The rapid advancement of artificial intelligence is driving the extensive application of industrial robots across diverse sectors such as aerospace, deep-sea exploration, automotive manufacturing, and textile production. Within the realm of automated production, the intelligent manufacturing paradigm, centered on digitization, networking, and intelligence, is effectively propelling the transformation and upgrading of industrial processes, facilitating the shift from “manufacturing” to “intelligent manufacturing.” For instance, a domestic apparel factory developed an “intelligent robot” capable of completing steps like fabric cutting, pattern accessory placement, and color matching within 18 seconds to produce a finished pair of jeans, representing an efficiency increase of several hundredfold compared to traditional methods.
Compared to traditional mobile robots, the bionic quadruped robot, inspired by biological understanding of life form structures and motion—particularly the morphology and movement of legged animals—possesses superior adaptability to complex environments and can execute tasks under challenging conditions. However, when traversing unstructured terrain—characterized by uneven surface material properties, irregular structures and dimensions, and the presence of obstacles and disturbances—these bionic robots often face risks of instability and loss of balance. Therefore, optimizing foot-end design to better adapt to various unstructured grounds is a primary challenge in this intelligent transformation.
The bionic quadruped robot is a complex system whose locomotion performance is influenced by numerous factors, including the robot’s mass, inertia, friction, and driving forces. To enhance gait stability control, agility, and robustness, enabling rapid adaptation to environmental changes and disturbances, it is crucial to establish its dynamic models and design effective control algorithms. In particular, meticulous design of the bionic robot’s foot-end process, gait patterns, and foot trajectory planning is essential for achieving stable motion in complex environments and realizing highly efficient industrial automation integration.
Foot-End Process Design for the Bionic Quadruped Robot
Strong flexibility and robustness are fundamental functionalities of a bionic robot and key metrics for evaluating its performance. To improve the performance of a quadruped robot’s bionic leg, a design utilizing continuous carbon fiber (CCF) as the reinforcement material and chopped carbon fiber-reinforced nylon as the matrix material can be employed. Employing 3D printing technology to fabricate the bionic leg allows for the simulation of detailed human leg structures, achieving a high degree of mimicry of biological form and motion. Simulation experiments of static walking on slopes under four common working conditions for the quadruped robot indicate significant improvements: a 19.06% increase in load-bearing capacity, an 18.85% reduction in weight, and a 43.07% decrease in deformation under standing conditions. This ensures stable and rapid walking in complex environments.
For operation on unstructured ground, enhancing the flexibility and balance of the bionic robot’s leg is critical. Researchers have developed DNGEs ink for 3D printing, short for “Double Network Granular Elastomers.” This is a high-tech material capable of altering its mechanical compliance and stiffness during the printing process. It boasts an ultimate tensile strain of up to 1400%, and its stiffness can be varied within a range of 0.1 to 1.8 MPa, thereby elevating mechanical performance to new levels and enabling robots to perform complex and dexterous manipulations. DNGEs will open new avenues for designing next-generation smart wearable devices and novel soft bionic robots.
Kinematic Modeling and Foot Trajectory Design for the Bionic Quadruped Robot
1. Three-Dimensional Modeling and Kinematic Analysis
The leg of the bionic quadruped robot is designed using 3D modeling software, accurately realizing a modular joint structure comprising the roll hip joint, pitch hip joint, and pitch knee joint. The roll hip joint is located inside the robot’s body on the front and rear sides. The pitch hip joint is connected to the output shaft end of the roll hip joint via a connecting frame. To simplify subsequent dynamic modeling, the pitch knee joint is designed to be coaxial with the pitch hip joint and is mounted on the output end of the pitch hip joint. The thigh link is connected to the housing of the pitch knee joint, receiving the output torque from the pitch hip joint. The shank link is connected to the end of the thigh link via a rotating shaft, employing a linkage transmission method to receive the output torque from the pitch knee joint.
The experimental bionic robot has a body length of 0.61 m, width of 0.4 m, and height of 0.2 m, with a thigh length of 0.5 m and a shank length of 0.45 m. The robot’s legs are numbered 1, 2, 3, and 4 in counterclockwise order. The Denavit-Hartenberg (D-H) convention is used to define the joint coordinates. The world coordinate frame {Ow} is located on the ground directly below the robot’s center of gravity. By determining the joint centers for the hip, thigh, knee, and foot-end—effectively defining their coordinate origins—frames {O0}, {O1}, {O2}, and {O3} are established. For a given leg (e.g., the Front-Right leg, FR), the D-H parameters are defined as shown in the table below. Z0 is the rotation axis for frame {O0}, pointing opposite to gravity. Z1 and Z2 are the rotation axes for frames {O1} and {O2}, respectively. X1 and X2 point along the thigh and shank links, respectively. The twist angles for the hip, knee, and abduction/adduction joints are denoted by θ1, θ2, and θ3, while the link lengths for the hip abductor, thigh, and shank are l0, l1, and l2.
| Link i | αi-1 (rad) | ai-1 (m) | di (m) | θi (rad) |
|---|---|---|---|---|
| 1 (Abduction) | −π/2 | 0 | 0 | θ3 |
| 2 (Hip) | 0 | l0 | 0 | θ1 |
| 3 (Knee) | 0 | l1 | 0 | θ2 |
| Foot End | 0 | l2 | 0 | 0 |
Based on the bionic robot’s parameters, the link lengths are: l0 = 0.1 m, l1 = 0.5 m, l2 = 0.45 m. The joint angle ranges are: $10^\circ < \theta_1 < 70^\circ$, $-150^\circ < \theta_2 < -30^\circ$, $-55^\circ < \theta_3 < 30^\circ$.
The forward kinematics from the body frame to the foot-end for a given leg can be derived using the homogeneous transformation matrix:
$$ ^{0}_{3}T = ^{0}_{1}T \cdot ^{1}_{2}T \cdot ^{2}_{3}T $$
Where each transformation $^{i-1}_{i}T$ is defined by the D-H parameters:
$$
^{i-1}_{i}T = \begin{bmatrix}
\cos\theta_i & -\sin\theta_i \cos\alpha_{i-1} & \sin\theta_i \sin\alpha_{i-1} & a_{i-1}\cos\theta_i\\
\sin\theta_i & \cos\theta_i \cos\alpha_{i-1} & -\cos\theta_i \sin\alpha_{i-1} & a_{i-1}\sin\theta_i\\
0 & \sin\alpha_{i-1} & \cos\alpha_{i-1} & d_i\\
0 & 0 & 0 & 1
\end{bmatrix}
$$
The foot-end position $P_f = [x_f, y_f, z_f]^T$ in the leg’s base frame {O0} is given by the first three elements of the fourth column of $ ^{0}_{3}T $.
2. Gait Design for the Bionic Quadruped Robot
The locomotion mode of a quadruped robot is described by its gait. A leg is in the stance phase when it is in contact with the ground, supporting the body. It is in the swing phase when it is lifted off the ground for repositioning. The core challenge in bionic robot motion control is achieving steady-state locomotion, which includes various gaits such as the crawl (wave) gait, trot (diagonal) gait, pace gait, bound, and gallop. This analysis focuses on the stability of the trot gait, a common and efficient gait for bionic robots.
In a trot gait, diagonally opposite legs (e.g., Front-Left and Rear-Right) move in synchrony, forming two pairs that alternate between stance and swing phases. This creates a stable, bouncing locomotion pattern. The phase relationship for a standard trot is summarized below:
| Leg | Phase Offset (Fraction of Cycle) |
|---|---|
| Front-Left (FL) | 0.0 |
| Rear-Right (RR) | 0.0 |
| Front-Right (FR) | 0.5 |
| Rear-Left (RL) | 0.5 |
To maintain balance during walking, the bionic robot must not only move forward in the desired direction and velocity but also follow a rationally designed foot trajectory. Taking the Front-Left leg as an example, the foot trajectory for both the stance and swing phases is planned. A common method is to use a compound cycloidal or polynomial curve for the swing phase to ensure smooth lift-off and touch-down with zero velocity. For simplicity, a parabolic trajectory is often used in the vertical direction (Z) during the swing phase, while the horizontal motion (X) is linearly interpolated.
Let $T$ be the gait cycle period, and $T_{swing}$ be the duration of the swing phase. For a swing leg moving from point $P_{start} = (x_s, y_s, z_s)$ to $P_{end} = (x_e, y_e, z_e)$, with a desired maximum foot clearance $H_{max}$, the trajectory as a function of normalized swing phase time $t’ = t / T_{swing}$ (where $t$ goes from 0 to $T_{swing}$) can be defined as:
$$ x(t’) = x_s + (x_e – x_s) \cdot t’ $$
$$ z(t’) = z_s + 4H_{max} \cdot (t’ – t’^2) \quad \text{(for a simple parabola)} $$
The corresponding joint angles $[\theta_1, \theta_2, \theta_3]$ for the bionic robot leg are then calculated using inverse kinematics based on the desired foot position $[x(t’), y(t’), z(t’)]^T$ relative to the hip joint. For the stance phase, the foot typically remains stationary relative to the ground, so its trajectory in the body frame is simply the reverse of the body’s planned motion, ensuring the foot provides a propulsive force.
Motion Trajectory Validation for the Bionic Quadruped Robot
1. Simulation Environment Setup for the Bionic Robot
The locomotion of the bionic quadruped robot, specifically a diagonal trot involving horizontal rotation, hybrid motion, linear translation, and slope traversal, was simulated. Key simulation parameters were set as follows: a control frequency of 1 kHz, a Model Predictive Control (MPC) horizon length of 10, a swing/step duration of 0.25 s, a coefficient of friction of 0.9 between the robot’s legs/body and the ground, and a gravitational acceleration of 9.8 m/s². The robot’s body center of mass height was initialized at 0.38 m. The trot cycle period was set to 1 s, with a phase difference of 0.5 s between ipsilateral legs.
The simulation was conducted using the Gazebo simulator within a Linux environment. The bionic robot model was defined via a Unified Robot Description Format (URDF) file generated from CAD software. The file described the robot’s physical structure, dividing it into components such as the main body and, for each leg, movable hip joints, thigh links, shank links, and foot-ends. The coordinate systems in the URDF were aligned with the kinematic definitions. The file specified links and the joints connecting them, along with physical parameters for each link including mass, center of mass, and inertial tensor, which are crucial for accurate dynamic simulation of the bionic robot.
2. Simulation on Unstructured Terrain
When a leg of the bionic robot makes contact with the ground during the stance phase, the force on that leg increases abruptly. The variation in the expected ground reaction force (GRF) clearly characterizes the motion of the trotting bionic robot and validates the effectiveness of the gait design and the Model Predictive Controller.
The MPC controller for the bionic robot outputs the desired foot-end reaction forces for legs 1 through 4. Analysis shows that the magnitude trends of the GRF for diagonally paired legs are similar. As the bionic robot moves forward, the diagonal support legs alternate, and the corresponding foot-end reaction forces also exhibit alternating changes due to the forward and backward shifting of the center of pressure.
On uneven ground, the contact condition between the foot-end and the terrain varies, necessitating robust control strategies. Simulation results for the robot’s body pose (Euler angles) and translational velocity indicate that the bionic robot maintains remarkable stability. The variations in the longitudinal (X) and lateral (Y) directions are minimal, close to zero, signifying stable motion in the horizontal plane. The position curve in the vertical (Z) direction approximates a straight line, confirming that the bionic robot advances at a relatively constant velocity. The robot’s angular velocity also shows almost no change, demonstrating its ability to maintain a straight-line trajectory and a stable posture while moving.
Furthermore, during rotational motion, the bionic robot’s rotational speed fluctuates slightly around the commanded value, maintaining relative stability. When commanded to rotate about the Z-axis at 0.01 rad/s, the robot’s body position relative to the world frame remains stable, its velocity exhibits minor fluctuations, and its rotational speed and posture are well-maintained. This indicates that even with small-magnitude motion commands, the bionic robot can remain stable on uneven, unstructured terrain. The simulation results collectively demonstrate that the bionic robot is capable of performing stable linear motion, rotation, and turning on randomly uneven ground. It can follow desired trajectories while maintaining a relatively stable body posture, confirming the feasibility and robustness of the implemented gait for the bionic robot.
Conclusion
This work has detailed an integrated approach to enhancing the performance of bionic quadruped robots for industrial applications. By leveraging the mechanical properties of 3D-printed composites, the foot-end process of the bionic robot was optimized, leading to significant improvements in load-bearing capacity and deformation resistance. Furthermore, through the establishment of a comprehensive simulation environment in Gazebo and the design of advanced control algorithms, the gait patterns and foot trajectory planning for the bionic robot were refined. Experimental simulations and kinematic calculations validated that the optimized bionic robot possesses strong adaptability, flexibility, and robustness, enabling it to navigate various complex, unstructured environments effectively. As these sophisticated bionic robots become increasingly integrated into industrial settings, they are poised to be a critical driving force in the rapid transformation and upgrading of traditional industrial models towards digitization, intelligence, and full automation. The continuous evolution of bionic robot technology represents not only a pinnacle of engineering but also a foundational technology for national competitiveness in the era of smart manufacturing.