In recent years, the motion control of bionic robots has garnered significant attention worldwide. Unlike traditional motor control, bionic robot control imposes higher demands on coordination, real-time performance, and adaptability. Among various types of robots, such as wheeled, legged, and underwater robots, the quadruped bionic robot stands out due to its balanced complexity, stability, load capacity, control difficulty, and manufacturing cost. This makes it a preferred form for applications in engineering exploration, military reconnaissance, terrain surveying, and disaster rescue. The gait of a bionic robot—referring to the sequence of leg lifting and placing—is crucial for stable locomotion, especially in complex environments like stair climbing. This article focuses on gait planning for a full-elbow joint quadruped bionic robot during stair climbing, leveraging static stability principles and experimental validation to ensure robustness.
The walking mechanism of the bionic robot is designed to mimic mammalian leg structures. Each leg features three joints: a hip joint for lateral swing, and thigh and calf joints for forward-backward swing. This configuration, known as full-elbow style, enhances flexibility and load-bearing capacity, making it suitable for navigating uneven terrains. The bionic robot employs servos to actuate joints, controlled by an STM32 motion control board that stores and executes pre-programmed gaits. A communication framework integrates the STM32 board with an Android control board, enabling remote operation via a mobile app. This setup allows for seamless gait invocation and real-time adjustments during experiments.
To address stair climbing, we first transform the bionic robot’s pose during ascent into a horizontal plane using a projection method. This simplification facilitates analysis by reducing the three-dimensional problem to two dimensions. The robot’s center of gravity (CoG) is critical for stability, and its movement is analyzed under ideal conditions: ignoring head and leg mass variations, assuming CoG shifts only longitudinally, and equal step distances for each leg. The CoG coordinates are calculated as:
$$ X_C = \frac{\sum_{i=1}^{n} m_i X_i}{\sum_{i=1}^{n} m_i}, \quad Y_C = \frac{\sum_{i=1}^{n} m_i Y_i}{\sum_{i=1}^{n} m_i} $$
where \( X_C \) and \( Y_C \) are the CoG coordinates, \( m_i \) represents the mass of each bionic robot component (e.g., torso, legs), and \( X_i, Y_i \) denote their centroid positions. By initializing the bionic robot with legs forming a parallelogram, we ensure symmetric gait analysis, with parameters like \( L_1 \) (longitudinal distance between front and rear legs) and \( L_2 \) (lateral offset) set to mimic realistic motion.
Gait planning for the bionic robot involves selecting from 24 possible crawling gaits, where only one leg is lifted at a time to maintain static stability—ensuring at least three legs support the body, with the CoG’s vertical projection within the triangle formed by these legs. Static stability margin (\( S_m \)) is a key metric, defined as the minimum distance from the CoG projection to the boundary of the support polygon. For an ideal bionic robot, the maximum stability margin in a gait cycle is derived from geometric analysis. For instance, during a two-leg support phase, after adjusting the torso to center the CoG, the stability margin becomes:
$$ S_{m2} = \frac{1}{4} L_1 $$
Similarly, for other phases, we compute margins to identify gaits that maximize \( S_m \). Among the 24 gaits, 14 achieve the maximum stability margin of \( \frac{1}{4} L_1 \). However, coordination—minimizing backward torso adjustments—is also vital. We analyze each gait for adjustment patterns; for example, in gait 2-1-3-4, a backward adjustment of \( -2S_m \) may occur after a cycle. By evaluating all gaits, we find six that eliminate backward adjustments when stability margins are sufficiently small: 1-3-4-2, 2-4-3-1, 3-1-2-4, 3-1-4-2, 4-2-1-3, and 4-2-3-1. These gaits are prioritized for stair climbing due to their enhanced stability and smooth motion.
The bionic robot’s motion space during stair climbing is defined by the maximum forward distance (\( l_f \)) and height difference (\( l_h \)) between front and rear feet. For a step with height \( H \) and width \( B \), the relationship is:
$$ l_h = H \times \left[ \text{int}\left( \frac{l_f}{B} \right) + 1 \right] $$
We design stairs with \( B = 150 \, \text{mm} \) and \( H = 55 \, \text{mm} \) to match the bionic robot’s adjustability. The absolute step distance \( \beta \) is set to 150 mm, and initial parameters \( L_1 = 1.5B \) and \( L_2 = \beta/2 \) yield \( l_f = 300 \, \text{mm} \) and \( l_h = 165 \, \text{mm} \), within the bionic robot’s operational limits. The experimental corridor width is 500 mm to prevent lateral deviations.
Experiments involve repeated trials for each gait, with failure criteria including exceeding the corridor or inability to move effectively for over 5 seconds. Success is defined as reaching the top platform. We conduct 50 trials per gait and record success rates. The results are summarized in the table below, highlighting the superiority of certain gaits for stair climbing in the bionic robot.
| Gait Sequence | Success Count | Success Rate (%) |
|---|---|---|
| 1-2-3-4 | 35 | 70 |
| 1-2-4-3 | 34 | 68 |
| 1-3-2-4 | 36 | 72 |
| 1-3-4-2 | 41 | 82 |
| 1-4-2-3 | 37 | 74 |
| 1-4-3-2 | 29 | 58 |
| 2-1-3-4 | 35 | 70 |
| 2-1-4-3 | 33 | 66 |
| 2-3-1-4 | 37 | 74 |
| 2-3-4-1 | 30 | 60 |
| 2-4-1-3 | 36 | 72 |
| 2-4-3-1 | 42 | 84 |
| 3-1-2-4 | 41 | 82 |
| 3-1-4-2 | 44 | 88 |
| 3-2-1-4 | 29 | 58 |
| 3-2-4-1 | 28 | 56 |
| 3-4-1-2 | 31 | 62 |
| 3-4-2-1 | 33 | 66 |
| 4-1-2-3 | 32 | 64 |
| 4-1-3-2 | 30 | 60 |
| 4-2-1-3 | 42 | 84 |
| 4-2-3-1 | 43 | 86 |
| 4-3-1-2 | 29 | 58 |
| 4-3-2-1 | 31 | 62 |
The data reveals that gaits like 3-1-4-2 and 4-2-3-1 achieve success rates above 85%, demonstrating their stability for the bionic robot in stair climbing. These gaits align with our theoretical analysis, which predicted minimal backward adjustments and high stability margins. It’s important to note that real-world factors, such as mass distribution and joint imperfections, can slightly reduce stability margins, but our selected gaits still perform robustly.
To further optimize the bionic robot’s performance, we derive mathematical models for gait transitions. The stability margin during a single-leg lift phase can be expressed as a function of leg positions. For a bionic robot with legs at coordinates \((x_i, y_i)\), the support polygon’s vertices are determined by the grounded legs. The CoG projection point \((X_C, Y_C)\) must satisfy linear inequalities based on the polygon edges. The minimum distance to any edge, \(d_{\text{min}}\), gives \(S_m\). For a triangular support with vertices \(A\), \(B\), and \(C\), the distance from point \(P\) (CoG) to line \(AB\) is:
$$ d_{AB} = \frac{|(y_2 – y_1)X_C – (x_2 – x_1)Y_C + x_2 y_1 – y_2 x_1|}{\sqrt{(y_2 – y_1)^2 + (x_2 – x_1)^2}} $$
By computing such distances for all edges, we assess stability dynamically. In our gait planning, we pre-calculate these for each phase to ensure \(S_m > 0\). Additionally, the bionic robot’s energy efficiency can be estimated using torque models for joint actuators. The torque \(\tau\) at a joint is proportional to the force required to move the leg mass \(m_{\text{leg}}\) and overcome gravity:
$$ \tau = m_{\text{leg}} g l \sin(\theta) + I \alpha $$
where \(g\) is gravity, \(l\) is limb length, \(\theta\) the angle, \(I\) inertia, and \(\alpha\) angular acceleration. By minimizing torque variations across gaits, we enhance the bionic robot’s durability and battery life.
Another aspect is the communication latency in the bionic robot’s control system. The STM32 board processes gait commands with a delay \(\Delta t\), which affects real-time adjustments. We model this as a discrete-time system, where the CoG update at step \(k\) is:
$$ \mathbf{X}_C[k+1] = \mathbf{X}_C[k] + \mathbf{v}[k] \Delta t $$
with velocity \(\mathbf{v}\) derived from leg movements. By keeping \(\Delta t\) under 10 ms, we ensure stable feedback for the bionic robot during stair climbing. The mobile app interface allows parameter tuning, such as adjusting \(\beta\) or \(L_1\), to adapt to different stair dimensions. This flexibility is key for deploying the bionic robot in varied environments.
In summary, this research provides a comprehensive framework for gait planning in quadruped bionic robots tackling stair climbing. Through projection methods, stability analysis, and experimental validation, we identify optimal gaits that balance stability and coordination. The bionic robot’s architecture—combining mechanical design with robust control—enables reliable performance. Future work will integrate sensor feedback for adaptive gait adjustments and explore dynamic gaits for faster ascent. The bionic robot’s potential in real-world applications continues to expand, driven by advances in gait optimization and control algorithms.