In this paper, we present a Lyapunov-based homogeneous controller for the stabilization of a perturbed chain of integrators of arbitrary order r ≥ 1. The proposed controller is based on homogeneous controller for stabilization of pure integrator chains. The control of homogeneity degree is also introduced and various controllers are designed using this concept, namely a bounded-controller with minimum amplitude of discontinuous control and a controller with fixed-time convergence. The performance of the controller is validated through simulations.
S. Laghrouche and M. Harmouche are with IRTES-Proof: This theorem is a generalization of Theorem 2 of [17], where it has been proven for P = Q = 1, and is established in the same way.
Among the huge number of functionalities that are required for autonomous navigation, the most important are localization, mapping, and path planning. In this article, investigation of the path planning problem of unmanned ground vehicle is based on optimal control theory and simultaneous localization and mapping. A new approach of optimal simultaneous localization, mapping, and path planning is proposed. Our approach is mainly affected by vehicle's kinematics and environment constraints. Simultaneous localization, mapping, and path planning algorithm requires two main stages. First, the simultaneous localization and mapping algorithm depends on the robust smooth variable structure filter estimate accurate positions of the unmanned ground vehicle. Then, an optimal path is planned using the aforementioned positions. The aim of the simultaneous localization, mapping, and path planning algorithm is to find an optimal path planning using the Shooting and Bellman methods which minimizes the final time of the unmanned ground vehicle path tracking. The simultaneous localization, mapping, and path planning algorithm has been approved in simulation, experiments, and including real data employing the mobile robot Pioneer P3ÀAT. The obtained results using smooth variable structure filter-simultaneous localization and mapping positions and the Bellman approach show path generation improvements in terms of accuracy, smoothness, and continuity compared to extended Kalman filter-simultaneous localization and mapping positions.
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