Passivity-Based adaptive bilateral teleoperation control for uncertain manipulators without jerk measurements

In this work, we consider the bilateral teleoperation problem of cooperative robotic systems in a Single-Master Multi-Slave (SM/MS) configuration, which is able to perform load transportation tasks in the presence of parametric uncertainty in the robot kinematic and dynamic models. The teleoperation architecture is based on the two-layer approach placed in a hierarchical structure, whose top and bottom layers are responsible for ensuring the transparency and stability properties respectively. The load transportation problem is tackled by using the formation control approach wherein the desired translational velocity and interaction force are provided to the master robot by the user, while the object is manipulated with a bounded constant force by the slave robots. Firstly, we develop an adaptive kinematic-based control scheme based on a composite adaptation law to solve the cooperative control problem for robots with uncertain kinematics. Secondly, the dynamic adaptive control for cooperative robots is implemented by means of a cascade control strategy, which does not require the measurement of the time derivative of force (which requires jerk measurements). The combination of the Lyapunov stability theory and the passivity formalism are used to establish the stability and convergence property of the closed-loop control system. Simulations and experimental results illustrate the performance and feasibility of the proposed control scheme.No presente trabalho, considera-se o problema de teleoperação bilateral de um sistema robótico cooperativo do tipo single-master e multiple-slaves (SM/MS) capaz de realizar tarefas de transporte de carga na presença de incertezas paramétricas no modelo cinemático e dinâmico dos robôs. A arquitetura de teleoperação está baseada na abordagem de duas camadas em estrutura hierárquica, onde as camadas superior e inferior são responsáveis por assegurar as propriedades de transparência e estabilidade respectivamente. O problema de transporte de carga é formulado usando a abordagem de controle de formação onde a velocidade de translação desejada e a força de interação são fornecidas ao robô mestre pelo operador, enquanto o objeto é manipulado pelos robôs escravos com uma força constante limitada. Primeiramente, desenvolve-se um esquema de controle adaptativo cinemático baseado em uma lei de adaptação composta para solucionar o problema de controle cooperativo de robôs com cinemática incerta. Em seguida, o controle adaptativo dinâmico de robôs cooperativos é implementado por meio de uma estratégia de controle em cascata, que não requer a medição da derivada da força (o qual requer a derivada da aceleração ou jerk). A teoria de estabilidade de Lyapunov e o formalismo de passividade são usados para estabelecer as propriedades de estabilidade e a convergência do sistema de controle em malha-fechada. Resultados de simulações numéricas ilustram o desempenho e viabilidade da estratégia de controle proposta

Putting reaction-diffusion systems into port-Hamiltonian framework

Reaction-diffusion systems model the evolution of the constituents distributed in space under the influence of chemical reactions and diffusion [6], [10]. These systems arise naturally in chemistry [5], but can also be used to model dynamical processes beyond the realm of chemistry such as biology, ecology, geology, and physics. In this paper, by adopting the viewpoint of port-controlled Hamiltonian systems [7] we cast reaction-diffusion systems into the portHamiltonian framework. Aside from offering conceptually a clear geometric interpretation formalized by a Stokes-Dirac structure [8], a port-Hamiltonian perspective allows to treat these dissipative systems as interconnected and thus makes their analysis, both quantitative and qualitative, more accessible from a modern dynamical systems and control theory point of view. This modeling approach permits us to draw immediately some conclusions regarding passivity and stability of reaction-diffusion systems. It is well-known that adding diffusion to the reaction system can generate behaviors absent in the ode case. This primarily pertains to the problem of diffusion-driven instability which constitutes the basis of Turing’s mechanism for pattern formation [11], [5]. Here the treatment of reaction-diffusion systems as dissipative distributed portHamiltonian systems could prove to be instrumental in supply of the results on absorbing sets, the existence of the maximal attractor and stability analysis. Furthermore, by adopting a discrete differential geometrybased approach [9] and discretizing the reaction-diffusion system in port-Hamiltonian form, apart from preserving a geometric structure, a compartmental model analogous to the standard one [1], [2] is obtaine