A Strategy for Multi-Robot Navigation

International audienceThe paper addresses the problem of trajectory regulation of driftless systems such that a stabilizing control input is assumed exists. The perturbed trajectory depends on a regulation control-input which must be designed such that the system's stability is preserved and some undesirable sets belonging to navigation area must be avoided. For the stability and regulation of a multi-robot system a converging attractive set around the target is constructed and a repulsive set around obstacles is emphasized. Taking into account a communication algorithm agents-agents to agents-target, we prove that the proposed regulation control-input preserves the navigation area invariance property and the system's stability. Simulation results illustrate the effectiveness of he proposed control algorithm

Stabilité et stabilisation en temps fini des systèmes dynamiques interconnectés et problème de consensus en temps fini

This manuscript is dedicated to the study of finite time stability and stabilization of interconnected dynamical systems and finite time consensus problem. After a general introduction, the first part of this thesis focuses on finite time stability and stabilization of perturbed systems and interconnected systems. The second part of this thesis is devoted to the problems of: finite-time consensus, average consensus and finite time stabilization of multi-agent systems. This concept has been addressed by targeting non-linear controlled dynamical systems: with and without drift term. Some protocols are proposed to solve the finite time consensus problem. Many applications and simulations are illustrated.Ce manuscrit est dédié à l'étude de la stabilité et la stabilisation en temps fini des systèmes dynamiques interconnectés et problème de consensus en temps fini. Après une large introduction, la première partie de ce mémoire se focalise sur la stabilité et stabilisation en temps fini des systèmes dynamiques perturbés et des systèmes dynamiques interconnectés. La deuxième partie de cette thèse est consacrée aux problèmes de : consensus en temps fini, consensus moyen en temps fini et stabilisation en temps fini des systèmes multi-agents. Cette notion a été abordé en ciblant les systèmes dynamiques contrôlés non linéaires et complexes de type avec et sans terme de dérive et affine en la commande. Des protocoles sont mis en exergue résolvant les problèmes de consensus/formation en temps fini entre les états de tels systèmes. De nombreuses applications avec des simulations permettent de confirmer les protocoles proposés

Generating timed trajectories foran autonomous robot

Tese de Doutoramento Programa Doutoral em Engenharia Electrónica e ComputadoresThe inclusion of timed movements in control architectures for mobile navigation has received an increasing attention over the last years. Timed movements allow modulat- ing the behavior of the mobile robot according to the elapsed time, such that the robot reaches a goal location within a specified time constraint. If the robot takes longer than expected to reach the goal location, its linear velocity is increased for compen- sating the delay. Timed movements are also relevant when sequences of missions are considered. The robot should follow the predefined time schedule, so that the next mission is initiated without delay. The performance of the architecture that controls the robot can be validated through simulations and field experiments. However, ex- perimental tests do not cover all the possible solutions. These should be guided by a stability analysis, which might provide directions to improve the architecture design in cases of inadequate performance of the architecture. This thesis aims at developing a navigation architecture and its stability analysis based on the Contraction Theory. The architecture is based on nonlinear dynamical systems and must guide a mobile robot, such that it reaches a goal location within a time constraint while avoiding unexpected obstacles in a cluttered and dynamic real environment. The stability analysis based on the Contraction Theory might provide conditions to the dynamical systems parameters, such that the dynamical systems are designed as contracting, ensuring the global exponential stability of the architecture. Furthermore, Contraction Theory provides solutions to analyze the success of the mis- sion as a stability problem. This provides formal results that evaluate the performance of the architecture, allowing the comparison to other navigation architectures. To verify the ability of the architecture to guide the mobile robot, several experi- mental tests were conducted. The obtained results show that the proposed architecture is able to drive mobile robots with timed movements in indoor environments for large distances without human intervention. Furthermore, the results show that the Con- traction Theory is an important tool to design stable control architectures and to analyze the success of the robotic missions as a stability problem.A inclusão de movimentos temporizados em arquitecturas de controlo para navegação móvel tem aumentado ao longo dos últimos anos. Movimentos temporizados permitem modular o comportamento do robô de tal forma que ele chegue ao seu destino dentro de um tempo especificado. Se o robô se atrasar, a sua velocidade linear deve ser aumen- tada para compensar o atraso. Estes movimentos são também importantes quando se consideram sequências de missões. O robô deve seguir o escalonamento da sequência, de tal forma que a próxima missão seja iniciada sem atraso. O desempenho da arqui- tectura pode ser validado através de simulações e experiências reais. Contudo, testes experimentais não cobrem todas as possíveis soluções. Estes devem ser conduzidos por uma análise de estabilidade, que pode fornecer direcções para melhorar o desempenho da arquitectura. O objectivo desta tese é desenvolver uma arquitectura de navegação e analisar a sua estabilidade através da teoria da Contracção. A arquitectura é baseada em sistemas dinâmicos não lineares e deve controlar o robô móvel num ambiente real, desordenado e dinâmico, de tal modo que ele chegue à posição alvo dentro de uma restrição de tempo especificada. A análise de estabilidade baseada na teoria da Contracção pode fornecer condições aos parâmetros dos sistemas dinâmicos de modo a desenha-los como contracções, e assim garantir a estabilidade exponencial global da arquitectura. Esta teoria fornece ainda soluções interessantes para analisar o sucesso da missão como um problema de estabilidade. Isto providencia resultados formais que avaliam o desem- penho da arquitectura e permitem a comparação com outras arquitecturas. Para verificar a habilidade da arquitectura em controlar o robô móvel, foram con- duzidos vários testes experimentais. Os resultados obtidos mostram que a arquitectura proposta é capaz de controlar robôs móveis com movimentos temporizados em ambi- entes interiores durante grandes distâncias e sem intervenção humana. Além disso, os resultados mostram que a teoria da Contracção é uma ferramenta importante para desenhar arquitecturas de controlo estáveis e para analisar o sucesso das missões efec- tuadas pelo robô como um problema de estabilidade.Portuguese Science and Technology Foundation (FCT) SFRH/BD/68805/2010