Multilevel Motion Planning: A Fiber Bundle Formulation

Motion planning problems involving high-dimensional state spaces can often be solved significantly faster by using multilevel abstractions. While there are various ways to formally capture multilevel abstractions, we formulate them in terms of fiber bundles, which allows us to concisely describe and derive novel algorithms in terms of bundle restrictions and bundle sections. Fiber bundles essentially describe lower-dimensional projections of the state space using local product spaces. Given such a structure and a corresponding admissible constraint function, we can develop highly efficient and optimal search-based motion planning methods for high-dimensional state spaces. Our contributions are the following: We first introduce the terminology of fiber bundles, in particular the notion of restrictions and sections. Second, we use the notion of restrictions and sections to develop novel multilevel motion planning algorithms, which we call QRRT* and QMP*. We show these algorithms to be probabilistically complete and almost-surely asymptotically optimal. Third, we develop a novel recursive path section method based on an L1 interpolation over path restrictions, which we use to quickly find feasible path sections. And fourth, we evaluate all novel algorithms against all available OMPL algorithms on benchmarks of eight challenging environments ranging from 21 to 100 degrees of freedom, including multiple robots and nonholonomic constraints. Our findings support the efficiency of our novel algorithms and the benefit of exploiting multilevel abstractions using the terminology of fiber bundles.Comment: Submitted to IJR

A Stability-Estimator to Unify Humanoid Locomotion: Walking, Stair-Climbing and Ladder-Climbing

The field of Humanoid robotics research has often struggled to find a unique niche that is not better served by other forms of robot. Unlike more traditional industrials robots with a specific purpose, a humanoid robot is not necessarily optimized for any particular task, due to the complexity and balance issues of being bipedal. However, the versatility of a humanoid robot may be ideal for applications such as search and rescue. Disaster sites with chemical, biological, or radiation contamination mean that human rescue workers may face untenable risk. Using a humanoid robot in these dangerous circumstances could make emergency response faster and save human lives. Despite the many successes of existing mobile robots in search and rescue, stair and ladder climbing remains a challenging task due to their form. To execute ladder climbing motions effectively, a humanoid robot requires a reliable estimate of stability. Traditional methods such as Zero Moment Point are not applicable to vertical climbing, and do not account for force limits imposed on end-effectors. This dissertation implements a simple contact wrench space method using a linear combination of contact wrenches. Experiments in simulation showed ZMP equivalence on flat ground. Furthermore, the estimator was able to predict stability with four point contact on a vertical ladder. Finally, an extension of the presented method is proposed based on these findings to address the limitations of the linear combination.Ph.D., Mechanical Engineering and Mechanics -- Drexel University, 201

Parameteranalyse eines redundanten Roboters mit Pivotpunkt-Restriktion

Roboter werden heutzutage nicht nur in Fertigungsstraßen eingesetzt, sondern finden auch im Bereich Medizin ihre Aufgabe. In dieser Arbeit wurde eine Analyse durchgeführt, welche sich auf einen seriellen, redundanten Roboter und seine Parameter bezieht. Die Pivotpunkt-Restriktion ergibt sich aus dem minimal-invasiven chirurgischen Szenario. Mit der Parameteranalyse wird die Roboterperformanz durch Indikatoren beurteilt, welche von den gewählten Parametern und dem Operationsgebiet abhängig sind