Bimodal hybrid control of rigid-body attitude based on unit quaternions

Title: Bimodal hybrid control of rigid-body attitude based on unit quaternions Author: Paulo Percio Mota Magro Supervisor: Prof. João Yoshiyuki Ishihara Co-Supervisor: Prof. Henrique Cezar Ferreira Programa de Pós-graduação em Engenharia de Sistemas Eletrônicos e de Automação Brasília, September 12th, 2017 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.