Kinematics and Local Motion Planning for Quasi-static Whole-body Mobile Manipulation

This thesis studies mobile robotic manipulators, where one or more robot manipulator arms are integrated with a mobile robotic base. The base could be a wheeled or tracked vehicle, or it might be a multi-limbed locomotor. As robots are increasingly deployed in complex and unstructured environments, the need for mobile manipulation increases. Mobile robotic assistants have the potential to revolutionize human lives in a large variety of settings including home, industrial and outdoor environments.

Mobile Manipulation is the use or study of such mobile robots as they interact with physical objects in their environment. As compared to fixed base manipulators, mobile manipulators can take advantage of the base mechanism’s added degrees of freedom in the task planning and execution process. But their use also poses new problems in the analysis and control of base system stability, and the planning of coordinated base and arm motions. For mobile manipulators to be successfully and efficiently used, a thorough understanding of their kinematics, stability, and capabilities is required. Moreover, because mobile manipulators typically possess a large number of actuators, new and efficient methods to coordinate their large numbers of degrees of freedom are needed to make them practically deployable. This thesis develops new kinematic and stability analyses of mobile manipulation, and new algorithms to efficiently plan their motions.

I first develop detailed and novel descriptions of the kinematics governing the operation of multi- limbed legged robots working in the presence of gravity, and whose limbs may also be simultaneously used for manipulation. The fundamental stance constraint that arises from simple assumptions about friction and the ground contact and feasible motions is derived. Thereafter, a local relationship between joint motions and motions of the robot abdomen and reaching limbs is developed. Baseeon these relationships, one can define and analyze local kinematic qualities including limberness, wrench resistance and local dexterity. While previous researchers have noted the similarity between multi- fingered grasping and quasi-static manipulation, this thesis makes explicit connections between these two problems.

The kinematic expressions form the basis for a local motion planning problem that that determines the joint motions to achieve several simultaneous objectives while maintaining stance stability in the presence of gravity. This problem is translated into a convex quadratic program entitled the balanced priority solution, whose existence and uniqueness properties are developed. This problem is related in spirit to the classical redundancy resoxlution and task-priority approaches. With some simple modifications, this local planning and optimization problem can be extended to handle a large variety of goals and constraints that arise in mobile-manipulation. This local planning problem applies readily to other mobile bases including wheeled and articulated bases. This thesis describes the use of the local planning techniques to generate global plans, as well as for use within a feedback loop. The work in this thesis is motivated in part by many practical tasks involving the Surrogate and RoboSimian robots at NASA/JPL, and a large number of examples involving the two robots, both real and simulated, are provided.

Finally, this thesis provides an analysis of simultaneous force and motion control for multi- limbed legged robots. Starting with a classical linear stiffness relationship, an analysis of this problem for multiple point contacts is described. The local velocity planning problem is extended to include generation of forces, as well as to maintain stability using force-feedback. This thesis also provides a concise, novel definition of static stability, and proves some conditions under which it is satisfied.

Cordectomía por sustracción pedicular en la columna dorsal y lumbar en fracturas traumáticas: experiencia en el hospital universitario mayor Mederi y revisión sistemática de la literatura

Objetivo: Presentar la experiencia con la técnica de corpectomia por sustracción pedicular en fracturas traumática a nivel de la columna dorsal y Lumbar en el Hospital Universitario Mayor en Bogotá y hacer una revisión sistemática de la literatura de esta técnica quirúrgica. Material y métodos: Se realizó un análisis retrospectivo de las historias clínicas de pacientes que consultaron al servicio de neurocirugía entre los años 2013 y 2015 con fracturas traumáticas a nivel de la columna dorsal y lumbosacra. Se realizó un análisis de déficit neurológico pre y posoperatorio por medio de la Clasificación neurológica estándar de lesión medular (ASIA), al igual que tiempos de cirugía, sangrado intraoperatorio y complicaciones. A su vez se realiza una revisión sistemática de la literatura sobre esta técnica quirúrgica. Resultados: El total de pacientes que se sometieron a cirugía fue de 32, de los cuales el tiempo quirúrgico promedio fue de 396 min, se obtuvo un ASIA prequirúrgico B: 50% C: 47% y E: 3%. El ASIA post operatorio fue de B: 9% C: 47% D: 38% E: 6%. Se obtuvo una mejoría del déficit neurológico en el 75% los pacientes intervenidos. El promedio de sangrado fue de 1,223 cc. Se tuvieron 4 complicaciones, 2 hematomas en lecho quirúrgico que requirió re intervención y dos fistulas de líquido cefalorraquídeo las cuales se manejaron con vendaje compresivo y reposo absoluto. Conclusiones: La corpectomia por sustracción pedicular requiere de un adecuado entrenamiento y un grupo multidisciplinario dentro de los que se incluye neuroanestesiologo, a su vez de neurocirujanos entrenados en columna. Este abordaje presenta grandes beneficios como disminución de tiempos quirúrgicos, disminución de sangrado intraoperatorio y disminución de morbilidad entre otras.

Specific shear-dependent viscoelastic third-grade fluid model

A specific modified constitutive equation for a third-grade fluid is proposed so that the model be suitable for applications where shear-thinning or shear-thickening may occur. For that, we use the Cosserat theory approach reducing the exact three-dimensional equations to a system depending only on time and on a single spatial variable. This one-dimensional system is obtained by integrating the linear momentum equation over the cross-section of the tube, taking a velocity field approximation provided by the Cosserat theory. From this reduced system, we obtain the unsteady equations for the wall shear stress and mean pressure gradient depending on the volume flow rate, Womersley number, viscoelastic coefficient and flow index over a finite section of the tube geometry with constant circular cross-section.