We have derived a new performance measure, product of minors of the Jacobian matrix, that tells how far kinematically redundant manipulators are from singularity. It was demonstrated that previously used performance measures, namely condition number and manipulability measure allowed to change configurations, caused repeatability problems and discontinuity effects. The new measure, on the other hand, assures that the arm solution remains in the same configuration, thus effectively preventing these problems.

Methods for resolving kinematic redundancies of manipulators by the effect on joint torque are examined. When the generalized inverse is formulated in terms of accelerations and incorporated into the dynamics, the effect of redundancy resolution on joint torque can be directly reflected. One method chooses the joint acceleration null-space vector to minimize joint torque in a least squares sense; when the least squares is weighted by allowable torque range, the joint torques tend to be kept within their limits. Contrasting methods employing only the pseudoinverse with and without weighting by the inertia matrix are presented. The results show an unexpected stability problem during long trajectories for the null-space methods and for the inertia-weighted pseudoinverse method, but rarely for the unweighted pseudoinverse method. Evidently a whiplash action develops over time that thrusts the endpoint off the intended path, and extremely high torques are required to overcome these natural movement dynamics.

Ο στόχος της εργασίας αυτής είναι η κατασκευή και ο έλεγχος ενός λαπαροσκοπικού εργαλείου με πλεονάζοντες βαθμούς ελευθερίας (ΒΕ). Ο βραχίονας αποτελείται από συνδεδεμένα τμήματα ή «σπονδύλους» που ενεργοποιούνται από καλώδια Ni-Ti, γνωστά και ως Shape Memory Alloys, που λειτουργούν ως δυαδικοί ενεργοποιητές με 2 καταστάσεις. Έτσι, εξασφαλίζεται η επαναληψιμότητα στις κινήσεις του βραχίονα και δεν απαιτούνται αισθητήρες για τη θέση των αρθρώσεων. Κάθε σπόνδυλος αποτελείται από 3 ενεργούς πρισματικούς ενεργοποιητές (SMA) τοποθετημένους έτσι ώστε να σχηματίζουν ένα τρίποδο, το οποίο παρέχει 3 ΒΕ σε κάθε άρθρωση (δύο περιστροφικούς και ένα μεταφορικό). Η ανεξάρτητη ενεργοποίηση κάθε άρθρωσης γίνεται από μικροελεγκτές που επικοινωνούν με το πρωτόκολλο I2C και είναι τοποθετημένοι στο εσωτερικό κάθε συνδέσμου. Θα παρουσιαστούν διάφορα ζητήματα σχεδιασμού, η κινηματική και η προσομοίωση του εργαλείου, καθώς και ένα αρχικό πείραμα. / The subject of this work is the development of a prototype hyper-redundant laparoscopic tool. The manipulator consists of cascaded modules which are powered by Shape Memory Alloy wires (NiTi), acting as binary actuators with two stable states. As a result, the repeatability of the manipulator’s movement is ensured, alleviating the need for sensing of the manipulator’s joint-positions. Each module is composed of three active prismatic actuators in a tripod configuration providing a 3-DOF (two rotational and one translational) maneuverability for each joint. I2C-networked microcontrollers activate the individual tendon in each joint. Certain design aspects as well as the kinematics of the binary manipulator are presented followed by simulation and experimental studies on the laparoscopic tool prototype.

No description available.

A formulation of impedance control for redundant manipulators is developed as a particular case of an optimal control problem. This formulation allows the planning and design of an impedance controller that benets from the stability and eficiency of an optimal controller. Moreover, to circumvent the high computational costs of computing an optimal controller, a sub-optimal feedback controller based on the state-dependent Ricatti equation (SDRE) approach is developed. This approach is then compared with the quadratic programming (QP) control formulation, commonly used to resolve redundancy of robotic manipulators. Numerical simulations of a redundant planar 4-DOF serial link manipulator show that the SDRE control formulation offers superior performance over the control strategy based QP, in terms of stability, performance and required control effort. / Uma formulação do controle de impedância para manipuladores redundantes é desenvolvida como um caso particular de um problema de controle ótimo. Essa formulação permite o planejamento e projeto de um controlador de impedância que se beneficia da estabilidade e eficiência de um controlador ótimo. Para evitar lidar com os elevados custos computacionais de se computar um controlador ótimo, um controlador em malha fechada sub-ótimo, baseado na abordagem das equações de Ricatti dependentes de estado (SDRE), é desenvolvido. Essa abordagem é comparada com a formulação de um controlador baseado em programação quadrática (QP), usualmente utilizado para resolver problemas de redundância em manipuladores robóticos. Simulações numéricas de um manipulador serial plano de quatro graus de liberdade mostram que o controlador baseado em SDRE oferece performance superior em relação a um controlador baseado em programação quadrática, em termos de estabilidade, performance e esforço de controle requerido do atuador.

A formulation of impedance control for redundant manipulators is developed as a particular case of an optimal control problem. This formulation allows the planning and design of an impedance controller that benets from the stability and eficiency of an optimal controller. Moreover, to circumvent the high computational costs of computing an optimal controller, a sub-optimal feedback controller based on the state-dependent Ricatti equation (SDRE) approach is developed. This approach is then compared with the quadratic programming (QP) control formulation, commonly used to resolve redundancy of robotic manipulators. Numerical simulations of a redundant planar 4-DOF serial link manipulator show that the SDRE control formulation offers superior performance over the control strategy based QP, in terms of stability, performance and required control effort. / Uma formulação do controle de impedância para manipuladores redundantes é desenvolvida como um caso particular de um problema de controle ótimo. Essa formulação permite o planejamento e projeto de um controlador de impedância que se beneficia da estabilidade e eficiência de um controlador ótimo. Para evitar lidar com os elevados custos computacionais de se computar um controlador ótimo, um controlador em malha fechada sub-ótimo, baseado na abordagem das equações de Ricatti dependentes de estado (SDRE), é desenvolvido. Essa abordagem é comparada com a formulação de um controlador baseado em programação quadrática (QP), usualmente utilizado para resolver problemas de redundância em manipuladores robóticos. Simulações numéricas de um manipulador serial plano de quatro graus de liberdade mostram que o controlador baseado em SDRE oferece performance superior em relação a um controlador baseado em programação quadrática, em termos de estabilidade, performance e esforço de controle requerido do atuador.

Motion planning and control synthesis are challenging problems for underactuated mechanical systems due to the presence of passive (non-actuated) degrees of freedom. For those systems that are additionally not feedback linearizable and with unstable internal dynamics there are no generic methods for planning trajectories and their feedback stabilization. For fully actuated mechanical systems, on the other hand, there are standard tools that provide a tractable solution. Still, the problem of generating efficient and optimal trajectories is nontrivial due to actuator limitations and motion-dependent velocity and acceleration constraints that are typically present. It is especially challenging for manipulators with kinematic redundancy. A generic approach for solving the above-mentioned problems is described in this work. We explicitly use the geometry of the state space of the mechanical system so that a synchronization of the generalized coordinates can be found in terms of geometric relations along the target motion with respect to a path coordinate. Hence, the time evolution of the state variables that corresponds to the target motion is determined by the system dynamics constrained to these geometrical relations, known as virtual holonomic constraints. Following such a reduction for underactuated mechanical systems, we arrive at integrable second-order dynamics associated with the passive degrees of freedom. Solutions of this reduced dynamics, together with the geometric relations, can be interpreted as a motion generator for the full system. For fully actuated mechanical systems the virtually constrained dynamics provides a tractable way of shaping admissible trajectories. Once a feasible target motion is found and the corresponding virtual holonomic constraints are known, we can describe dynamics transversal to the orbit in the state space and analytically compute a transverse linearization. This results in a linear time-varying control system that allows us to use linear control theory for achieving orbital stabilization of the nonlinear mechanical system as well as to conduct system analysis in the vicinity of the motion. The approach is applicable to continuous-time and impulsive mechanical systems irrespective of the degree of underactuation. The main contributions of this thesis are analysis of human movement regarding a nominal behavior for repetitive tasks, gait synthesis and stabilization for dynamic walking robots, and description of a numerical procedure for generating and stabilizing efficient trajectories for kinematically redundant manipulators.