In recent years, the advancement of robot technology has led to the development of various robotic systems tailored for specific applications, particularly in inspection tasks such as outdoor monitoring, park security, and scenic area services. However, when performing these duties, robots often encounter unstructured terrains, exemplified by roads with speed bumps, which induce significant perturbations in body posture—specifically pitch and roll angles. These disturbances can compromise operational accuracy and driving stability, highlighting the need for robust posture control mechanisms. To address this, I propose a novel Four Wheel-Legged Robot (FWLR) equipped with active posture control capabilities, leveraging a wheel-leg mechanism. Furthermore, I introduce a Skyhook-PID posture control strategy grounded in model dimensionality reduction principles, which simplifies the control system while enhancing performance. Through posture following experiments and unstructured terrain tests, I validate the effectiveness of this approach, demonstrating improved convergence and terrain adaptability. This research underscores the potential of robot technology in expanding the applicability of inspection robots across diverse environments.
The design of the FWLR integrates passive suspension, four-wheel steering, and drive systems with an active posture control framework, enabling enhanced maneuverability and vibration isolation on uneven surfaces. The wheel-leg structure, as illustrated in the accompanying figure, utilizes actuators to drive linkages connected to spring-damper systems, facilitating leg motion and overall posture adjustment. This configuration allows the robot to maintain stability by coordinating the movements of its four legs, absorbing terrain-induced shocks effectively. The funnel-shaped body houses power batteries and additional equipment, ensuring structural integrity and functionality. With dimensions of 1.3m × 1.2m, the FWLR employs a CAN bus communication system for seamless control of posture, driving, and steering operations, including pivot steering for reduced turning radius. This innovative design in robot technology promotes adaptability in non-paved environments, crucial for reliable inspection tasks.
To model the FWLR’s dynamics, I first develop a full-dimensional representation with 11 degrees of freedom (DOF), accounting for the body’s vertical, pitch, and roll motions, as well as the movements of the linkages and wheels. The equations of motion are derived using Lagrangian and Newtonian dynamics, resulting in a state-space formulation with 30 system variables. For instance, the vertical motion of the body is given by:
$$ \sum_{i=1}^{4} F_{fi} = m \ddot{z}_f $$
where \( m \) is the body mass, \( z_f \) is the vertical displacement, and \( F_{fi} \) represents the actuator force. The pitch and roll motions are described by:
$$ I_{pf} \ddot{\theta}_f = a \left( \sum_{i=1}^{2} F_{fi} – \sum_{i=3}^{4} F_{fi} \right) $$
$$ I_{rf} \ddot{\phi}_f = b \left( \sum_{i=1}^{4} (-1)^{i+1} F_{fi} \right) $$
Here, \( \theta_f \) and \( \phi_f \) denote pitch and roll angles, \( I_{pf} \) and \( I_{rf} \) are moments of inertia, and \( a \) and \( b \) are half the wheelbase and track width, respectively. The linkage and wheel dynamics involve spring-damper interactions, such as:
$$ m_{si} \ddot{z}_{sfi} + c_{si} (\dot{z}_{sfi} – \dot{z}_{wfi}) + k_{si} (z_{sfi} – z_{wfi}) = F_{fi} $$
where \( m_{si} \), \( c_{si} \), and \( k_{si} \) are the linkage mass, damping, and stiffness, and \( z_{sfi} \) and \( z_{wfi} \) are linkage and wheel displacements. A second-order low-pass filter is incorporated to mitigate high-frequency oscillations, leading to a comprehensive state equation:
$$ \dot{x}_f = A_f x_f + B_f u_f + D_f w_f $$
with \( x_f \) as the 30-dimensional state vector, \( u_f \) as the input, and \( w_f \) as terrain disturbances. However, this full model’s complexity poses challenges for real-time control in robot technology applications, necessitating a reduced-order approach.
I apply model dimensionality reduction to simplify the system, focusing on retaining essential dynamics while discarding less influential states. The reduced model condenses the FWLR to 7 DOF, with 14 state variables, by eliminating linkage-related states and filter outputs. The key equations for the reduced system include body vertical motion:
$$ m_r \ddot{z}_r = \sum_{i=1}^{4} \left[ c_{si} (\dot{z}_{bri} – \dot{z}_{wri}) + k_{si} (z_{bri} – z_{wri}) \right] $$
pitch motion:
$$ I_{pr} \ddot{\theta}_r = a \left( \sum_{i=1}^{2} \left[ c_{si} (\dot{z}_{bri} – \dot{z}_{wri}) + k_{si} (z_{bri} – z_{wri}) \right] – \sum_{i=3}^{4} \left[ c_{si} (\dot{z}_{bri} – \dot{z}_{wri}) + k_{si} (z_{bri} – z_{wri}) \right] \right) $$
and roll motion:
$$ I_{rr} \ddot{\phi}_r = b \sum_{i=1}^{4} (-1)^{i+1} \left[ c_{si} (\dot{z}_{bri} – \dot{z}_{wri}) + k_{si} (z_{bri} – z_{wri}) \right] $$
The wheel dynamics remain similar to the full model. The state-space representation simplifies to:
$$ \dot{x}_r = A_r x_r + D_r w_r $$
where \( x_r \) is the reduced state vector. This dimensionality reduction aligns with advancements in robot technology by minimizing computational load and facilitating hardware implementation, without sacrificing control accuracy.
For posture control, I design a Skyhook-PID strategy based on the reduced model. This approach imagines a “sky” reference point, with actuators applying counter-forces to suppress body oscillations. The PID layer enhances robustness, with the control law formulated as:
$$ u_i = K_p e_i + K_i \int e_i \, dt + K_d \dot{e}_i $$
where \( e_i \) is the error between desired and actual posture angles, and \( K_p = 1 \), \( K_i = 5 \), \( K_d = 0 \) are tuned gains. The actuator model incorporates a servo mechanism, where the extension velocity \( \dot{y}_{ri} \) relates to input pulses:
$$ \dot{y}_{ri} = \frac{p}{i_{rs}} \cdot \frac{e_{ri}}{e} $$
Here, \( p \) is the lead screw pitch, \( i_{rs} \) is the transmission ratio, \( e \) is the encoder resolution, and \( e_{ri} \) is the pulse input. This integration of robot technology ensures precise control execution, with a sample period of \( T = 0.01 \, \text{s} \) and a baud rate of 500 kbps on the vehicle control unit (VCU).
In posture following experiments, I compare the reduced-model Skyhook-PID controller with a full-model enhanced sliding mode controller (ESMC). The initial posture has zero pitch and roll angles, and the target posture is set to \( \theta = -0.1 \, \text{rad} \) and \( \phi = 0.04 \, \text{rad} \). Results indicate that both strategies achieve accurate tracking, but the reduced-model approach exhibits faster convergence, reaching steady state in 0.7 seconds compared to 0.8 seconds for the full model. The tracking errors for both pitch and roll angles approach zero, as summarized in the following equations for error analysis:
$$ e_\theta = \theta_{\text{target}} – \theta_{\text{actual}} $$
$$ e_\phi = \phi_{\text{target}} – \phi_{\text{actual}} $$
The superiority of the reduced model is evident in its rapid response, which is critical for dynamic environments in robot technology.
For unstructured terrain tests, I configure a course with speed bumps spaced 3 meters apart. The FWLR navigates this terrain under three conditions: no posture control, full-model control, and reduced-model control. The results demonstrate that both control strategies significantly reduce posture fluctuations, but the reduced-model controller outperforms in minimizing peak absolute values of pitch and roll angles. Quantitative data is presented in the table below, showing improvements of up to 50% for pitch and 55% for roll angles with the reduced-model approach. The posture angles during testing are described by:
$$ \theta(t) = \theta_0 + \Delta \theta \sin(\omega t) $$
$$ \phi(t) = \phi_0 + \Delta \phi \cos(\omega t) $$
where \( \Delta \theta \) and \( \Delta \phi \) are amplitude reductions achieved through control. The enhanced performance underscores the efficacy of model dimensionality reduction in robot technology for real-world applications.
| Performance Metric | Control Type | Max Absolute Value and Improvement |
|---|---|---|
| Pitch Angle (rad) | No Control | 0.038 rad |
| Full-Model Control | 0.023 rad (↓39.5%) | |
| Reduced-Model Control | 0.019 rad (↓50%) | |
| Roll Angle (rad) | No Control | 0.040 rad |
| Full-Model Control | 0.022 rad (↓45%) | |
| Reduced-Model Control | 0.018 rad (↓55%) |
In conclusion, the FWLR with active posture control, supported by a dimensionality-reduced model and Skyhook-PID strategy, exhibits remarkable stability on unstructured terrains. This approach not only accelerates response times but also reduces hardware demands, making it a viable solution for inspection robots. Future work will explore integration with path tracking algorithms to further enhance operational precision in robot technology. The continuous evolution of robot technology promises to unlock new potentials in autonomous systems, driving innovation in various sectors.