Dynamics and Control of Nonholonomic Systems with Internal Degrees of Freedom

Nonholonomic systems model many robots as well as animals and other systems. Although such systems have been studied extensively over the last century, much work still remains to be done on their dynamics and control. Many techniques have been developed for controlling kinematic nonholonomic systems or simplified dynamic versions, however control of high dimensional, underactuated nonholonomic systems remains to be addressed. This dissertation helps fill this gap by developing a control algorithm that can be applied to systems with three or more configuration variables and just one input. We also analyze the dynamic effects of passive degrees of freedom and elastic potentials which are commonly observed in such systems showing that the addition of a passive degree of freedom can even be used to improve the locomotion characteristics of a system. Such elastic potentials can be present due to compliant mechanisms or origami, both of which can exhibit bistability and many other properties that can be useful in the design of robots

Dynamic Modeling and Control of Spherical Robots

In this work, a rigorous framework is developed for the modeling and control of spherical robotic vehicles. Motivation for this work stems from the development of Moball, which is a self-propelled sensor platform that harvests kinetic energy from local wind fields. To study Moball's dynamics, the processes of Lagrangian reduction and reconstruction are extended to robotic systems with symmetry-breaking potential energies, in order to simplify the resulting dynamic equations and expose mathematical structures that play an important role in subsequent control-theoretic tasks. These results apply to robotic systems beyond spherical robots. A formulaic procedure is introduced to derive the reduced equations of motion of most spherical robots from inspection of the Lagrangian. This adaptable procedure is applied to a diverse set of robotic systems, including multirotor aerial vehicles. Small time local controllability (STLC) results are derived for barycentric spherical robots (BSR), which are spherical vehicles whose locomotion depends on actuating the vehicle's center of mass (COM) location. STLC theorems are introduced for an arbitrary BSR on flat, sloped, or smooth terrain. I show that STLC depends on the surjectivity of a simple steering matrix. An STLC theorem is also derived for a class of commonly encountered multirotor vehicles. Feedback linearizing and PID controllers are proposed to stabilize an arbitrary spherical robot to a desired trajectory over smooth terrain, and direct collocation is used to develop a feedforward controller for Moball specifically. Moball's COM is manipulated by a novel system of magnets and solenoids, which are actuated by a "ballistic-impulse" controller that is also presented. Lastly, a motion planner is developed for energy-harvesting vehicles. This planner charts a path over smooth terrain while balancing the desire to achieve scientific objectives, avoid hazards, and the imperative of exposing the vehicle to environmental sources of energy such as local wind fields and topology. Moball's design details and experimental results establishing Moball's energy-harvesting performance (7W while rolling at a speed of 2 m/s), are contained in an Appendix.</p

Control of multiple model systems

This thesis considers the control of multiple model systems. These are systems for which only one model out of some finite set of models gives the system dynamics at any given time. In particular, the model that gives the system dynamics can change over time. This thesis covers some of the theoretical aspects of these systems, including controllability and stabilizability. As an application, ``overconstrained' mechanical systems are modeled as multiple model systems. Examples of such systems include distributed manipulation problems such as microelectromechanical systems and many wheeled vehicles such as the Sojourner vehicle of the Mars Pathfinder mission. Such systems are typified by having more Pfaffian constraints than degrees of freedom. Conventional classical motion planning and control theories do not directly apply to overconstrained systems. Control issues for two examples are specifically addressed. The first example is distributed manipulation. Distributed manipulation systems control an object's motion through contact with a high number of actuators. Stability results are shown for such systems and control schemes based on these results are implemented on a distributed manipulation test-bed. The second example is that of overconstrained vehicles, of which the Mars rover is an example. The nonlinear controllability test for multiple model systems is used to answer whether a kinematic model of the rover is or is not controllable