In the rapidly evolving field of robot technology, master-slave control systems have become indispensable for applications ranging from industrial automation to medical procedures. These systems enable operators to remotely control robotic manipulators, but they often face challenges such as inefficiency, low controllability, and significant feedback errors. To address these issues, our research integrates force perception with an optimized path planning algorithm, combining Gaussian Potential Field (GPF) and Rapidly-exploring Random Tree (RRT*) to enhance the precision and responsiveness of robot technology in master-slave configurations. This approach not only improves the dynamic interaction between the master and slave ends but also ensures smoother and safer operations in complex environments.
The core of our methodology lies in leveraging force perception to model the inertial dynamics of the master controller, which is crucial for accurate force feedback in robot technology. By applying the Lagrangian formulation, we describe the relationship between joint forces and motions, incorporating principles like virtual work and D’Alembert’s principle to handle non-conservative forces. For instance, the dynamic equation of the robot’s movable joints is represented as: $$\tau = M(\theta) \ddot{\theta} + C(\theta, \dot{\theta}) + G(\theta)$$ where $\tau$ denotes the joint torque, $M(\theta)$ is the inertia matrix, $\ddot{\theta}$ is the angular acceleration, $C(\theta, \dot{\theta})$ accounts for centrifugal forces, and $G(\theta)$ represents gravitational effects. This formulation allows us to capture the operator’s applied forces and translate them into precise movements, minimizing errors in robot technology applications.
To further refine the control, we employ the Jacobian matrix to map joint velocities to the end-effector’s Cartesian velocities, enhancing the coordination in robot technology systems. The velocity relationship is given by: $$\dot{x} = J(q) \dot{q}$$ where $\dot{x}$ is the velocity vector of the end-effector, $J(q)$ is the Jacobian matrix, and $\dot{q}$ is the joint angular velocity vector. For multi-link systems, the velocity of each link’s center of mass can be expressed as: $$\begin{bmatrix} V_{ci} \\ \omega_c \end{bmatrix} = \begin{bmatrix} J_{vi} \\ J_{oi} \end{bmatrix} \dot{q}$$ with $J_{vi}$ and $J_{oi}$ representing the linear and angular velocity components, respectively. This mathematical foundation ensures that force perceptions are accurately converted into actionable commands, a key advancement in robot technology.
Path planning is another critical aspect where robot technology benefits from algorithmic improvements. Traditional RRT* algorithms, while effective in exploring environments, often suffer from suboptimal path quality and excessive computation. Our integration of GPF with RRT* introduces a hybrid approach that uses Gaussian functions to create attractive and repulsive potential fields, guiding the robot toward the goal while avoiding obstacles. The node expansion in the random tree is optimized using: $$F(n) = G(n) + A(n) + R(n)$$ where $F(n)$ is the growth function, $G(n)$ optimizes the path, $A(n)$ is the attraction force toward the goal, and $R(n)$ is the repulsion force from obstacles. The new node position is calculated as: $$P_{\text{new}} = P_{\text{near}} + \rho \cdot \frac{P_{\text{rand}} – P_{\text{near}}}{\| P_{\text{rand}} – P_{\text{near}} \|} + R(n) + A(n)$$ Here, $\rho$ is the adaptive step size, $P_{\text{near}}$ is the nearest node, and $P_{\text{rand}}$ is a random sample point. This combination reduces redundant nodes and shortens paths, making robot technology more efficient in dynamic settings.
For smoother trajectory generation, we apply cubic B-spline curves, defined as: $$P_{0,3}(u) = p_0 \cdot B_{0,3}(u) + p_1 \cdot B_{1,3}(u) + p_2 \cdot B_{2,3}(u) + p_3 \cdot B_{3,3}(u)$$ where $p_0$ to $p_3$ are control points and $B_{i,3}(u)$ are the basis functions. This ensures continuous and collision-free paths, enhancing the reliability of robot technology in master-slave operations. Additionally, we implement an incremental mapping strategy in Cartesian space to maintain consistency between the master and slave workspaces. The position update is given by: $$\Delta x_s = K \cdot {}^s R_m \cdot \Delta x_m$$ where $\Delta x_s$ is the slave’s position change, $\Delta x_m$ is the master’s position change, ${}^s R_m$ is the rotation matrix, and $K$ is the scaling factor. This approach allows flexible control across different operational scales, a significant boost for robot technology.
Our control architecture incorporates virtual fixtures (VF) and an impedance model to provide haptic feedback and reduce lag. The impedance control framework processes position errors and converts them into joint torque adjustments, ensuring real-time correction. This is vital for applications in robot technology where precision is paramount, such as in surgical or assembly tasks. The overall system framework integrates motion capture, environmental perception, and algorithmic planning to deliver seamless master-slave interactions.
To validate our approach, we conducted extensive experiments using a Geomagic Touch force feedback device as the master controller and a UR5e collaborative robot as the slave manipulator. The setup included Vicon motion capture cameras and a RealSense D435i depth camera for environmental sensing. We compared our GPF-RRT* algorithm against existing methods like Improved Sparrow Search Algorithm PID (ISSA-PID), Location Domain Control (LDC), and Fuzzy Self-tuning Bacterial Foraging Algorithm (FS-BFA). The results demonstrated superior performance in path planning and force tracking, underscoring the advancements in robot technology.
In terms of path planning efficiency, our GPF-RRT* algorithm achieved shorter average planning times and path lengths across various iterations. For example, as shown in Table 1, the average planning time for GPF-RRT* was consistently below 5 seconds, whereas other methods exceeded 10 seconds in some cases. Similarly, the path length was optimized to under 140 cm, with fewer iterations required for convergence. This efficiency is crucial for real-time applications in robot technology, where rapid response is essential.
| Algorithm | Average Iterations | Average Path Length (mm) | Average Planning Time (s) |
|---|---|---|---|
| GPF-RRT* | 50 | 1300 | 4.5 |
| FS-BFA | 65 | 1350 | 6.8 |
| LDC | 70 | 1500 | 10.2 |
| ISSA-PID | 75 | 1450 | 9.5 |
Force tracking accuracy was another key metric, where our method minimized errors compared to alternatives. The force output error for GPF-RRT* remained within 15 N, while other algorithms showed fluctuations exceeding 20 N. This precision enhances the safety and effectiveness of robot technology in sensitive tasks. Furthermore, we tested the algorithm’s adaptability in different scenarios, such as simple, complex, and confined environments. Table 2 summarizes the results, highlighting GPF-RRT*’s robustness across various conditions, which is a testament to its versatility in robot technology.
| Environment Type | Average Iterations | Average Path Length (mm) | Average Time (s) | Time Variance (s²) |
|---|---|---|---|---|
| Simple (A1) | 31.4 | 1012.5 | 0.93 | 0.061 |
| Moderate (A2) | 58.4 | 1030.7 | 0.89 | 0.068 |
| Complex (A3) | 84.3 | 1098.3 | 1.23 | 0.098 |
| Confined (A4) | 91.3 | 1179.4 | 1.42 | 0.104 |
The follow-up control performance was evaluated using different mapping coefficients (K). When K=1, the slave robot closely mirrored the master’s trajectory with minimal deviation, achieving near-ideal synchronization. This alignment is critical for applications in robot technology that require high fidelity, such as remote surgery or precision manufacturing. The force feedback mechanism, combined with the optimized path planning, ensured that operational errors were kept below 5%, significantly improving the overall controllability and user experience in robot technology systems.
In conclusion, our integration of force perception with the GPF-RRT* algorithm represents a significant leap forward in robot technology for master-slave control. By addressing key issues like path inefficiency and force feedback errors, we have developed a system that offers enhanced precision, adaptability, and real-time performance. Future work will focus on expanding the sensory feedback capabilities, incorporating advanced vision systems, and exploring applications in diverse fields such as autonomous navigation and human-robot collaboration. As robot technology continues to evolve, such innovations will play a pivotal role in shaping the next generation of intelligent robotic systems.