# Adaptive Visual Servoing Control for Hoisting Positioning Under Disturbance Condition
## 5 Simulations  
The proposed visual servo positioning method is applied to the simulation platform. Simulations are conducted to investigate the control performance of the proposed controller in the presence of system uncertainties and disturbance. Consistent with the actual project, we adopt the eye-in-hand style in the simulation platform. To simulate the real camera projection, the controller needs the parameters of the camera, and we use a visual toolbox with the following parameters: focal length 8 mm, imaging pixel frame \(1024\times 1024\). The intention of this simulation is to drive the manipulator to the desired pose. The system parameters are set as \(k_{p}=diag\{0.8,0.8,0.68,0.4,0,0\}\), \(k_{s}=diag\{0.6,0.6,0.6,0.35,0,0\}\), the disturbance term \([5.5,\ 5.5,\ 5.5,\ 0.1,0,0]^{\mathrm{T}}\) is exerted on control quantities. The sampling time is set as \(t=10\) ms. In the simulation, the delay is not considered, which means that, in the ideal state, the time of visual feature extraction and processing is not calculated, and the visual error curve is smooth. We will take the data sampled as the updated data for subsequent analyses and calculations. In this way, the simulation of hoisting positioning with disturbance is carried out to verify the superiority of the method proposed in this paper. The initial pose of the manipulator is set as \([-0.6,0.4,0.5,\ \pi/12,0,0]^{\mathrm{T}}\). The initial feature points and the desired feature points in the image plane are shown in Figure 7a; \(s_{1},s_{2},s_{3},s_{4}\) represent the initial points, and \(s_{1}^{*},s_{2}^{*},s_{3}^{*},s_{4}^{*}\) represent the desired points. In Figure 7b, the blue dotted lines represent the trajectories of four points; we can see that, although there is a large displacement between the initial  
Figure 6: The visual servo structure of adaptive control with Nonlinear Disturbance Observer (NDO) for hoisting positioning. position and the desired position, the manipulator can still be driven to the exact position. During the whole motion process, we take the feature center point as the record point to display its trajectory in 3D space, as shown in Figure 7c. The curvature of the simulation curve in three-dimensional space is small, which means that the proposed method can drive the control object to the target position in a shorter path. After the convergence of visual error, it is stable at zero, which shows that our method still has satisfactory accuracy in the presence of uncertainty and disturbance. Although the position curves have tiny tilt angles, the final position converges and stabilizes at zero. In our method, an adaptive sliding mode control algorithm is employed to decrease the influence of external disturbance, and the coefficient of the slide surface is established based on the adaptive gain. Obviously, this can drive the object to the target position smoothly. Figure 7: Visual servoing performances of the proposed method. Furthermore, we compare the proposed method with the other methods, including proportional control (PC) visual servo, PSMC visual servo [35] and Kalman Filtering (KF) visual servo [36]. The PSMC visual servo proposes a combination of proportional control with the sliding mode control method. Image moments of circular markers labeled are selected as visual features to control the three translational degrees of freedom (DOFs) of the manipulator. The KF visual servo presents an image-based servo control approach with a Kalman neural network filtering scheme; this uses a neural network to estimate and compensate the errors of Kalman filtering (KF). A computer with Intel Corei5 2.67 GHz CPU, 4 GB RAM is used in this comparison. The diagonal positive definite gain matrix \(K_{p}\) in the PC visual servo is set as the same as our controller; the diagonal positive definite gain matrices \(\lambda\), \(K_{p}\), \(K_{s}\) in [35] and the minimum sum squared error (MSE) in [36] are set according to their default values.