Este trabalho apresenta uma metodologia de controle de posição das juntas passivas de um manipulador subatuado de uma maneira subótima. O termo subatuado se refere ao fato de que nem todas as juntas ou graus de liberdade do sistema serem equipados com atuadores, o que ocorre na prática devido a falhas ou como resultado de projeto. As juntas passivas de manipuladores desse tipo são indiretamente controladas pelo movimento das juntas ativas usando as características de acoplamento da dinâmica de manipuladores. A utilização de redundância de atuação das juntas ativas permite a minimização de alguns critérios, como consumo de energia, por exemplo. Apesar da estrutura cinemática de manipuladores subatuados ser idêntica a do totalmente atuado, em geral suas características dinâmicas diferem devido a presença de juntas passivas. Assim, apresentamos a modelagem dinâmica de um manipulador subatuado e o conceito de índice de acoplamento. Este índice é utilizado na seqüência de controle ótimo do manipulador. A hipótese de que o número de juntas ativas seja maior que o número de passivas permite o controle ótimo das juntas passivas, uma vez que na etapa de controle destas há mais entradas (torques nos atuadores das juntas ativas), que elementos a controlar (posição das juntas passivas). Neste ponto reside a contribuição desta tese ao estado da arte, uma vez que não há até o momento publicação que proponha o controle ótimo das juntas passivas neste caso. / This work presents a control methodologie for the position of the passive joints of an underactuated manipulator in a suboptimal way. The term underactuated refers to the fact that not all the joints or degrees of freedom of the system are equipped with actuators, which occurs in practice due to failures or as design result. The passive joints of manipulators like this are indirectly controlled by the motion of the active joints using the dynamic coupling characteristics. The utilization of actuation redundancy of the active joints allows the minimization of some criteria, like energy consumption, for example. Although the kinematic structure of an underactuated manipulator is identical to that of a similar fully actuated one, in general their dynamic characteristics are different due to the presence of passive joints. Thus, we present the dynamic modelling of an underactuated manipulator and the concept of coulpling index. This index is used in the sequence of the optimal conirol of the manipulator. The hipotheses that the number of active joints is greatter than the number of passives (na>np) allows the optimal control of the passive joints, since there are more inputs (torques at the actuators of the active joints), than elements to be controlled (position of the passive joints). At this point resides the contribution of this dissertation to the state of the art, once there is no publication that proposes the optimal control of the passive joints in this case.

Este trabalho apresenta uma metodologia de controle de posição das juntas passivas de um manipulador subatuado de uma maneira subótima. O termo subatuado se refere ao fato de que nem todas as juntas ou graus de liberdade do sistema serem equipados com atuadores, o que ocorre na prática devido a falhas ou como resultado de projeto. As juntas passivas de manipuladores desse tipo são indiretamente controladas pelo movimento das juntas ativas usando as características de acoplamento da dinâmica de manipuladores. A utilização de redundância de atuação das juntas ativas permite a minimização de alguns critérios, como consumo de energia, por exemplo. Apesar da estrutura cinemática de manipuladores subatuados ser idêntica a do totalmente atuado, em geral suas características dinâmicas diferem devido a presença de juntas passivas. Assim, apresentamos a modelagem dinâmica de um manipulador subatuado e o conceito de índice de acoplamento. Este índice é utilizado na seqüência de controle ótimo do manipulador. A hipótese de que o número de juntas ativas seja maior que o número de passivas permite o controle ótimo das juntas passivas, uma vez que na etapa de controle destas há mais entradas (torques nos atuadores das juntas ativas), que elementos a controlar (posição das juntas passivas). Neste ponto reside a contribuição desta tese ao estado da arte, uma vez que não há até o momento publicação que proponha o controle ótimo das juntas passivas neste caso. / This work presents a control methodologie for the position of the passive joints of an underactuated manipulator in a suboptimal way. The term underactuated refers to the fact that not all the joints or degrees of freedom of the system are equipped with actuators, which occurs in practice due to failures or as design result. The passive joints of manipulators like this are indirectly controlled by the motion of the active joints using the dynamic coupling characteristics. The utilization of actuation redundancy of the active joints allows the minimization of some criteria, like energy consumption, for example. Although the kinematic structure of an underactuated manipulator is identical to that of a similar fully actuated one, in general their dynamic characteristics are different due to the presence of passive joints. Thus, we present the dynamic modelling of an underactuated manipulator and the concept of coulpling index. This index is used in the sequence of the optimal conirol of the manipulator. The hipotheses that the number of active joints is greatter than the number of passives (na>np) allows the optimal control of the passive joints, since there are more inputs (torques at the actuators of the active joints), than elements to be controlled (position of the passive joints). At this point resides the contribution of this dissertation to the state of the art, once there is no publication that proposes the optimal control of the passive joints in this case.

The motivation of this research is to propose innovative nonlinear and optimal control design algorithms, which can be used in real life. The algorithms need to be computationally efficient, should deal with control constraints and should operate under state feedback. To show the efficacy of algorithms, automatic therapy for different cancer problems is chosen to be the field of application. In this thesis, first an advanced control design technique called ’optimal dynamic in-version’ has been successfully experimented with control constraints. The proposed approach has subsequently been shown to be quite effective in proposing automatic drug delivery schemes with simultaneous application of chemo and immunotherapy drugs for complete elimination of cancer cells in melanoma (a skin cancer) as well as glioma (a brain cancer). As per the current practice, the amount of drug dosages are generally given based on some apriori statistical study with a very small sample size, which in reality may either also lead to drug toxicity (due to excessive drug) or may become ineffective (due to insufficient drug) for a particular patient. Subject to the fidelity of the mathematical model (which has been taken from published literature), it has been shown in this thesis that nonlinear control theory can be used for computation of drug dosages, which can then be used in a feedback strategy, thereby customizing the drug for the patient’s condition, to cure the disease successfully. Next, attention has been shifted to impulsive control of systems. Such impulsive con-trol systems appear in many other applications such as control of swings, control of spacecrafts and rockets using reaction control system, radiotherapy in cancer treatment and so on. Two impulsive control design philosophies are proposed in this thesis. In one approach, recently proposed model predictive static programming (MPSP) has been extended for impulsive control systems and has been named as impulsive-MPSP (I-MPSP). In other approach, another recent development, namely the Pseudospectral method has been utilized to consider both the magnitude of the control impulses as well as the time instants at which they are applied as the decision variables. It can be noted, that to the best of the knowledge of the author, the time instants of control application, being considered as decision variables is being proposed for the first time in the nonlinear and optimal control framework. Both I-MPSP and Pseudospectral methods are computationally quite efficient and hence can be used for feedback control (I-MPSP happens to be computationally more efficient than the Pseudospectral method). Applicability of the proposed extensions have been shown by solving various benchmark problems such as (i) a scalar linear problem, (ii) Van der Pol’s oscillator problem and (iii) an inverted pendulum problem. Finally the applicability of the proposed I-MPSP strategy has been shown by solving challenging problems such as radiotherapy treatment of head and neck and adenocarcimona cancers. Radio-therapy model is considered with oxygen effect, in which radiosensitivity parameters are considered in different forms. Head and neck cancer is considered with constant radiosensitivity parameters and adenocarcinoma is considered with constant, linear, quadratic and saturation model of radiosensitivity parameters. Note that toxicity constraints on normal tissue, which are nonlinear control constraints, are also successfully incorporated in this control design.