In recent decades, the rapid advancement of robot technology has profoundly transformed various industries and daily life. As applications of robot technology expand into non-structured environments, such as service tasks and complex interactions, the demand for intelligent and adaptive robotic systems has surged. Traditional robotic systems often operate in structured settings like assembly lines, but emerging scenarios require robots to exhibit enhanced safety, compliance, and flexibility. This is particularly critical in tasks involving physical contact with uncertain environments, where precise force control is essential to prevent damage and ensure efficiency. In this context, we explore an admittance-based force control method for collaborative robots, focusing on a glass-cleaning application to demonstrate its effectiveness. By leveraging admittance control, we aim to achieve stable and accurate contact force tracking, thereby improving the overall performance of robot technology in real-world applications.
The integration of robot technology into diverse fields, such as maintenance and cleaning, highlights the need for robust control strategies. For instance, in glass-cleaning tasks, maintaining a consistent contact force between the end-effector (e.g., a brush) and the glass surface is vital to avoid scratches or ineffective cleaning. Traditional position-based controls may fall short in such scenarios due to environmental uncertainties. Thus, we propose an admittance control approach, which models the interaction dynamics to regulate forces effectively. This method not only enhances the adaptability of robot technology but also contributes to its evolution toward more autonomous and intelligent systems. In this article, we detail the system setup, theoretical foundations, parameter analyses, and simulation experiments, all aimed at validating the proposed force control method for collaborative robots.
To implement admittance-based force control, we first constructed a simulated glass-cleaning robotic system. This system comprises a six-degree-of-freedom robotic arm equipped with a multi-axis force sensor at the wrist, a circular brush as the end-effector, a control unit, and a glass panel representing the cleaning surface. The force sensor continuously measures the actual contact force between the brush and glass, providing real-time feedback for control adjustments. The overall setup mimics real-world scenarios where robot technology must handle variable interactions, ensuring that the system can respond to disturbances and maintain desired force levels. By simulating this environment, we can rigorously test the admittance controller under controlled conditions, paving the way for practical implementations in advanced robot technology applications.
The core of our approach lies in the admittance control principle, which models the robot-environment interaction as a dynamic system. Admittance control relates force deviations to positional adjustments, enabling the robot to behave like a spring-damper-mass system when in contact with an object. This is expressed mathematically through a second-order differential equation. Let $F_d$ represent the desired contact force, $F_c$ the actual contact force measured by the sensor, and $\Delta F = F_d – F_c$ the force error. The admittance model defines the relationship between this force error and the positional compensation $\Delta X$ as follows:
$$ M \Delta \ddot{X} + B \Delta \dot{X} + K \Delta X = \Delta F $$
where $M$, $B$, and $K$ are the inertia, damping, and stiffness matrices of the admittance model, respectively. $\Delta X$, $\Delta \dot{X}$, and $\Delta \ddot{X}$ denote the position, velocity, and acceleration compensations. Taking the Laplace transform of this equation yields the transfer function of the admittance control system:
$$ G(s) = \frac{\Delta X(s)}{\Delta F(s)} = \frac{1}{Ms^2 + Bs + K} $$
The poles of this system are given by $s = \frac{-B \pm \sqrt{B^2 – 4MK}}{2M}$, and for stability, the damping must satisfy $B \geq 2\sqrt{MK}$. This ensures that the system does not oscillate uncontrollably, which is crucial for reliable robot technology implementations. The admittance controller operates in an outer loop, generating position adjustments based on force errors, while an inner position controller executes these adjustments. This dual-loop structure allows the robot to adapt its trajectory in real-time, maintaining the desired contact force even in the presence of environmental variations.
To design an effective admittance controller, it is essential to analyze the impact of parameters $M$, $B$, and $K$ on system performance. We conducted a series of simulations using a single-factor method, varying one parameter at a time while keeping others constant. The goal was to observe how each parameter influences response speed, overshoot, and steady-state behavior. Below is a summary of our findings in table form, which highlights the trade-offs involved in tuning these parameters for optimal robot technology applications.
| Parameter | Effect on Response Speed | Effect on Overshoot | Effect on Steady-State | Stability Consideration |
|---|---|---|---|---|
| Inertia (M) | Decreases as M increases | Increases with larger M | Minimal effect | Must be balanced with damping |
| Damping (B) | Decreases as B increases | Reduces overshoot | No direct effect | Must satisfy $B \geq 2\sqrt{MK}$ |
| Stiffness (K) | No significant effect | Can induce oscillations if too low | Higher K reduces steady-state error | High K may cause hardware stress |
For example, increasing the inertia parameter $M$ accelerates the system’s response but can lead to undesirable overshoot, as shown in simulation results where $M$ values of 1, 10, and 20 kg were tested. Conversely, higher damping $B$ slows the response but enhances stability by minimizing oscillations. Stiffness $K$ affects the steady-state force tracking; excessively high $K$ may result in insufficient position compensation, risking damage to the robot or environment, while low $K$ could cause the system to reach the desired force prematurely. Thus, parameter selection must be tailored to specific tasks in robot technology, considering factors like environmental stiffness and required responsiveness.
Building on this theoretical foundation, we implemented a simulation in the MATLAB/Simscape environment to validate the admittance control method. The robotic system model included the six-degree-of-freedom arm, force sensor, brush end-effector, and a glass panel with defined contact properties. Key parameters were set as follows: simulation time of 10 seconds, stiffness $K = 30 \text{N/mm}$, damping $B = 70 \text{N·s/m}$, inertia $M = 3 \text{kg}$, and desired cleaning force $F_d = 10 \text{N}$. To simulate real-world disturbances, such as encountering an obstacle on the glass surface, we introduced a transient force disturbance of 5 N at 3 seconds, lasting 0.01 seconds. This tested the robustness of the control strategy in unpredictable environments, a common challenge in robot technology.
| Parameter | Value | Description |
|---|---|---|
| Simulation Time | 10 s | Duration of the experiment |
| Stiffness (K) | 30 N/mm | Admittance model stiffness |
| Damping (B) | 70 N·s/m | Admittance model damping |
| Inertia (M) | 3 kg | Admittance model inertia |
| Desired Force (F_d) | 10 N | Target contact force |
| Disturbance Force | 5 N at t=3 s | External disturbance applied |
The simulation results demonstrated that the admittance controller achieved rapid and stable force tracking. Within less than 1 second, the actual contact force converged to the desired 10 N, with force tracking errors confined to within ±1 N under normal conditions. Upon introducing the disturbance, the force momentarily deviated by approximately ±2 N but recovered to the steady state within 0.5 seconds, showcasing the system’s resilience. The position compensation $\Delta X$ adjusted dynamically based on force errors, as predicted by the admittance model. These outcomes underscore the efficacy of admittance control in enhancing the compliance and accuracy of robot technology, particularly in applications requiring precise physical interactions.
Further analysis of the force response can be described using the admittance model equations. For instance, the steady-state position compensation $\Delta X_{ss}$ under a constant force error $\Delta F$ is given by $\Delta X_{ss} = \frac{\Delta F}{K}$, derived from the steady-state condition where derivatives are zero. In our case, with $K = 30 \text{N/mm}$, a force error of 1 N would yield $\Delta X_{ss} \approx 0.033 \text{mm}$, illustrating the fine adjustments made by the controller. Additionally, the system’s bandwidth, determined by the parameters, affects how quickly it can respond to changes. The natural frequency $\omega_n$ and damping ratio $\zeta$ are given by:
$$ \omega_n = \sqrt{\frac{K}{M}}, \quad \zeta = \frac{B}{2\sqrt{MK}} $$
For our parameters, $\omega_n \approx 3.16 \text{rad/s}$ and $\zeta \approx 1.85$, indicating an overdamped system that avoids oscillations, which is desirable for stable force control in robot technology. This mathematical insight helps in optimizing parameters for various tasks, ensuring that robotic systems can handle diverse operational conditions.
In conclusion, our study on admittance-based force control for collaborative robot end-effectors highlights its potential to advance robot technology in non-structured environments. Through systematic parameter analysis and simulations, we validated that this method enables quick, accurate, and stable force tracking, even in the presence of disturbances. The integration of admittance control into robotic systems not only improves safety and compliance but also expands the scope of applications, from industrial automation to service robotics. Future work could focus on adaptive parameter tuning and real-world deployments to further enhance the capabilities of robot technology. Overall, this approach represents a significant step toward more intelligent and responsive robotic systems, aligning with the ongoing evolution of robot technology.