Many robotic manipulation tasks are constrained due to kinematic limitations placed on the object being manipulated. This increases the complexity of manipulation tasks that operate in high dimensions, leading to increased risk that sampling based planners are unable to find optimal solutions. Whilst trajectory optimisation methods provide guaranteed optimal solutions when implementing constraints, they only provide locally optimal solutions in sequential decision-making and struggle to provide globally optimal paths. These constraints can be incorporated into the probabilistic latent spaces by using demonstrations that satisfy the constraint function. However whenever constraints change or a manipulator must perform different tasks the network must be retrained to accommodate the new constraints. In this paper, we provide an approach that allows the training of a single learned manifold that can be augmented to determine the constraint manifold for the manipulation task. Using this manifold, the geodesic between two points can be computed using policy search to solve the cost function associated with the geodesic curve length ${\mathcal{L}_\gamma }$. We provide comparisons in terms of path length against popular path planning algorithms with different kinematic constraints, demonstrating our method’s ability to find optimal shortest paths on constraint manifolds.

Datacenter workloads demand high computational capabilities, flexibility, power efficiency, and low cost. It is challenging to improve all of these factors simultaneously. To advance datacenter capabilities beyond what commodity server designs can provide, we have designed and built a composable, reconfigurable fabric to accelerate portions of large-scale software services. Each instantiation of the fabric consists of a 6×8 2-D torus of high-end Stratix V FPGAs embedded into a half-rack of 48 machines. One FPGA is placed into each server, accessible through PCIe, and wired directly to other FPGAs with pairs of 10 Gb SAS cables. In this paper, we describe a medium-scale deployment of this fabric on a bed of 1,632 servers, and measure its efficacy in accelerating the Bing web search engine. We describe the requirements and architecture of the system, detail the critical engineering challenges and solutions needed to make the system robust in the presence of failures, and measure the performance, power, and resilience of the system when ranking candidate documents. Under high load, the largescale reconfigurable fabric improves the ranking throughput of each server by a factor of 95% for a fixed latency distribution—or, while maintaining equivalent throughput, reduces the tail latency by 29%.

Dempster’s rule is traditionally interpreted as an operator for fusing belief functions. While there are different types of belief fusion, there has been considerable confusion regarding the exact type of operation that Dempster’s rule performs. Many alternative operators for belief fusion have been proposed, where some are based on the same fundamental principle as Dempster’s rule, and others have a totally different basis, such as the cumulative and averaging fusion operators. In this article, we analyze Dempster’s rule from a statistical and frequentist perspective and compare it with cumulative and averaging belief fusion. We prove, and illustrate by examples on colored balls, that Dempster’s rule in fact represents a method for serial combination of stochastic constraints. Consequently, Dempster’s rule is not a method for cumulative fusion of belief functions under the assumption that subjective beliefs are an extension of frequentist beliefs. Having identified the true nature of Dempster’s rule, appropriate applications of Dempster’s rule of combination are described such as the multiplication of orthogonal belief functions, and the combination of preferences dictated by different parties.