Summary: In this paper, we provide a new nonconservative upper bound for the settling time of a class of fixed‐time stable systems. To expose the value and the applicability of this result, we present four main contributions. First, we revisit the well‐known class of fixed‐time stable systems, to show the conservatism of the classical upper estimate of its settling time. Second, we provide the smallest constant that the uniformly upper bounds the settling time of any trajectory of the system under consideration. Third, introducing a slight modification of the previous class of fixed‐time systems, we propose a new predefined‐time convergent algorithm where the least upper bound of the settling time is set a priori as a parameter of the system. At last, we design a class of predefined‐time controllers for first‐ and second‐order systems based on the exposed stability analysis. Simulation results highlight the performance of the proposed scheme regarding settling time estimation compared to existing methods.

This paper aims to provide a methodology for generating autonomous and non-autonomous systems with a fixed-time stable equilibrium point where an Upper Bound of the Settling Time (UBST) is set a priori as a parameter of the system. Furthermore, some conditions for such an upper bound to be the least one are provided. This construction procedure is a relevant contribution compared with traditional methodologies for generating fixed-time algorithms satisfying time constraints since current estimates of an UBST may be too conservative. The proposed methodology is based on time-scale transformations and Lyapunov analysis. It allows the presentation of a broad class of fixed-time stable systems with predefined UBST, placing them under a common framework with existing methods using time-varying gains. To illustrate the effectiveness of our approach, we generate novel, autonomous and non-autonomous, fixed-time stable algorithms with predefined least UBST.

This paper presents a high performance vision-based system with a single static camera for traffic surveillance, for moving vehicle detection with occlusion handling, tracking, counting, and One Class Support Vector Machine (OC-SVM) classification. In this approach, moving objects are first segmented from the background using the adaptive Gaussian Mixture Model (GMM). After that, several geometric features are extracted, such as vehicle area, height, width, centroid, and bounding box. As occlusion is present, an algorithm was implemented to reduce it. The tracking is performed with adaptive Kalman filter. Finally, the selected geometric features: estimated area, height, and width are used by different classifiers in order to sort vehicles into three classes: small, midsize, and large. Extensive experimental results in eight real traffic videos with more than 4000 ground truth vehicles have shown that the improved system can run in real time under an occlusion index of 0.312 and classify vehicles with a global detection rate or recall, precision, and F-measure of up to 98.190%, and an F-measure of up to 99.051% for midsize vehicles.

This paper presents a method for online trajectory planning in known environments. The proposed algorithm is a fusion of sampling-based techniques and model-based optimization via quadratic programming. The former is used to efficiently generate an obstacle-free path while the latter takes into account the robot dynamical constraints to generate a time-dependent trajectory. The main contribution of this work lies on the formulation of a convex optimization problem over the generated obstacle-free path that is guaranteed to be feasible. Thus, in contrast with previously proposed methods, iterative formulations are not required. The proposed method has been compared with state-of-the-art approaches showing a significant improvement in success rate and computation time. To illustrate the effectiveness of this approach for online planning, the proposed method was applied to the fluid autonomous navigation of a quadcopter in multiple environments consisting of up to 200 obstacles. The scenarios hereinafter presented are some of the most densely cluttered experiments for online planning and navigation reported to date. A video of the experiments can be found at https://youtube/DJ1IZRL5t1Q.