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Abstract In the early days,designer emphasized that human-like robotic hands should have high degree of freedoms(DOFs) and fully simulate all motions of human hands.It makes the system to be too expensive and complex. In recent years, the performance of grasp is no longer depend on the DOFs only after the concept of underactuated is applied. In this article, we discussed the designs and mechanisms of robotic hands and the design principle of underactuated. The SYS-1 underactuated human-like robotic hand uses only six actuator to control ten DOFs, the fingers of SYS-1 consist of underactuated six-bar linkage that simulate human¡¦s fingers motion. The ejection effect is also well controlled. Every finger is an independent module and can be separate or deploy according to the needs. The conduit-tendon system let SYS-1 can work in the water or high temperature environment without any damage. We also analysis the motion characteristic and grasp performance of SYS-1 and compare to the other similar designs.

Master of Science / Department of Mechanical Engineering / Warren N. White / The subject of linear control is a mature subject that has many proven powerful techniques. Recent research generally falls into the area of non-linear control. A subsection of non-linear control that has garnered a lot of research recently has been in underactuated dynamic systems. Many applications of the subject exist in robotics, aerospace, marine, constrained systems, walking systems, and non-holonomic systems. This thesis proposes a sliding mode control law for the tracking control of an underactuated dynamic system. A candidate Lyapunov function is used to build the desired tracking control. The proposed control method does not require the integration of feedback as does its predecessor. The proposed control can work on a variety of underactuated systems. Its predecessor only worked on those dynamic systems that are simply underactuated (torques acting on some joints, no torques acting on others). For dynamic systems that contain a roll without slip constraint, often a desired trajectory to follow is related to dynamic coordinates through a non-holonomic constraint. A navigational control is shown to work in conjunction with the sliding mode control to allow tracking of these desired trajectories. The methodology is applied through simulations to a holonomic case of the Segbot, an inverted cart-pole, a non-holonomic case of Segbot, and a rolling wheel. The methodology is implemented on an actual Segbot and shown to provide more favorable tracking results than linear feedback gains.

Doctor of Philosophy / Department of Mechanical and Nuclear Engineering / Warren N. White / There are a number of different types of mechanical systems which can be termed as underactuated. The degrees of freedom (DOF) of a system are defined by the system’s number of independent movements. Underactuated mechanical systems have fewer actuators than DOF. Some examples such as satellites, air craft, overhead crane loads, and missiles have at least one unactuated DOF. The work presented here develops a nonlinear control law for the asymptotic stabilization of underactuated systems. This is accomplished by finding the solution of matching conditions that arise from Lyapunov’s second method, analogous to the dissipation of energy. The direct Lyapunov approach (DLA) offers a wide range of applications for underactuated systems due to the fact that the algebraic equations, ordinary differential equations, and partial differential equations stemming from the matching conditions are more tractable than those appearing in other approaches. Two lemmas of White et al. (2007) are applied for the positive definiteness and symmetry condition of the KD matrix which is used to define an analogous kinetic energy for the system. The defined KD matrix and the Lyapunov candidate function are developed to ensure stability. The KD matrix is analogous to the mass matrix of the dynamic system. The candidate Lyapunov function, involving the analogous kinetic energy and an undefined potential of the generalized position coordinates, is presented. By computing the time derivative of the Lyapunov candidate function, three equations called matching conditions emerge and parts of their solution provide the nonlinear control law that stabilizes the system. This dissertation presents the derivation of the DLA, provides a new method to solve the first matching condition (FMC), and shows the tools for the control law design. The stability is achieved from the proper shape of the potential, the positive definiteness of the KD matrix, and the non-positive rate of change of the Lyapunov function. The ball and beam, the inverted pendulum cart, and, a more complicated system, the ball and arc are presented to demonstrate the importance of the results because the methods to solve the matching equations, emerging from the system examples, are simple and easier. The presented controller design formulation satisfies the FMC exactly without introducing control law terms that are quadratic in the velocities or approximations. This methodology allows the development of the first nonlinear stabilizing control law for the ball and arc system, a simple and effective formulation to find a control law for the inverted pendulum cart, and a stabilizing control of the ball and beam apparatus without the necessity of approximations to solve the FMC. To illustrate the formulation, the derivation is performed using the symbolic manipulation program Maple and it is simulated in the Matlab/Simulink environment. The dissertation on the solvability of the first matching condition for stabilization is organized into six different chapters. The introduction of the problem and the previous approaches are presented in Chapter 1. Techniques for solving of the first matching condition, as well as the limitations, are provided in Chapter 2. The application of this general strategy to the ball and beam system appears in Chapter 3. Chapter 4 and 5 present the application of the method to the ball and arc apparatus and to the inverted pendulum cart, respectively. The difficulties for each application are also presented. Particularly, Chapter 5 shows the application of the produced material to obtain an easier formulation for the inverted pendulum cart compared to previous published controller examples. Finally, some conclusions and recommendations for future work are presented.

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This paper presents the design of an underactuated lower body exoskeleton to assist with walking. It reduces the amount of bodyweight going through the user's leg by providing a supporting force to the user that is engaged and disengaged depending on the stage of the gait cycle the user is in. It is engaged when the leg is in stance, effectively pushing between the ball of the foot and the hips, and is disengaged during leg swing. This support force is provided by a linear actuator on each leg that consists of a compression spring, ball screw, and motor. It works by having the motor turn the ball screw, which moves a metal plate to either compress or decompress the spring. The actuator is designed to always be able to extend, to avoid limiting the user's motion. The spring is disengaged while the leg is in swing in order to reduce any impedance to the user's natural stride. The exoskeleton is also designed to minimize any range of motion limitations to reduce its restrictiveness. The exoskeleton was found to be able to provide 19 lbs (85 N) of support to the user per leg. / Master of Science / Exoskeletons are external devices worn to assist the user's natural movement or strength. This paper outlines the design of an exoskeleton that assists the user in walking by providing a supporting force on any leg that the user's weight is on. This effectively reduces the load on the user's legs, which could help reduce leg strain and fatigue. The exoskeleton releases this force when weight is removed from the leg to allow the user to easily swing their leg forward to step. The exoskeleton was designed to minimize limitations to the range of motion of the leg joints while walking, squatting, or sitting to ensure that the exoskeleton did not feel restricting or uncomfortable. Testing revealed that the exoskeleton was able to provide a supporting force of approximately 19 lbs (85 N) to the user per leg and met all the joint range of motion requirements to avoid restrictiveness.

An underactuated exoskeleton design for walking assistance is presented and evaluated. The exoskeleton uses one motor per leg and makes use of a pantograph to reduce the overall profile and allow the exoskeleton to closely follow the shape of the user's leg. Support is provided between the ball of the user's foot and their waist by compressing a spring in parallel with the user's leg during Stance Phase. The exoskeleton has a mass of 14.0 kg (30.8 lbs) and was tested up to a supplied spring force of 323.6 N (72.75 lbf) which equates to around 161.8 N (36.38 lbf) of assistive force at the waist. Range of motion tests showed minimal restriction at the knee and ankle, but some restriction of the hip. Human subject experiments using a simple gait detection method based on GRF at walking speeds from 0.45 m/s to 1.12 m/s (1.0 mph to 2.5 mph) were performed and showed an increase in the time between actual heel strike and predicted heel strike of approximately 0.05 seconds to 0.1 seconds. Lastly, calculations are presented examining the effect of exoskeleton assistance on the biological joint moments and optimizing the actuator design to reduce power consumption. The actual performance of the exoskeleton is compared with the calculations based on the joint angles during a typical walking cycle. / Master of Science / A design for an exoskeleton capable of providing walking assistance without requiring a motor for every joint is presented and evaluated. The exoskeleton uses one motor per leg and makes use of a pantograph to reduce the required size and allow the exoskeleton to closely follow the shape of the user's leg. Support is provided between the ball of the user's foot and their waist by compressing a spring attached beside the user's leg while the user's foot is on the ground. The exoskeleton weighs 14.0 kg (30.8 lbs) and was tested up to a supplied spring force of 323.6 N (72.75 lbf) which equates to around 161.8 N (36.38 lbf) of assistive force at the waist. Range of motion tests showed minimal restriction at the knee and ankle, but some at the hip. Testing with a human participant using a simple method for determining when to apply support and remove it based on the forces measured at the user's foot were performed at walking speeds of 0.45 m/s to 1.12 m/s (1.0 mph to 2.5 mph). These tests showed an increase in the time between when the heel of the foot initially hits the ground and when the exoskeleton code determined that it occurred of approximately 0.05 seconds to 0.1 seconds. Lastly, calculations are presented examining how exoskeleton assistance affects what is felt at the joints of the user and determining what spring stiffness would best reduce the power required from the motors. The actual performance of the exoskeleton is compared with the calculations based on the joint angles during normal human walking.

Master of Science / Department of Mechanical and Nuclear Engineering / Warren N. White / Mechanical systems play an integral part in our everyday lives. A subset of these systems can be described as underactuated; the defining characteristic of underactuated mechanical systems is that they have fewer control inputs than degrees of freedom. Airplanes, rockets, helicopters, overhead crane loads, surface vessels, and underwater vehicles are all examples of such systems. The control challenges associated with these systems arise from both the underactuation of the control input and the nonlinear nature of the dynamic equations describing the system’s motion. In this work, a control method for stabilization and tracking based on Lyapunov stability theory is presented. The remarkable result of this tracking controller development is that we arrive at three matching equations that are (with the exception of ) identical to matching equations developed for stabilization as shown in White et al. (2006, 2007, 2008). Asymptotic stabilization of the tracking errors (s) is not obtained. However, the norm of s (||s||) will decrease until an ultimate bound is reached, then it will stay within this bound. A lemma is provided for estimating this bound and it is shown that the magnitude of the bound depends upon the eigenvalues and norms of certain matrices in the Lyapunov formulation. Three examples are presented to illustrate the effectiveness of the direct Lyapunov approach. Two examples of holonomic systems are presented. The first is an inverted pendulum cart which is used to illustrate the formulations performance to tracking a desired path on the cart position or actuated axis. The second example is a ball and beam system in which a desired path is tracked by the ball or unactuated axis. The tracking control technique is also applied to an example of a nonholonomic system, a rolling wheel. The control technique is applied in two alternate manners. Finally, the controller is implemented on a laboratory inverted pendulum cart system in hard real time. A desired trajectory for the cart position is tracked and the control law is used to define the desired pendulum trajectory.

Este trabalho apresenta os resultados da aplicação de três técnicas de controle utilizadas no projeto e implementação do controle de um manipulador subatuado planar de três juntas em série e de elos rígidos, projetado e construído pela Universidade Carnegie Mellon, EUA. Devido ao alto grau de não-linearidade deste sistema, seria muito difícil implementar um controlador H2, H&#8734 ou H2/H&#8734 que atuasse sozinho. Assim, propõe-se a utilização de um método de controle combinado: torque computado/H2, H&#8734 ou H2/H&#8734. No controle combinado, a porção correspondente ao torque computado lineariza e pré-compensa a dinâmica do modelo da planta nominal, enquanto a porção correspondente ao controle H2, H&#8734 ou H2/H&#8734 realiza uma pós-compensação dos erros residuais, que não foram completamente eliminados pelo método torque computado. Testes de acompanhamento de trajetória e testes de robustez são realizados aqui para comprovar a eficiência destes controladores, com resultados de implementação bastante satisfatórios. / This work presents the application results of three control techniques used for the control design and implementation of a serial planar underactuated manipulator with three joints and rigid links, designed and built by the Carnegie Mellon University, USA. Due to the high non-linearity degree of this system, it would be very difficult to implement an H2, H&#8734 or H2/ H&#8734 control which would actuate on the system by itself. Therefore, it is proposed a combined control method: computed torque/ H2, H&#8734 or H2/H&#8734. In the combined control, the portion corresponding to the computed torque linearizes and pre-compensates the dynamics of the nominal model, while the portion corresponding to the H2, H&#8734 or H2/H&#8734 control realizes a pos-compensation of the residual errors, not completely removed by the computed torque method. Trajetory tracking and robustness tests are performed here to demonstrate the efficiency of these controllers, with very satisfatory implementation results.

Este trabalho apresenta os resultados da aplicação de três técnicas de controle utilizadas no projeto e implementação do controle de um manipulador subatuado planar de três juntas em série e de elos rígidos, projetado e construído pela Universidade Carnegie Mellon, EUA. Devido ao alto grau de não-linearidade deste sistema, seria muito difícil implementar um controlador H2, H&#8734 ou H2/H&#8734 que atuasse sozinho. Assim, propõe-se a utilização de um método de controle combinado: torque computado/H2, H&#8734 ou H2/H&#8734. No controle combinado, a porção correspondente ao torque computado lineariza e pré-compensa a dinâmica do modelo da planta nominal, enquanto a porção correspondente ao controle H2, H&#8734 ou H2/H&#8734 realiza uma pós-compensação dos erros residuais, que não foram completamente eliminados pelo método torque computado. Testes de acompanhamento de trajetória e testes de robustez são realizados aqui para comprovar a eficiência destes controladores, com resultados de implementação bastante satisfatórios. / This work presents the application results of three control techniques used for the control design and implementation of a serial planar underactuated manipulator with three joints and rigid links, designed and built by the Carnegie Mellon University, USA. Due to the high non-linearity degree of this system, it would be very difficult to implement an H2, H&#8734 or H2/ H&#8734 control which would actuate on the system by itself. Therefore, it is proposed a combined control method: computed torque/ H2, H&#8734 or H2/H&#8734. In the combined control, the portion corresponding to the computed torque linearizes and pre-compensates the dynamics of the nominal model, while the portion corresponding to the H2, H&#8734 or H2/H&#8734 control realizes a pos-compensation of the residual errors, not completely removed by the computed torque method. Trajetory tracking and robustness tests are performed here to demonstrate the efficiency of these controllers, with very satisfatory implementation results.