## 7 Experiments and Results
### Experiment  
Figure 23 illustrates our prebuilt spatial CDPM that contains two redundant actuators. Its configuration is similar to the first configuration of the simulated system and its main parameters are shown in Table 1. Figure 24 describes the control system of our prototype CDPM which consists of four similar groups. Each group contains two sets of actuator/sensors controlled by 1 PLC Siemens S7-1200. Each cable housed inside a winch is driven by a 220 V Delta AC Servo Motor ECMA-C20604 RS with capacity of 400 W. The unstrained length and the cable tension force of cable is measured via an encoder and a load cell fixed on the winch, respectively. The value measured on the encoder will provide feedback to the driver, while the other, measured on the loadcell, is amplified and transmitted to PC via PLC. The PC is powered by Intel(r) coreTM I3-2100 processor 3.10 MHz. It is used to generate and control signal for four groups through our application. One more response of PC is to synchronize signals from four PLCs, hence, the wireless communication is employed. Due to the limit of technique in measurement positioning accuracy, the experimental evaluation is done in the static state. By employing the proposed method in static state, the valid minimum tension sets in the whole size of robot is obtained. The set of the testing position is randomly taken from this. Thereby, the proposed model is applied and the robot is controlled to these points. Our robot is ordered  
Figure 23: Our prebuilt spatial CDPM with 2 redundant actuators used in experiment (**a**) perspective view; (**b**) end-effector. Figure 24: Diagram of the control system of our proposed prototype. to move point-to-point with the linear trajectory generated by the two-loop control system. The outer loop takes the cable tension forces and current pose of moving platform as its input, compares these values to the values of reference trajectory and aims at the response of the inner loop reference input. The inner loop is mainly based on the PID controller. It directly controls an actuator and feedback by the encoder. The linear trajectory is generated based on a 5 th order trajectory generator with low speed. At each point, the robot is ordered to stop while measurement and error calculation is done. Table 2 summarizes the test in this section, that includes testing desired positions, actual positions, and positioning errors obtained by applying Equation (56). Amplified load-cells and difference of cable lengths taken from encoders signals are also plotted in Figures 25 and 26 while the control system is manipulating the test. The test was done in about 14 min with 100 samples/s. However, for the convenience in tracking the signals while the moving platform is ordered to move to difference points, the intervals for stopping and calculating were replaced by vertical dash-lines represented in Figures 25 and 26. The test begins and finishes at home position \(\mathbf{P}_{0}=\left[ \begin{array}{cc}0&0&1.5\\ \end{array} \right]^{T}\). The torque fluctuation at the time the moving platform starts to move always has the largest amplitude and decreases gradually until it is stabilized, resulting in a jerk at the beginning. This is due to the overshooting of the PID controller. However, this jerk does not last long (about 2 s from the beginning) and the moving platform moves reliably for the rest of given trajectory. Figure 27 shows the position of the desired point of the moving platform in 3D. The size of each point indicates the positioning error. This error is produced by many sources: the accuracy of proposed model, the measurement method, the accuracy of measures, non-ideal characteristics of cable material,  
Figure 26: Different cable lengths are obtained by integrating the encoder signal while the moving platform moves point-to-point with the linear trajectory. Figure 25: Amplified signals are taken from load-cells while the moving platform moves point-to-point with the linear trajectory. latency sync, transmission error and the cumulative error.