# Nonlinear Robust Adaptive Control of Universal Manipulators Based on Desired Trajectory
## 4 Experiment and Discussion
### Analysis and Discussion  
The results of the above experiment are analyzed and discussed below. Table 3 gives the performance indices when selecting different control strategies for the trajectory tracking tasks.  
Figure 11: Control inputs of the proposed method (joint 1–joint 4).  
Figure 12: The adaptation results of the friction coefficients.  
Based on the above results, the analysis and discussion are as follows:  
1. The traditional PID control method does not take into consideration the dynamics of the manipulator; all the performance indices are significantly behind other control methods which consider the dynamics of the robot.
2. Dynamic feedforward control directly compensates the nominal dynamic model as a feedforward quantity. Due to the uncertainties of the real dynamic model compared to our given nominal dynamic model, the performance indices under this control strategy are higher than that of PID, but there is still much room for improvement.
3. The robust adaptive control method based on the desired trajectory proposed in this article considers the uncertainties in the real dynamic model, uses the corresponding control term to compensate the perturbation of the inertial parameters of the links, and corrects the friction coefficients of the joints online. Compared with the dynamic feedforward control method, all the performance indices have significant advantages.
4. Compared to the real-time robust adaptive control method, which compensates for uncertainties in real time, the control method proposed in this article uses the desired trajectory to compute most of the control terms offline. In terms of the regression matrix, its dimensions are 6 \(\times\) 60 for a six-degree-of-freedom manipulator with respect to its link inertial parameters, where each element is a complex nonlinear function containing the six joint state variables of the manipulator. The real-time robust adaptive control method substitutes the real-time signals measured by the sensors into the calculation to obtain the regression matrix, which is computationally intensive and requires a significant amount of processing time. Similarly, the novel robust adaptive method relies on real-time measured state variables to compute the regression matrix. On the contrast, the control method proposed in this article calculates the regression matrix offline from the a priori known desired trajectory. During the actual control process, the regression matrix at each moment is directly output by looking up the table, and then the subsequent calculation is carried out, thus eliminating the need for real-time calculation of complex regression matrix. Therefore, the control method proposed in this paper exhibits significantly lower real-time computational complexity compared to the real-time robust adaptive control and the novel robust adaptive control.
5. Observing the performance indices in Table 3, under the condition that the universal manipulator used in the experiment has poor computing performance, the control strategy with desired trajectory compensation slightly outperforms the control strategy with real-time computation in terms of several performance indices. Furthermore, the method proposed in this paper still exhibits better performance when compared with the novel robust adaptive method.