# A Cooperative Control Method for Excavation Support Robot with Desired Position/Posture
## 3 Cooperative Control Method
### Desired Position/Posture Coordination Strategy  
The ESR moves along a preset path for a certain displacement, which requires timely adjustment of the positional deviation and support posture and is specifically expressed as the adjustment phase in which one side of the ESR is raised to a supported fixed posture and the other side of the ESR is lowered to the initial supported position. The desired position/posture coordination adjustment process of the ESR is illustrated in Figure 10.  
Figure 8: The general configuration of desired position/posture adjustment control system for ESR. As shown in Figure 10, once the initial position and support posture are fixed and maintained in a steady state, the ESR enters the left and right position/real-time posture adjustment process after completing a certain stroke, and then judges the monitoring data such as the unilateral declination angle, scroll angle, and edge wall distance value of the ESR in turn. The stroke adjustment amounts \(\Delta L_{1},\Delta L_{2},\Delta L_{3},\Delta R_{1},\Delta R_{2}\), and \(\Delta R_{3}\) of the lateral AHC are set based on the desired position/posture. Coordinate the ESR declination angle, scroll angle, and distance to the edge walls on both sides one by one until the most expected position/posture is adjusted. It can be seen from the kinematic model in the previous chapter that if the declination angle of the ESR on the left and right sides is adjusted to the desired value, the stroke coordination amounts \(\Delta L_{1}\) and \(\Delta R_{1}\) of the lateral AHC between the ESRs are written as  
\[\left\{ \begin{array}{l}\Delta L_{1}\approx-\left((\frac{L}{2}-m)\sin\alpha_ {Le}+(d_{1}+\frac{b}{2})\cos\alpha_{L}\right)+x_{L}\\ \Delta R_{1}\approx-\left((\frac{L}{2}-m)\sin\alpha_{Re}+(d_{5}+\frac{b}{2}) \cos\alpha_{R}\right)+x_{R}\end{array} \right. \tag{27}\]  
Figure 9: The position/posture morphological motion trend sets of ESR. If the scroll angles of the ESRs on both sides are adjusted close to the desired expected values [31], the stroke coordination amounts \(\Delta L_{2}\) and \(\Delta R_{2}\) of the lateral AHC between the ESRs are expressed as  
\[\left\{ \begin{array}{l}\Delta L_{2}\approx-\left(\frac{H}{2}\sin\gamma_{Le}+( d_{2}+\frac{b}{2})\cos\gamma_{L}\right)+y_{L}\\ \Delta R_{2}\approx-\left(\frac{H}{2}\sin\gamma_{Re}+(d_{6}+\frac{b}{2})\cos \gamma_{R}\right)+y_{R}\end{array} \right. \tag{28}\]  
Figure 10: Desired position/posture coordination adjustment process of the ESR. Assuming that the distance between the ESR and the edge sidewall is adjusted to the most desired expected value, first determine the minimum distance between the left and right ESRs and the edge sidewall, let the left \(d_{mL}=\min(d_{1},d_{2},d_{3},d_{4})\) and the right \(d_{mR}=\min(d_{5},d_{6},d_{7},d_{8})\) hold true, and comparing \(d_{mL}\) and \(d_{mR}\) with the expected distance \(d_{Le}\) and \(d_{Re}\) of the edge sidewall, the amounts of stroke coordination \(\Delta L_{3}\) and \(\Delta R_{3}\) for the lateral AHC between the ESRs are identified as  
\[\Delta L_{3}=\left\{ \begin{array}{l}d_{mL}-d_{Le}\ (d_{mL}\geq d_{Le})\\ d_{Le}-d_{mL}\ (d_{mL}<d_{Le})\end{array} \right. \tag{29}\]  
\[\Delta R_{3}=\left\{ \begin{array}{l}d_{mR}-d_{Re}\ (d_{mR}\geq d_{Re})\\ d_{Re}-d_{mR}\ (d_{mR}<d_{Re})\end{array} \right. \tag{30}\]  
To sum up, the ESRs on the left and right sides are pre-adjusted to achieve the most desired position/posture, and the stroke coordination amount of the lateral AHC is denoted as:  
\[\left\{ \begin{array}{l}\Delta L=\Delta L_{1}+\Delta L_{2}+\Delta L_{3}\\ \Delta R=\Delta R_{1}+\Delta R_{2}+\Delta R_{3}\end{array} \right. \tag{31}\]  
where if the lateral AHC shrinks, the values \(\Delta L_{i}\) and \(\Delta R_{i}\) are negative, and when the lateral AHC extends, the values \(\Delta L_{i}\) and \(\Delta R_{i}\) are positive.