The most important advantage of the cascade structure is that the inner loop directly regulates the most significant error (the orientation error), which minimizes the impact of the external disturbances upon the outer loop.
where and represent the clothoid horizontal curvature parameters, and stand for the clothoid vertical curvature parameters, while,, and are the lateral error and orientation error with regard to the centre of the lane and the width of the lane, respectively.
The orientation-error Kalman filter at the top estimates errors in orientation and errors in gyroscope bias.
To ensure that the lateral error ((e^{text{l}})), orientation error ((e^{theta })), and speed error ((e^{{v_{x} }})) converge to zero, three PID controllers were implemented.
When only magnetometers are used, the trajectory measurements cannot compensate for the errors in orientation, rendering larger positioning errors.
We observed in both polyhedra that while panels folded first along edge connections, vertex connections enabled panels to lock together, thereby correcting for any errors in orientation.
This is likely due to that the large subunit has more weight to contribute to the final projection, leading to a smaller error of orientation determination.
Quantitative results obtained by processing synthetic data reveal a tracking position error of 25 ±7μm and orientation error of 1.7 ± 1.3 degrees.
In a direct response to these problems, this paper presents a simple geometric approach to computing the exact local maximum position error and local maximum orientation error, given actuator inaccuracies.
On the other hand, by defining new state variables based on the integral and differential of position and orientation errors of the grasped object, the error system of coordinated robot manipulators is constructed.
