# Model-Based Adaptive Collaboration of Multi-Terminal Internal Force Tracking
## 4 Experiments  
### Experimental Description  
The experiments were carried out using two self-made six-degrees-of-freedom manipulators, with two actuator terminals at the ends and robotic arms with two parallel contact points at the actuator terminals. The specific dimensions of the robotic arms are shown in Table 1. A three-dimensional bionic optical force sensor was installed at each contact point to measure the contact force. All sensors and motors were connected to a PC via a hub. The absolute and relative motion were controlled with classic proportional gain, and an adaptive time-varying force-tracking control algorithm was used to integrate the overall controller based on the force/bit hybrid control model. Due to its length, mature algorithms are not mentioned. For further details, the reader is referred to [19].  
To prove the performance of the proposed algorithm, a multi-terminal system was designed to manipulate two objects with different shapes and stiffnesses:  
1. The first manipulated object is softly wrapped, and its surface is soft and uneven.
2. The second manipulated object is a container with a hard and flat surface.  
The geometry of the manipulated object and its related dimensions, position, and stiffness are arbitrary and unknown. In addition, experiments were performed under unknown nonideal conditions (e.g., deformable objects of any shape; arbitrary clamping; and arbitrary position, direction trajectories, sliding, and friction), which are suitable for nonstructural applications such as rescue. Under the above experimental setup, the reliability and robustness of the proposed multi-terminal adaptive collaboration method are verified.  
The software architecture is based on a robot operating system (ROS), the communication method is RS services, and the implementation of the control module benefits from a set of software packages that implement the control algorithms. When autonomous control is realized, it can communicate with the robot through the read-write port. The key posture of the entire operation task of the software package is shown in Figure 6. Figure 7a,b present the expected experimental trajectories. The soft-body package exhibits a change in position and direction, while the container has only a position translation, where the translational trajectory is the same as for the soft-body package.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Module** & **Length (mm)** & **Width (mm)** \\ \hline Link 1 & 480 & \\ Link 2 & 480 & \\ Link 3 & 373.5 & \\ Link 4 & 126.5 & \\ Link 5 & 110.5 & \\ Link 6 & 54.5 & \\ Terminal & 100 & 50 \\ Sensor center distance & 25 & \\ Terminal axis spacing & 57 & \\ \hline \hline \end{tabular}
\end{table}
Table 1: The relevant dimensions of the robotic arm.  
Figure 6: The key pose of the entire operation task for the soft-package.  
The reference trajectory Terminal-j, \((j=b,c,d)\) requires some time to stabilize and smooth the reference trajectory by \(p_{rje}^{r1}=p_{rje}^{r}(1-e^{-\mu t^{\#}}),j=b,c,d\). Therefore, starting from 0, \(p_{rje}^{r1}\) is gradually dominated by \(p_{rje}^{r}\). In all cases, we set \(\mu=0.02,\eta=2\).  
Regarding the remaining parameters, the initial values are \(\overset{\wedge}{k}=10,\overset{\wedge}{k}=0\), \(\left[\overset{\wedge}{b}_{0},\overset{\wedge}{c}_{0},\overset{\wedge}{d}_{0} \right]=[0.55,0.55,0.55]\), \(\left[\overset{\wedge}{b}_{0},\overset{\wedge}{c}_{0},\overset{\wedge}{d}_{0} \right]=[0,0,0]\), \(\left[\overset{\wedge}{b}_{1},\overset{\wedge}{c}_{1},\overset{\wedge}{d}_{1} \right]=[0,0,0]\), \(\left[\overset{\wedge}{b}_{1},\overset{\wedge}{c}_{1},\overset{\wedge}{d}_{1} \right]=[0,0,0]\), \(\left[\overset{\wedge}{b}_{2},\overset{\wedge}{c}_{2},\overset{\wedge}{d}_{2} \right]=[0,0,0]\), and \(\left[\overset{\wedge}{b}_{2},\overset{\wedge}{c}_{2},\overset{\wedge}{d}_{2} \right]=[0,0,0]\). MBK is given as \(M\)= diag[0.01, 0.01, 0.01], \(B\)= diag[0.1, 0.1, 0.1], and \(K\)= diag[5, 5, 5].