Automatic Differentiation of Rigid Body Dynamics for Optimal Control and Estimation

Many algorithms for control, optimization and estimation in robotics depend on derivatives of the underlying system dynamics, e.g. to compute linearizations, sensitivities or gradient directions. However, we show that when dealing with Rigid Body Dynamics, these derivatives are difficult to derive analytically and to implement efficiently. To overcome this issue, we extend the modelling tool `RobCoGen' to be compatible with Automatic Differentiation. Additionally, we propose how to automatically obtain the derivatives and generate highly efficient source code. We highlight the flexibility and performance of the approach in two application examples. First, we show a Trajectory Optimization example for the quadrupedal robot HyQ, which employs auto-differentiation on the dynamics including a contact model. Second, we present a hardware experiment in which a 6 DoF robotic arm avoids a randomly moving obstacle in a go-to task by fast, dynamic replanning

Gastrointestinal stromal tumor (GIST) of the Treitz’s angle– a very rare cause of high bowel obstruction

Gastrointestinal stromal tumors (GIST) are somewhat rare gastrointestinal tumors - approximately 1% to 3% incidence, but they are the most common mesenchymal neoplasms of the gastrointestinal tract. GISTs are usually found in the stomach or small intestine but can occur anywhere within the gastrointestinal tract, even in extremely uncommon locations like duodeno-jejunal flexure. Only 3% – 5% of GISTs are located in the duodenum and tumors occurring in the angle of Treitz are even rarer, most published studies being case reports. These tumors have a size ranging from small lesions to large masses and can cause digestive bleeding or high bowel obstruction. This paper is a case presentation illustrating an emergency situation involving a high bowel obstruction caused by a small tumor with an unusual location in the Treitz’s angle. A large percentage of duodenal GISTs are localized in the third and fourth part of the duodenum and may not be found through standard upper endoscopy; only the barium study of the upper gastrointestinal tract highlights the obstruction point. Preoperative diagnosis is difficult but non-invasive imaging techniques like ultrasonography and computed tomography of the abdomen can be helpful. Recently, targeted therapy with inhibitors of tyrosine kinase receptors (IMATINIB) has been introduced for the management of advanced and metastatic tumors. In our opinion the surgical resection with curative intent is the treatment of choice

PennyLane: Automatic differentiation of hybrid quantum-classical computations

PennyLane is a Python 3 software framework for optimization and machine learning of quantum and hybrid quantum-classical computations. The library provides a unified architecture for near-term quantum computing devices, supporting both qubit and continuous-variable paradigms. PennyLane's core feature is the ability to compute gradients of variational quantum circuits in a way that is compatible with classical techniques such as backpropagation. PennyLane thus extends the automatic differentiation algorithms common in optimization and machine learning to include quantum and hybrid computations. A plugin system makes the framework compatible with any gate-based quantum simulator or hardware. We provide plugins for Strawberry Fields, Rigetti Forest, Qiskit, Cirq, and ProjectQ, allowing PennyLane optimizations to be run on publicly accessible quantum devices provided by Rigetti and IBM Q. On the classical front, PennyLane interfaces with accelerated machine learning libraries such as TensorFlow, PyTorch, and autograd. PennyLane can be used for the optimization of variational quantum eigensolvers, quantum approximate optimization, quantum machine learning models, and many other applications.Comment: Code available at https://github.com/XanaduAI/pennylane/ . Significant contributions to the code (new features, new plugins, etc.) will be recognized by the opportunity to be a co-author on this pape

Conjugate gradient algorithms and the Galerkin boundary element method

Original article can be found at: http://www.sciencedirect.com/science/journal/08981221 Copyright Elsevier Ltd. DOI: 10.1016/j.camwa.2004.02.002Peer reviewe

Effective computer-aided assessment of mathematics; principles, practice and results

This article outlines some key issues for writing effective computer-aided assessment (CAA) questions in subjects with substantial mathematical or statistical content, especially the importance of control of random parameters and the encoding of wrong methods of solution (mal-rules) commonly used by students. The pros and cons of using CAA and different question types are discussed. Issues surrounding the selection and encoding of mal-rules are highlighted, especially for multi-choice and responsive numerical input questions. These generate mal-rule-specific feedback, the mal-rule used being deduced 15 from the student’s selection or input. Student answer file data from the use of over 800 questions and their embedding within an overall assessment regime is analysed and presented to show that this has had a very beneficial effect on the examination performance of a large cohort of first-year economics students in their mathematics module over the last 6 years. Question analysis of over 270,000 question attempts, identifying the most 20 difficult/discriminating questions, shows that the questions are robust, valid and span an appropriate range of difficulties. The idea of underlying mal-rules is examined to see how far this explains this range