218 research outputs found
Pose consensus based on dual quaternion algebra with application to decentralized formation control of mobile manipulators
This paper presents a solution based on dual quaternion algebra to the
general problem of pose (i.e., position and orientation) consensus for systems
composed of multiple rigid-bodies. The dual quaternion algebra is used to model
the agents' poses and also in the distributed control laws, making the proposed
technique easily applicable to time-varying formation control of general
robotic systems. The proposed pose consensus protocol has guaranteed
convergence when the interaction among the agents is represented by directed
graphs with directed spanning trees, which is a more general result when
compared to the literature on formation control. In order to illustrate the
proposed pose consensus protocol and its extension to the problem of formation
control, we present a numerical simulation with a large number of free-flying
agents and also an application of cooperative manipulation by using real mobile
manipulators
Task space consensus in networks of heterogeneous and uncertain robotic systems with variable time-delays
This work deals with the leader-follower and the leaderless consensus problems in networks of multiple robot manipulators. The robots are non-identical, kinematically different (heterogeneous), and their physical parameters are uncertain. The main contribution of this work is a novel controller that solves the two consensus problems, in the task space, with the following features: it estimates the kinematic and the dynamic physical parameters; it is robust to interconnecting variable-time delays; it employs the singularity-free unit-quaternions to represent the orientation; and, using energy-like functions, the controller synthesis follows a constructive procedure. Simulations using a network with four heterogeneous manipulators illustrate the performance of the proposed controller.Peer ReviewedPostprint (author's final draft
Synchronization of multiple rigid body systems: a survey
The multi-agent system has been a hot topic in the past few decades owing to
its lower cost, higher robustness, and higher flexibility. As a particular
multi-agent system, the multiple rigid body system received a growing interest
since its wide applications in transportation, aerospace, and ocean
exploration. Due to the non-Euclidean configuration space of attitudes and the
inherent nonlinearity of the dynamics of rigid body systems, synchronization of
multiple rigid body systems is quite challenging. This paper aims to present an
overview of the recent progress in synchronization of multiple rigid body
systems from the view of two fundamental problems. The first problem focuses on
attitude synchronization, while the second one focuses on cooperative motion
control in that rotation and translation dynamics are coupled. Finally, a
summary and future directions are given in the conclusion
Controle hÃbrido bimodal de atitude de corpos rÃgidos baseado em quatérnios unitários
Tese (doutorado)—Universidade de BrasÃlia, Faculdade de Tecnologia, Departamento de Engenharia Elétrica, 2017.Esta tese tem como objetivo principal o desenvolvimento de um controlador hÃbrido capaz de resolver o problema de regulação de atitude de um corpo rÃgido (a partir do repouso) com melhor desempenho que o controlador hÃbrido histerético existente na literatura em termos de tempo de estabilização ou consumo de energia. A natureza hÃbrida do controlador é um requisito essencial para se obter um controle global e robusto a ruÃdos de medição e impedir efeitos indesejáveis como unwinding e chattering. A representação da atitude é feita com quatérnio unitário por possuir o menor número de parâmetros (quatro) que não apresenta singularidades. Propõe-se dois controladores distintos, ambos com duas variáveis de estado lógicas binárias, para o controle de atitude. O primeiro controlador, denominado HY, tem a variável principal determinada por um controle onoff com histerese para indicar qual representação em quatérnio da atitude de referência deve ser seguida e uma outra variável determinada por um controle on-off sem histerese para indicar a proximidade à região crÃtica sujeita a chattering. Esse esquema oferece mais oportunidades de atualização da variável principal que o controlador hÃbrido histerético, por exemplo quando há uma variação abrupta na atitude de referência. Isso reduz as chances do corpo seguir na direção da rotação mais longa. Contudo, essa estratégia impõe restrições na forma como o controlador é implementado (jumps não podem ter prioridade sobre flows). No segundo controlador proposto, denominado bimodal, ambas as variáveis são determinadas por um controle on-off com histerese. A variável principal indica qual representação em quatérnio da atitude de referência deve ser seguida e a outra variável indica a proximidade à região crÃtica sujeita a chattering. Essa estratégia elimina as restrições sobre a forma de implementação do controlador, porém torna a dinâmica dessas variáveis mais complexas, dado que uma variável interfere no comportamento da outra. O efeito resultante é que a banda de histerese do controle on-off referente à variável principal, se adapta de acordo com o estado da outra variá- vel, sendo ora igual, ora a metade do valor do parâmetro banda de histerese. Esse controlador é uma solução intermediária em termos de custo entre o controlador descontÃnuo e o controlador hÃbrido histerético. São apresentadas provas formais da estabilidade global do sistema e de sua robustez contra ruÃdos de medi- ção para ambos os controladores propostos. A eficácia dos controladores é mostrada por meio de simulações. Os resultados indicam que os controladores propostos apresentam vantagens quando a velocidade angular inicial e final é baixa. No caso do controlador bimodal, mesmo para outras velocidades angulares iniciais, o consumo de energia do sistema é, em média, inferior quando comparado com o controlador hÃbrido histerético. Melhores desempenhos em termos de consumo de energia ocorrem quando a banda de histerese é maior como no caso em que são usados sensores mais baratos ou em ambientes onde há muito ruÃdo eletromagnético. Como extensão dos resultados anteriormente citados, foram propostas mais duas contribuições. A primeira refere-se ao problema de sincronização de atitude de uma rede de corpos rÃgidos (agentes). Foi proposto um controle distribuÃdo com propriedade de estabilidade global e assintótica e robustez contra ruÃdos de medição para uma rede de agentes representada por um grafo não direcionado e conexo (cÃclico ou acÃclico). A segunda está relacionada com o controle cinemático da pose de um corpo rÃgido dentro do grupo de quatérnio dual unitário. Foi proposta uma extensão do controlador de atitude bimodal para pose. Em ambos os casos as provas formais são apresentadas e resultados de simulação ilustram as vantagens dos controladores propostos.Coordenação de Aperfeiçoamento de Pessoal de NÃvel Superior (CAPES).The main objective of this thesis is the development of a hybrid controller capable of solving the restto-rest attitude control problem with better performance than the hysteretic hybrid controller of literature in terms of settling time or energy consumption. The hybrid nature of the controller, in this case, is an essential requirement to achieve global control robust against measurement noise and to prevent undesirable effects such as unwinding and chattering. The attitude is represented by a unit quaternion since it provides the minimum number of parameters that does not present representation singularities. It is proposed two distinct controllers, both with two binary logic variables for the control of attitude. The first designed controller, named HY, has the main variable determined by an on-off control with hysteresis that indicates which quaternion representation of the reference attitude should be followed and the other variable determined by an on-off control without hysteresis that indicates the chattering prone region. This scheme offers more opportunities of updating the main variable than the hysteretic hybrid controller, for instance, when there is an abrupt variation in the reference attitude. As a consequence, the body is more likely to being pulled towards the shortest rotation direction. However, this strategy restricts the way the controller is implemented (jumps can not have higher priority than flows). In the second proposed controller, called bimodal, both variables are determined by an on-off control with hysteresis. The main variable indicates which quaternion representation of the reference attitude should be followed and the other variable indicates the chattering prone region. This strategy eliminates restrictions on the way the controller is implemented, but makes the dynamics of these variables more complex, since one variable influences the behavior of the other. The resulting effect is that the hysteresis width of the on-off control for the main variable adapts according to the state of the other variable being either equal or half of the value of the hysteresis width parameter. This controller is a middle term solution in terms of cost between the memoryless discontinuous and the hysteretic hybrid control. It is presented a formal proof that the two proposed controls lead to global stability without unwinding and are robust against measurement noise. The effectiveness of the controllers is shown through simulations. The results indicate that the proposed controllers have advantages when the initial and final angular velocities are low. In the case of the bimodal controller, even for other initial angular velocities, the energy consumption of the system is, on average, lower compared to the hysteretic hybrid controller. Better performances in terms of energy consumption occur when the hysteresis band is larger as is the case when cheaper sensors are used or in noisy electromagnetic environments. As an extension of the results mentioned above, two other contributions were proposed. One of them refers to the problem of attitude synchronization of a network of rigid bodies (agents). A distributed control with globally asymptotically stability property and robustness against noise measurement was proposed for an undirected connected network (cyclic or acyclic) of agents. The other one is related to the kinematic control of the pose of a rigid body within the unit dual quaternion group. It was proposed an extension of the bimodal attitude controller for the pose. For both cases, formal proofs are presented and simulation results illustrate the advantages of the proposed controllers
Consensus-Based Attitude Maneuver of Multi-spacecraft with Exclusion Constraints
Some space missions involve cooperative multi-vehicle teams, for such purposes as interferometry and optimal sensor coverage, for example, NASA Terrestrial Planet Finder Mission. Cooperative navigation introduces extra constraints of exclusion zones between the spacecraft to protect them from damaging each other. This is in addition to external exclusion constraints introduced by damaging or blinding celestial objects. This work presents a quaternion-based attitude consensus protocol, using the communication topology of the team of spacecraft. The resulting distributed Laplacians of their communication graph are applied by semidefinite programming (SDP), to synthesize a series of time-varying optimal stochastic matrices. The matrices are used to generate various cooperative attitude maneuvers from the initial attitudes of the spacecraft. Exclusion constraints are satisfied by quaternion-based quadratically constrained attitude control (Q-CAC), where both static and dynamic exclusion zones are identified every time step, expressed as time-varying linear matrix inequalities (LMI) and solved by semidefinite programming
Multi-Spacecraft Attitude Path Planning Using Consensus with LMI-Based Exclusion Constraints
Space missions involving multi-vehicle teams require the cooperative navigation and attitude slewing of the spacecraft or satellites, for such purposes as interferometry and optimal sensor coverage. This introduces extra constraints of exclusion zones between the spacecraft, in addition to the default exclusion constraints already introduced by damaging or blinding celestial objects. In this work, we present a quaternion-based attitude consensus protocol by using the communication topology of the spacecraft team. By using the Laplacian matrix of their communication graph and a semidefinite program, a synthesis of a time-varying optimal stochastic matrix P is done, which is used to generate various consensus and cooperative attitude trajectories from the initial attitudes of the spacecraft. The concept of quaternion-based quadratically constrained attitude control is then employed to satisfy cone avoidance constraints, where exclusion zones are identified, expressed as linear matrix inequalities (LMI), and solved by semidefinite programming (SDP)
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