A Proportional Integral Derivative (PID) controller is commonly used to carry out tasks like position tracking in the industrial robot manipulator controller; however, over time, the PID integral gain generates degradation within the controller, which then produces reduced stability and bandwidth. A proportional derivative (PD) controller has been proposed to deal with the increase in integral gain but is limited if gravity is not compensated for. In practice, the dynamic system non-linearities frequently are unknown or hard to obtain. Adaptive controllers are online schemes that are used to deal with systems that present non-linear and uncertainties dynamics. Adaptive controller use measured data of system trajectory in order to learn and compensate the uncertainties and external disturbances. However, these techniques can adopt more efficient learning methods in order to improve their performance. In this work, a nominal control law is used to achieve a sub-optimal performance, and a scheme based on a cascade neural network is implemented to act as a non-linear compensation whose task is to improve upon the performance of the nominal controller. The main contributions of this work are neural compensation based on a cascade neural networks and the function to update the weights of neural network used. The algorithm is implemented using radial basis function neural networks and a recompense function that leads longer traces for an identification problem. A two-degree-of-freedom robot manipulator is proposed to validate the proposed scheme and compare it with conventional PD control compensation.
The extended Kalman filter (EKF) simultaneous localization and mapping (SLAM) requires the uncertainty to be Gaussian noise. This assumption can be relaxed to bounded noise by the set membership SLAM. However, the published set membership SLAMs are not suitable for largescale and online problems. In this paper, we use ellipsoid algorithm for solving SLAM problem. The proposed ellipsoid SLAM has advantages over EKF SLAM and the other set membership SLAMs, in noise condition, online realization, and large-scale problem. By bounded ellipsoid technique, we analyze the convergence and stability of the ellipsoid SLAM. Simulation and experimental results show that the proposed ellipsoid SLAM is effective for online and large-scale problems such as Victoria Park dataset.
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