# Moving Object Tracking and Its Application to an Indoor Dual-Robot Path
## 3 Control Scheme  
The proposed control scheme is performed through experiment verification by an omnidirectional WMR, as shown in Figure 9. The omnidirectional WMR's chassis size is 240 mm radius. Three omni wheels are configured in space 120\({}^{\circ}\) and three 12V-DC motors are installed to provide rated torque of 68 mNm. The robot is 600 mm in length, 400 mm in width, and 850 mm high. It has mechanical arms and fingers that are able to grip things; their length is 470 mm and 150 mm, respectively. The robot arms have six MX-64 motors, two in the shoulder and one in the elbow on both sides. MX-64 is 40.2 mm in length, 41 mm in width, and 61.1 mm high. Its stall torque is 6.0 mNm. There are two MX-28 motors at the wrist on both sides. MX-28 is 35.6 mm in length, 35.5 mm in width, and 50.6 mm high. Its stall torque is 2.5 mNm. The motors are shown in Figure 10.  
Figure 8: Steps for tracking a moving object against a dynamic background: (**a**) Find the object; (**b**) scroll right; (**c**) the object moves forward; (**d**) the object moves; (**e**) keep tracking the object. The omnidirectional WMR kinematic model [6; 7] is described as follows. First, we assume the WMR is set on a coordinate system as shown in Figure 11, where \(v_{m}\) is the speed of target direction, \(v_{1}\),\(v_{2}\),\(v_{3}\) are the forward speed of each wheel, \(\dot{x}_{m}\), \(\dot{y}_{m}\) are the decomposition of \(v_{m}\), and \(\alpha\) is the angle between the target and WMR. Figure 11: Omnidirectional WMR coordinate system. Figure 9: Omnidirectional WMR. In Figure 12, we know \(v_{m}\) vector consists of \(\dot{x}_{m}\) and \(\dot{y}_{m}\). So we can get the \(v_{2}\) speed for the \(v_{m}\) direction as in Equation (15):  
\[ \begin{array}{ll}v_{2}&=-\sin\left(\xi\right)\dot{x}_{m}+\cos\left(\delta \right)\dot{y}_{m}+L\dot{\phi}\\ &=-\sin(30)v_{m}\sin\left(\alpha\right)+\cos\left(30\right)v_{m}\cos\left( \alpha\right)\\ &=\left(-0.5\sin\left(\alpha\right)+0.866\cos\left(\alpha\right)\right)v_{m} \end{array} . \tag{15}\]  
Then we also know how to get \(v_{1}\) and \(v_{3}\) for \(v_{m}\) direction as in Equations (16) and (17):  
\[v_{1}=\left(-0.5\sin\left(\alpha\right)-0.866\cos\left(\alpha\right)\right)v_{m} \tag{16}\]  
\[v_{3}=\sin\left(\alpha\right)v_{m}. \tag{17}\]  
There are six ultrasonic sensors installed in front of the second layer of the chassis and they are PARALLAX PING ultrasonic distance sensor. The detection distance is approximately 2 cm to 3 m, the burst frequency is 40 KHz, the current is 30 mA, and the voltage is 5 V, as shown in Figure 13. The sensors are used to measure the distance and detect and avoid obstacles. Fuzzy theory is applied to obstacle avoidance control. The fuzzy control structure has four inputs and one output. Ultrasonic signals S1, S3, and S6 are inputs and the value is distance. Fuzzy sets are F (far), M (medium), and N (near). Output DA is the angle for left or right; fuzzy sets are VL, L, S, R, and VR. Fuzzy rules are shown as follows, and the fuzzy sets are shown in Figure 14.  
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Rule 26: If S1 is F and S3 is F and S6 is M then DA is S.  
Rule 27: If S1 is F and S3 is F and S6 is F, then DA is S.  
Figure 12: Simplified kinematic model of omnidirectional WMR. A flowchart of the control sequence is shown in Figure 15. First, the robot will search for the predefined door in the experimental environment. When the robot detects the specified color target, it moves forward. On the way to this objective, the robot will correct its path by detecting the image range at all times. When the robot reaches the specified distance from the door, it will correct its angle to aim at the door. Then it recognizes the room color and checks whether it has reached the destination or not. If the room color represents the desired destination, the robot moves to the door and RFID, as shown in Figure 16, reconfirms at the specified distance to verify the target. If the room is not the destination, the robot will search for the next similar target.