Construction of a WMR for trajectory tracking control: experimental results.

This paper reports a solution for trajectory tracking control of a differential drive wheeled mobile robot (WMR) based on a hierarchical approach. The general design and construction of the WMR are described. The hierarchical controller proposed has two components: a high-level control and a low-level control. The high-level control law is based on an input-output linearization scheme for the robot kinematic model, which provides the desired angular velocity profiles that the WMR has to track in order to achieve the desired position (x∗, y∗) and orientation (φ∗). Then, a low-level control law, based on a proportional integral (PI) approach, is designed to control the velocity of the WMR wheels to ensure those tracking features. Regarding the trajectories, this paper provides the solution or the following cases: (1) time-varying parametric trajectories such as straight lines and parabolas and (2) smooth curves fitted by cubic splines which are generated by the desired data points {(x1∗, y1∗),..., (x(n)∗, y(n)∗)}. A straightforward algorithm is developed for constructing the cubic splines. Finally, this paper includes an experimental validation of the proposed technique by employing a DS1104 dSPACE electronic board along with MATLAB/Simulink software.

Exact Calculation of the Circle of Least Confusion of a Rotationally Symmetric Mirror. II.

We compute the radius and the position of the center of the circle of least confusion, in an exact way and by using the third-order approximation, of a rotationally symmetric mirror when the point source is located at any position on the optical axis. For the spherical case we find that for some positions of the point source there is a considerable difference between the exact computations and those obtained by working up to third-order aberrations.