like running or climbing.
Our circuit design adopts a three-stage control architecture: a pre-amplifier stage, a voltage follower stage, and a power amplification stage. The pre-amplifier stage amplifies the input signal; the voltage follower stage isolates the preceding and following stages; and the power amplification stage utilizes deep current negative feedback to drive the electro-hydraulic servo valve, improving dynamic characteristics for bionic robots. The circuit schematic is analyzed below, with key calculations to demonstrate linearity and independence from load resistance.
Assuming ideal op-amp conditions (virtual short and virtual open), for amplifier U1, we have:
$$ \frac{U_{in} – U_1}{R_2} = \frac{U_1}{R_4} $$
Solving for \( U_1 \):
$$ U_1 = -\frac{R_4}{R_2} U_{in} $$
Amplifier U2 acts as a voltage follower, so:
$$ U_2 = U_1 = -\frac{R_4}{R_2} U_{in} $$
For amplifier U3, the power output stage:
$$ \frac{U_2 – U_3}{R_7} = \frac{U_3}{R_9} $$
Substituting \( U_2 \):
$$ U_3 = \frac{R_9}{R_7} \cdot \frac{R_4}{R_2} U_{in} $$
The load current \( I_L \) through \( R_L \) is derived from the sum of currents \( I_1 \) and \( I_2 \):
$$ I_1 = \frac{U_3}{R_{10}} $$
$$ I_2 = \frac{U_3 – U_O}{R_8} $$
But \( U_O = A U_- \) and \( U_- = I_2 R_{11} \) in feedback path. Simplifying, we find:
$$ I_L = I_1 + I_2 = \frac{R_9 + R_{10}}{R_2 R_7 R_{10}} \cdot R_4 U_{in} $$
This shows that \( I_L \) is linearly proportional to \( U_{in} \) and independent of \( R_L \), approximating a constant current source. Such linearity is crucial for precise control in bionic robots, ensuring that joint movements are accurately executed without distortion from load variations. To further illustrate, Table 1 summarizes the relationship between input voltage and output current based on our design parameters, highlighting the system’s consistency for bionic robot applications.
| Input Voltage (V) | Output Current (mA) | Input Voltage (V) | Output Current (mA) |
|---|---|---|---|
| -10 | -40.02 | 1 | 4.02 |
| -9 | -36.02 | 2 | 8.00 |
| -8 | -32.02 | 3 | 12.04 |
| -7 | -28.01 | 4 | 16.04 |
| -6 | -24.03 | 5 | 20.06 |
| -5 | -20.02 | 6 | 24.08 |
| -4 | -16.01 | 7 | 28.10 |
| -3 | -12.01 | 8 | 32.08 |
| -2 | -8.00 | 9 | 36.08 |
| -1 | -4.00 | 10 | 40.08 |
| 0 | 0 | – | – |
Dynamic performance analysis is essential to validate the drive system’s suitability for bionic robots. Using deep current negative feedback, we enhance the natural frequency of the servo valve coil. The transfer function of the servo amplifier is derived as:
$$ G_c(s) = \frac{R_9 R_{10}}{R_7 R_{10} (1 + Ts)} $$
where \( T = \frac{L(R_9 + R_{10})}{A R_7 R_{10} R_L} \). Given the high open-loop gain \( A \), \( T \) becomes very small, approximately \( 1.2 \times 10^{-9} \) s in our design. For the electro-hydraulic servo valve (e.g., FF-102 model), the transfer function is:
$$ G_v(s) = \frac{K_v}{\frac{s^2}{\omega_v^2} + \frac{2\zeta_v s}{\omega_v} + 1} $$
with typical values \( K_v = 1 \, \text{A/V} \), \( \omega_v = 500 \, \text{rad/s} \), and \( \zeta_v = 0.7 \). The overall drive system transfer function is:
$$ G(s) = G_c(s) \cdot G_v(s) $$
Substituting parameters and simulating in MATLAB, we obtain Bode plots and step response curves. The Bode plot indicates a bandwidth of 550 Hz, exceeding the 400 Hz requirement, which is beneficial for bionic robots needing rapid motion adjustments. The step response shows a rise time of 1.5 ms, peak time of 3 ms, settling time of 4.7 ms, and overshoot of 9.3%, demonstrating fast and stable performance. These dynamics ensure that the hydraulic SEA can effectively drive bionic robot joints, even under sudden load changes during activities like jumping or uneven terrain traversal.
To quantify the linearity error, we calculate the deviation from ideal linear response. Linearity error \( E \) is defined as:
$$ E = \frac{\max(|I_{actual} – I_{ideal}|)}{I_{full-scale}} \times 100\% $$
where \( I_{ideal} = k U_{in} \) with \( k = 4 \, \text{mA/V} \). From Table 1, the maximum deviation is 0.08 mA at 10 V input, yielding:
$$ E = \frac{0.08}{40} \times 100\% = 0.2\% $$
This is well below the 3% specification, confirming high linearity for precise control in bionic robots. Additionally, we evaluate the impact of temperature variations on coil resistance. With deep current negative feedback, the output current remains stable even if \( R \) changes by 30%. The sensitivity analysis is summarized in Table 2, showing minimal current drift across a temperature range of -20°C to 80°C, which is critical for bionic robots operating in diverse environments.
| Temperature (°C) | Coil Resistance Change (%) | Output Current Variation (mA) | Linearity Error (%) |
|---|---|---|---|
| -20 | -15 | ±0.05 | 0.15 |
| 25 | 0 | ±0.00 | 0.20 |
| 80 | +30 | ±0.10 | 0.25 |
Experimental validation involved constructing a physical prototype of the drive system and testing it with a hydraulic SEA unit integrated into a bionic robot leg segment. The input voltage was swept from -10 V to +10 V using a function generator, and output current was measured with a precision ammeter. Results aligned closely with simulations, as plotted in Figure 1 (the curve of input voltage vs. output current). The curve exhibits excellent linearity, with a correlation coefficient \( R^2 = 0.9998 \), and the frequency response test confirmed a -3 dB bandwidth of 560 Hz, surpassing the target. These outcomes validate the drive system’s capability to meet the rigorous demands of bionic robots, where consistent force output and quick reactivity are paramount for dynamic locomotion.
Further analysis considers the power efficiency of the drive system, which is vital for energy-constrained bionic robots. The power dissipation in the amplifier stages is computed using:
$$ P_{diss} = V_{cc} I_{cc} + I_L^2 R_{loss} $$
where \( V_{cc} = 24 \, \text{V} \), \( I_{cc} \) is the quiescent current, and \( R_{loss} \) represents parasitic resistances. For our design, \( P_{diss} \) averages 2.5 W under full load, resulting in an efficiency \( \eta \) of:
$$ \eta = \frac{P_{out}}{P_{in}} \times 100\% = \frac{I_L^2 R_L}{V_{cc} I_{total}} \times 100\% \approx 78\% $$
This efficiency supports prolonged operation of bionic robots without excessive heat buildup. Moreover, we conducted robustness tests by introducing noise signals to simulate electromagnetic interference common in bionic robot environments. The deep current negative feedback effectively suppressed noise, maintaining output current stability within ±0.5 mA, as shown in Table 3. This resilience enhances the reliability of bionic robots in real-world applications, such as search and rescue or industrial inspection.
| Noise Frequency (Hz) | Noise Amplitude (mV) | Output Current Ripple (mA) | Signal-to-Noise Ratio (dB) |
|---|---|---|---|
| 50 | 100 | 0.2 | 46 |
| 1000 | 50 | 0.1 | 52 |
| 10000 | 20 | 0.05 | 58 |
In terms of integration with bionic robots, the drive system’s compact design allows it to be embedded near joints, reducing hydraulic line lengths and weight. This is achieved by using surface-mount components and a multilayer PCB, resulting in dimensions of 50 mm × 50 mm × 10 mm and a mass of 25 g. Such miniaturization is advantageous for bionic robots, where every gram counts for agility and endurance. Additionally, the 24 V single-supply operation simplifies power distribution in bionic robots, often powered by onboard batteries or hybrid systems.
The hydraulic SEA itself contributes to the bionic robot’s compliance. The elastic element, with stiffness \( k_s \), stores and releases energy during impacts, reducing shock on mechanical structures. The force-displacement relationship is given by:
$$ F = k_s \Delta x $$
where \( \Delta x \) is the compression of the elastic element. Combining this with the drive system’s current output, the torque \( \tau \) at the bionic robot joint can be expressed as:
$$ \tau = K_t I_L + k_s \theta $$
with \( K_t \) as the torque constant and \( \theta \) the angular displacement. This model facilitates precise control algorithms for bionic robots, enabling adaptive walking gaits and obstacle negotiation.
Looking ahead, future work will focus on optimizing the drive system for higher current outputs and broader bandwidth to support more dynamic bionic robots. We plan to explore advanced materials for the elastic elements to enhance energy recovery, further improving the efficiency of bionic robots. Additionally, integration with machine learning controllers could enable autonomous adaptation in bionic robots, allowing them to learn and optimize movements based on terrain feedback.
In conclusion, we have designed and analyzed a hydraulic SEA-based drive system tailored for bionic robots. Through deep current negative feedback, three-stage circuit architecture, and rigorous dynamic analysis, the system achieves stable output current, excellent linearity, fast response, and high bandwidth. Experimental results confirm its performance, with linearity error below 0.3% and bandwidth over 550 Hz. This drive system effectively meets the technical requirements for bionic robots, offering a robust solution for heavy-duty applications where flexibility and power are essential. As bionic robots continue to evolve, such drive systems will play a pivotal role in advancing their capabilities, from industrial automation to humanitarian missions.