Demand for high-performance, robust, and safe autonomous systems has grown substantially in recent years. These objectives motivate the desire for efficient safety-theoretic reasoning that can be embedded in core decision-making tasks such as motion planning, particularly in constrained environments. On one hand, Monte-Carlo (MC) and other sampling-based techniques provide accurate collision probability estimates for a wide variety of motion models but are cumbersome in the context of continuous optimization. On the other, "direct" approximations aim to compute (or upper-bound) the failure probability as a smooth function of the decision variables, and thus are convenient for optimization. However, existing direct approaches fundamentally assume discrete-time dynamics and can perform unpredictably when applied to continuous-time systems ubiquitous in the real world, often manifesting as severe conservatism. State-of-the-art attempts to address this within a conventional discrete-time framework require additional Gaussianity approximations that ultimately produce inconsistency of their own. In this paper we take a fundamentally different approach, deriving a risk approximation framework directly in continuous time and producing a lightweight estimate that actually converges as the underlying discretization is refined. Our approximation is shown to significantly outperform state-of-the-art techniques in replicating the MC estimate while maintaining the functional and computational benefits of a direct method. This enables robust, risk-aware, continuous motion-planning for a broad class of nonlinear and/or partially-observable systems.

NEW YORK, NY - APRIL 09: A working Enigma cipher machine that along with the 1942 56-page notebook ... [ ] belonging to codebreaker Alan Turing is to be auctioned Bonham's auction house on April 9, 2015 in New York City. The notebook is to be auctioned in New York on Monday. The notebook alone is expected to go for $1 million. Turing's life and work were recently brought to life in the 2014 blockbuster "The Imitation Game", which drew eight Oscar nominations. The Swiss government's Spiez Laboratory, one of whose specialisations is the study of deadly toxins and infectious diseases, is located right in the heart of Switzerland, incidentally not too far away from the Reichenbach Falls, where Sherlock Holmes vanquished Professor Moriarty (more about him later) in'The Final Problem'.

The hoax seems harmless enough. A few thousand AI researchers have claimed that computers can read and write literature. They've alleged that algorithms can unearth the secret formulas of fiction and film. That Bayesian software can map the plots of memoirs and comic books. That digital brains can pen primitive lyrics1 and short stories--wooden and weird, to be sure, yet evidence that computers are capable of more. But the hoax is not harmless. If it were possible to build a digital novelist or poetry analyst, then computers would be far more powerful than they are now. They would in fact be the most powerful beings in the history of Earth. Their power would be the power of literature, which although it seems now, in today's glittering silicon age, to be a rather unimpressive old thing, springs from the same neural root that enables human brains to create, to imagine, to dream up tomorrows.

British-born artificial intelligence (AI) expert Geoffrey Hinton has won the Turing Award, sometimes referred to as "the Nobel Prize of computing". Mr Hinton, who now lives in Canada, shares the award with Yoshua Bengio and Yann LeCun - two other proponents of deep learning, a popular form of AI. "The three of us have been the people who most believed in this approach," he told BBC News. "It's very nice to be recognised now that it is fashionable." A deep neural network uses many layers of artificial neurons, loosely mimicking the structure of animal brains. Such AI is increasingly used in products that people use every day - from smart speakers to Facebook.

Artificial intelligence is not a new concept. The underpinnings of AI have been kicked around, at times inadvertently, by an amazing series of mankind's most famous philosophers and thinkers, mathematicians and computer scientists, theoreticians and psychologists. AI has, in its own peculiar DNA, a neural network of the greatest thoughts and minds of humankind. Consider this star-runged ladder of human thought: Aristotle bestowed us logic and reason. Descartes declared "I think, therefore I am," proposing a duality of mind and body.

In his report, Von Neumann outlined the architecture of a stored-program digital computer, an ancestor of most computers in use today. But the existence of both the computer and Google can be traced to a much earlier date. It was 150 years ago that George Boole published his literary classic The Laws of Thought, wherein he devised a mathematical language for dealing with mental machinations of logic. It was a symbolic language of thought -- an algebra of logic (algebra is the branch of mathematics that uses letters and other general symbols to represent numbers and quantities in formulas and equations). In doing so, he provided the raw material needed for the design of the modern high-speed computer.