In modern manufacturing, the integration of robot technology has revolutionized processes such as grinding, where precision and adaptability are paramount. However, robotic grinding in unknown or uncertain environments poses significant challenges due to the lack of prior knowledge about environmental parameters, leading to issues like low compliance, force overshoot, and instability. To address these problems, we propose a novel control method that combines adaptive sliding mode control, environmental parameter estimation, and adaptive variable impedance control. This approach enables real-time estimation of unknown environmental parameters and adaptive adjustment of impedance parameters, ensuring constant force control during robotic grinding operations. Through extensive simulations and experimental validations, we demonstrate the effectiveness of our method in achieving stable force tracking with minimal overshoot and enhanced adaptability. This advancement in robot technology paves the way for more intelligent and flexible manufacturing systems.
The core of our method lies in a dual-loop control structure. The inner loop employs adaptive sliding mode control to ensure rapid tracking of reference positions by the actual position of the grinding tool, thereby improving disturbance rejection. The outer loop integrates environmental parameter estimation and adaptive variable impedance control to estimate unknown parameters like environmental stiffness and position, and indirectly adjust impedance parameters through position compensation. Together, these loops form a closed-control system that enhances the robot’s ability to maintain constant force in unpredictable environments. Key equations governing the inner loop include the state equation of the end-effector system:
$$ \begin{cases} \dot{X}_1 = X_2 \\ \dot{X}_2 = \frac{u}{m} – \frac{d}{m} X_2 – \frac{k}{m} X_1 \end{cases} $$
where \( X_1 \) represents the actual position, \( u \) is the control law, \( m \) is the mass, \( d \) is the damping, and \( k \) is the stiffness. The sliding mode function is defined as \( s = \hat{c} e + \dot{e} \), with \( \hat{c} > 0 \), and the adaptive law for \( \hat{c} \) is derived as \( \hat{c} = r_c \int s e \, dt + k_{c0} \). This adaptive mechanism allows the system to quickly converge to the sliding surface, reducing chattering and improving robustness.
For environmental parameter estimation, we model the contact force as \( F_e = K_e (X_c – X_e) \) when \( X_c \geq X_e \), where \( K_e \) is the environmental stiffness and \( X_e \) is the environmental position. The estimation rules are formulated as:
$$ \begin{cases} \hat{K}_e(t) = \hat{K}_e(0) – \zeta_1 \int_0^t (F_m – \hat{F}_e) X_c \, dt \\ \hat{X}_e(t) = \hat{X}_e(0) + \frac{1}{\hat{K}_e(0)} \left[ \zeta_2 \int_0^t (F_m – \hat{F}_e) (1 – \hat{K}_e X_c) \, dt \right] \end{cases} $$
where \( \hat{F}_e = \hat{K}_e (\hat{X}_e – X_c) \) is the estimated contact force, and \( \zeta_1 \), \( \zeta_2 \) are tuning factors. This estimation enables the generation of a desired position \( X_d = \hat{X}_e + F_d / \hat{K}_e \), which helps in smoothly contacting the workpiece surface without excessive force spikes.
The adaptive variable impedance control builds on the traditional impedance model \( M_d (\ddot{X}_c – \ddot{X}_d) + B_d (\dot{X}_c – \dot{X}_d) + K_d (X_c – X_d) = F_d – F_m \), but incorporates a position compensation term \( \delta_x \) to adjust impedance parameters indirectly. The compensation is given by \( \delta_x = g(t) + p(t) \hat{e}_F + d(t) \dot{\hat{e}}_F \), where \( \hat{e}_F = F_d – \hat{F}_e \) is the estimated force error. Using model reference adaptive control (MRAC), we derive update laws for \( p(t) \), \( d(t) \), and \( g(t) \) to ensure system stability. For instance, the adaptive rules include:
$$ \begin{cases} p(t) = p(0) – \mu_2 \int_0^t \chi \hat{e}_F \, dt – \sigma_2 p(t) \\ d(t) = d(0) – \mu_3 \int_0^t \chi \dot{X}_c \, dt – \sigma_3 d(t) \end{cases} $$
where \( \chi = -\lambda_p \hat{e}_F – \lambda_v \dot{X}_c \), and \( \mu_i \), \( \sigma_i \) are adaptive gains. This approach allows the robot to adapt to varying environmental conditions, a crucial aspect of advanced robot technology.
To validate our method, we conducted simulation experiments using a virtual prototype built in Adams and controlled via Matlab/Simulink. The system included a 6-DOF grinding robot and a 3-DOF force-controlled end-effector. We compared our method with fuzzy impedance control under different environmental stiffness values (e.g., 100,000 N/mm, 150,000 N/mm, and 200,000 N/mm) and constant desired forces (20 N and 30 N). The results, summarized in the table below, show that our method significantly reduces force overshoot and fluctuations, albeit with slightly longer rise and settling times.
| Grinding Scenario | Control Method | Force Overshoot (%) | Force Fluctuation (±N) | Rise Time (s) | Settling Time (s) |
|---|---|---|---|---|---|
| 20 N, 150,000 N/mm | Fuzzy Impedance | 3.76 | 1.81 | 0.40 | 0.74 |
| 20 N, 150,000 N/mm | Our Method | 0 | 1.46 | 1.21 | 1.27 |
| 30 N, 200,000 N/mm | Fuzzy Impedance | 14.81 | 2.74 | 0.22 | 0.66 |
| 30 N, 200,000 N/mm | Our Method | 3.93 | 1.89 | 0.13 | 1.09 |
Furthermore, dynamic force tracking tests with ramp, step, and sinusoidal desired forces confirmed the adaptability of our approach. For example, with a sinusoidal desired force and stiffness of 150,000 N/mm, our method achieved zero overshoot and a force fluctuation of ±1.64 N, compared to ±1.98 N with fuzzy impedance control. The environmental parameter estimation was also verified through position tracking curves, where the actual position closely followed the reference position, minimizing errors. The table below summarizes position tracking performance under different desired forces.
| Desired Force Type | Stiffness (N/mm) | Position Average Error (mm) |
|---|---|---|
| Constant 20 N | 150,000 | 5.66 × 10⁻⁵ |
| Constant 30 N | 150,000 | 4.77 × 10⁻⁵ |
| Ramp Signal | 150,000 | 4.15 × 10⁻⁵ |
| Step Signal | 150,000 | 3.18 × 10⁻⁴ |
| Sinusoidal Signal | 150,000 | 3.87 × 10⁻⁵ |
In real-world experiments, we deployed a robotic platform consisting of a 6-DOF grinding robot and a 3-DOF force-controlled end-effector to grind aluminum and iron plates with unknown stiffness. The results, as shown in the table below, demonstrate that our method reduces force overshoot by up to 25.96% and force fluctuations by up to 56.15% compared to fuzzy impedance control. For instance, at a desired force of 30 N on an iron plate, our method limited overshoot to 4.67% and fluctuations to ±3.42 N, whereas fuzzy impedance control resulted in 30.63% overshoot and ±7.80 N fluctuations. Surface roughness measurements further confirmed the superiority of our approach, with average roughness values decreasing by 10.97% to 31.15% across different scenarios, highlighting the impact of advanced robot technology on manufacturing quality.
| Workpiece Material | Desired Force (N) | Control Method | Force Overshoot (%) | Force Fluctuation (±N) | Surface Roughness (μm) |
|---|---|---|---|---|---|
| Aluminum | 20 | Fuzzy Impedance | 11.0 | 2.99 | 1.044 |
| Aluminum | 20 | Our Method | 0 | 2.13 | 0.903 |
| Iron | 30 | Fuzzy Impedance | 30.63 | 7.80 | 1.451 |
| Iron | 30 | Our Method | 4.67 | 3.42 | 0.999 |
| Aluminum | 40 | Fuzzy Impedance | 20.22 | 5.23 | 1.367 |
| Aluminum | 40 | Our Method | 10.75 | 4.10 | 1.217 |
| Iron | 40 | Fuzzy Impedance | 41.25 | 8.99 | 1.751 |
| Iron | 40 | Our Method | 18.50 | 6.87 | 1.392 |
In conclusion, our proposed method for adaptive variable impedance constant force control in robotic grinding effectively addresses the challenges of unknown environments by integrating real-time environmental parameter estimation and adaptive control strategies. The inner loop’s adaptive sliding mode control ensures precise position tracking, while the outer loop’s estimation and impedance adjustment enhance compliance and stability. Simulation and experimental results validate that our approach minimizes force overshoot and fluctuations, leading to improved surface quality and adaptability. This contribution to robot technology underscores the potential for more intelligent and reliable robotic systems in industrial applications. Future work will focus on optimizing the control parameters to reduce rise and settling times while maintaining high performance, further advancing the capabilities of robot technology in complex manufacturing tasks.
The development of such adaptive control methods is a significant step forward in robot technology, as it enables robots to handle uncertainties in real-time, making them more autonomous and efficient. By leveraging mathematical models and adaptive algorithms, we can push the boundaries of what robot technology can achieve in grinding and other contact-rich operations. The continuous evolution of robot technology will undoubtedly lead to smarter manufacturing ecosystems, where robots seamlessly adapt to dynamic environments, ensuring high-quality outcomes with minimal human intervention.