Generalized Matrix Chains (GMCs) are products of matrices where each matrix carries features (e.g., general, symmetric, triangular, positive-definite) and is optionally transposed and/or inverted. GMCs are commonly evaluated via sequences of calls to BLAS and LAPACK kernels. When matrix sizes are known, one can craft a sequence of kernel calls to evaluate a GMC that minimizes some cost, e.g., the number of floating-point operations (FLOPs). Even in these circumstances, high-level languages and libraries, upon which users usually rely, typically perform a suboptimal mapping of the input GMC onto a sequence of kernels. In this work, we go one step beyond and consider matrix sizes to be symbolic (unknown); this changes the nature of the problem since no single sequence of kernel calls is optimal for all possible combinations of matrix sizes. We design and evaluate a code generator for GMCs with symbolic sizes that relies on multi-versioning. At compile-time, when the GMC is known but the sizes are not, code is generated for a few carefully selected sequences of kernel calls. At run-time, when sizes become known, the best generated variant for the matrix sizes at hand is selected and executed. The code generator uses new theoretical results that guarantee that the cost is within a constant factor from optimal for all matrix sizes and an empirical tuning component that further tightens the gap to optimality in practice. In experiments, we found that the increase above optimal in both FLOPs and execution time of the generated code was less than 15% for 95% of the tested chains.

Expressions that involve matrices and vectors, known as linear algebra expressions, are commonly evaluated through a sequence of invocations to highly optimised kernels provided in libraries such as BLAS and LAPACK. A sequence of kernels represents an algorithm, and in general, because of associativity, algebraic identities, and multiple kernels, one expression can be evaluated via many different algorithms. These algorithms are all mathematically equivalent (i.e., in exact arithmetic, they all compute the same result), but often differ noticeably in terms of execution time. When faced with a decision, high-level languages, libraries, and tools such as Julia, Armadillo, and Linnea choose by selecting the algorithm that minimises the FLOP count. In this paper, we test the validity of the FLOP count as a discriminant for dense linear algebra algorithms, analysing ”anomalies”: problem instances for which the fastest algorithm does not perform the least number of FLOPs.

Tensor decompositions, such as CANDECOMP/PARAFAC (CP), are widely used in a variety of applications, such as chemometrics, signal processing, and machine learning. A broadly used method for computing such decompositions relies on the Alternating Least Squares (ALS) algorithm. When the number of components is small, regardless of its implementation, ALS exhibits low arithmetic intensity, which severely hinders its performance and makes GPU offloading ineffective. We observe that, in practice, experts often have to compute multiple decompositions of the same tensor, each with a small number of components (typically fewer than 20), to ultimately find the best ones to use for the application at hand. In this article, we illustrate how multiple decompositions of the same tensor can be fused together at the algorithmic level to increase the arithmetic intensity. Therefore, it becomes possible to make efficient use of GPUs for further speedups; at the same time, the technique is compatible with many enhancements typically used in ALS, such as line search, extrapolation, and non-negativity constraints. We introduce the Concurrent ALS algorithm and library, which offers an interface to MATLAB, and a mechanism to effectively deal with the issue that decompositions complete at different times. Experimental results on artificial and real datasets demonstrate a shorter time to completion due to increased arithmetic intensity.

Summary Triangular linear systems are central to the solution of general linear systems and the computation of eigenvectors. In the absence of floating‐point exceptions, substitution runs to completion and solves a system which is a small perturbation of the original system. If the matrix is well‐conditioned, then the normwise relative error is small. However, there are well‐conditioned systems for which substitution fails due to overflow. The robust solvers xLATRS from LAPACK extend the set of linear systems which can be solved by dynamically scaling the solution and the right‐hand side to avoid overflow. These solvers are sequential and apply to systems with a single right‐hand side. This paper presents algorithms which are blocked and parallel. A new task‐based parallel robust solver (Kiya) is presented and compared against both DLATRS and the non‐robust solvers DTRSV and DTRSM. When there are many right‐hand sides, Kiya performs significantly better than the robust solver DLATRS and is not significantly slower than the non‐robust solver DTRSM.

Configuration planning is a form of task planning that takes into consideration both causal and information dependencies in goal achievement. This type of planning is interesting, for instance, in smart home environments which contain various sensors and robots to provide services to the inhabitants. Requests for information, for instance from an activity recognition system, should cause the smart home to configure itself in such a way that all requested information will be provided when it is needed. This paper addresses temporal configuration planning in which information availability and goals are linked to temporal intervals which are subject to constrains. Our solutions are based on constraint-based planning which uses different types of constraints to model different types of knowledge. We propose and compare two approaches to configuration planning. The first one models information via conditions and effects of planning operators and essentially reduces configuration planning to constraint-based temporal planning. The second approach solves information dependencies separately from task planning and optimizes the cost of reaching individual information goals. We compare these approaches in terms of the time it takes to solve problems and the quality of the solutions they provide.

Planning for robots in environments co-inhabited by humans entails handling exogenous events during plan execution. Such events require plans to be continuously adapted to ensure that they remain "human-aware", i.e., adherent to human preferences and needs. We use an approach whereby human-awareness is enforced through so-called interaction constraints. Interaction constraints are used to infer context and appropriate goals online. The current plan is modified at run time so as to achieve courses of action that are continuously human-aware. The approach is evaluated in a research facility environment in which we simulate multiple days of planning and execution.

Consider a family whose home is equipped with several service robots. The actions planned for the robots must adhere to Interaction Constraints (ICs) relating them to human activities and preferences. These constraints must be sufficiently expressive to model both temporal and logical dependencies among robot actions and human behavior, and must accommodate incomplete information regarding human activities. In this paper we introduce an approach for automatically generating plans that are conformant wrt. given ICs and partially specified human activities. The approach allows to separate causal reasoning about actions from reasoning about ICs, and we illustrate the computational advantage this brings with experiments on a large-scale (semi-)realistic household domain with hundreds of human activities and several robots.

The QR algorithm is the method of choice for computing all eigenvalues of a dense nonsymmetric matrix A . After an initial reduction to Hessenberg form, a QR iteration can be viewed as chasing a small bulge from the top left to the bottom right corner along the subdiagonal of A . To increase data locality and create potential for parallelism, modern variants of the QR algorithm perform several iterations simultaneously, which amounts to chasing a chain of several bulges instead of a single bulge. To make effective use of level 3 BLAS, it is important to pack these bulges as tightly as possible within the chain. In this work, we show that the tightness of the packing in existing approaches is not optimal and can be increased. This directly translates into a reduced chain length by 33% compared to the state-of-the-art LAPACK implementation of the QR algorithm. To demonstrate the impact of our idea, we have modified the LAPACK implementation to make use of the optimal packing. Numerical experiments reveal a uniform reduction of the execution time, without affecting stability or robustness.

Early detection and adaptive support to changing individual needs related to ageing is an important challenge in today's society. In this paper we present a system called GiraffPlus that aims at addressing such a challenge and is developed in an on-going European project. The system consists of a network of home sensors that can be automatically configured to collect data for a range of monitoring services; a semi-autonomous telepresence robot; a sophisticated context recognition system that can give high-level and long term interpretations of the collected data and respond to certain events; and personalized services delivered through adaptive user interfaces for primary users. The system performs a range of services including data collection and analysis of long term trends in behaviors and physiological parameters (e.g. relating to sleep or daily activity); warnings, alarms and reminders; and social interaction through the telepresence robot. The latter is based on the Giraff telepresence robot, which is already in place in a number of homes. A distinctive aspect of the project is that the GiraffPlus system will be installed and evaluated in at least 15 homes of elderly people. This paper provides a general overview of the GiraffPlus system and its evaluation.

The combination of task and motion planning presents us with a new problem that we call geometric backtracking. This problem arises from the fact that a single symbolic state or action may be geometrically instantiated in infinitely many ways. When a symbolic action cannot be geometrically validated, we may need to backtrack in the space of geometric configurations, which greatly increases the complexity of the whole planning process. In this paper, we address this problem using intervals to represent geometric configurations, and constraint propagation techniques to shrink these intervals according to the geometric constraints of the problem. After propagation, either (i) the intervals are shrunk, thus reducing the search space in which geometric backtracking may occur, or (ii) the constraints are inconsistent, indicating the non-feasibility of the sequence of actions without further effort. We illustrate our approach on scenarios in which a two-arm robot manipulates a set of objects, and report experiments that show how the search space is reduced.

Techniques and algorithms for efficient in-place conversion to and from standard and blocked matrix storage formats are described. Such functionality is required by numerical libraries that use different data layouts internally. Parallel algorithms and a software package for in-place matrix storage format conversion based on in-place matrix transposition are presented and evaluated. A new algorithm for in-place transposition which efficiently determines the structure of the transposition permutation a priori is one of the key ingredients. It enables effective load balancing in a parallel environment.

Consider a house cleaning robot planning its activities for the day. Assume that the robot expects the human inhabitant to first dress, then have breakfast, and finally go out. Then, it should plan not to clean the bedroom while the human is dressing, and to clean the kitchen after the human has had breakfast. In general, robots operating in inhabited environments, like households and future factory floors, should plan their behavior taking into account the actions that will be performed by the humans sharing the same environment. This would improve human-robot cohabitation, for example, by avoiding undesired situations for the human. Unfortunately, current task planners only consider the robot's actions and unexpected external events in the planning process, and cannot accommodate expectations about the actions of the humans. In this article, we present a human-aware planner able to address this problem. Our planner supports alternative hypotheses of the human plan, temporal duration for the actions of both the robot and the human, constraints on the interaction between robot and human, partial goal achievement and, most importantly, the possibility to use observations of human actions in the policy generated for the robot. Our planner has been tested both as a stand-alone component and within a full framework for human-robot interaction in a real environment.

The minimal block storage Distributed Square Block Packed (DSBP) format for distributed memory computing on symmetric and triangular matrices is presented. Three algorithm variants (Basic, Static, and Dynamic) of the blocked right-looking Cholesky factorization are designed for the DSBP format, implemented, and evaluated. On our target machine, all variants outperform standard full-storage implementations while saving almost half the storage. Communication overhead is shown to be virtually eliminated by the Static and Dynamic variants, both of which take advantage of hardware parallelism to hide communication costs. The Basic variant is shown to yield comparable or slightly better performance than the full-storage ScaLAPACK routine PDPOTRF while clearly outperformed by both Static and Dynamic. Models of execution assuming zero communication costs and overhead are developed. For medium- and larger-sized problems, the Static schedule is near optimal on our target machine based on comparisons with these models and measurements of synchronization overhead.

We consider multi-robot systems where robots need to cooperate tightly by sharing functionalities with each other. There are methods for automatically configuring a multi-robot system for tight cooperation, but they only produce a single configuration. In this paper, we show how methods for automatic configuration can be integrated with methods for task planning in order to produce a complete plan were each step is a configuration. We also consider the issues of monitoring and replanning in this context, and we demonstrate our approach on a real multi-robot system, the PEIS-Ecology.

We describe a novel intelligent execution monitoring approach for mobile robots acting in indoor environments such as offices and houses. Traditionally, monitoring execution in mobile robotics amounted to looking for discrepancies between the model-based predicted state of executing an action and the real world state as computed from sensing data. We propose to employ semantic knowledge as a source of information to monitor execution. The key idea is to compute implicit expectations, from semantic domain information, that can be observed at run time by the robot to make sure actions are executed correctly. We present the semantic knowledge representation formalism, and how semantic knowledge is used in monitoring. We also describe experiments run in an indoor environment using a real mobile robot.

We consider an ecology of robots in which robots can help each other by offering information-producing functionalities. A functional configuration of this ecology is a way to allocate and connect functionalities among the participating robots. In general, different configurations can be used to solve the same task, depending on the current situation, and some tasks require sequences of different configurations to be solved. In this paper, we propose a plan-based approach to automatically generate a preferred configuration for a given task, environment, and set of resources. We also describe how our configuration planner can be integrated with an action planner to deal with tasks that require sequences of configurations. We illustrate these ideas on a specific instance of an ecology of robots, called a PEIS Ecology. We also show an experiment run on our PEIS Ecology testbed, in which a sequence of configurations for an olfactory task is automatically generated and executed.

Executing plans by mobile robots, in real world environments, faces the challenging issues of uncertainty and environment dynamics. Thus, execution monitoring is needed to verify that plan actions are executed as expected. Semantic domain-knowledge has been proposed as a source of information to derive and monitor implicit expectations of executing actions. For instance, when a robot moves into a room asserted to be an office, it would expect to see a desk and a chair. We propose to extend the semantic knowledge-based execution monitoring to take uncertainty in actions and sensing into account when verifying the expectations derived from semantic knowledge. We consider symbolic probabilistic action models, and show how semantic knowledge is used together with a probabilistic sensing model in the monitoring process of such actions. Our approach is illustrated by showing test scenarios run in an indoor environment using a mobile robot.

There is a tendency today toward the study of distributed systems consisting of many heterogeneous, networked, cooperating robotic devices. We refer to a system of this type as an ecology of robots. We call functional configuration of this ecology a way to allocate and connect functionalities among its robots. In general, the same ecology can perform different tasks by using different configuration. Moreover, the same task can often be solved using different configurations, and which is the best one depends on the available resources. This potential flexibility of a robot ecology is reduced by the fact that, in most current approaches, configurations are pre-programmed by hand. In this paper, we propose a plan-based approach to automatically generate a preferred configuration of a robot ecology given a task, environment, and set of resources. In contrast to previous approaches, the state of the ecology is automatically acquired at planning time, and it is monitored during execution in order to reconfigure if a functionality fails. We illustrate these ideas on a specific instance of an ecology of robots, called PEIS Ecology. We also show an experiment run on our PEIS Ecology testbed, in which a robot needs to reconfigure when the original configuration fails.

In the near future, autonomous mobile robots are expected to help humans by performing service tasks in many different areas, including personal assistance, transportation, cleaning, mining, or agriculture. In order to manage these tasks in a changing and partially unpredictable environment without the aid of humans, the robot must have the ability to plan its actions and to execute them robustly and safely. The robot must also have the ability to detect when the execution does not proceed as planned and to correctly identify the causes of the failure. An execution monitoring system allows the robot to detect and classify these failures. Most current approaches to execution monitoring in robotics are based on the idea of predicting the outcomes of the robot's actions by using some sort of predictive model and comparing the predicted outcomes with the observed ones. In contrary, this paper explores the use of model-free approaches to execution monitoring, that is, approaches that do not use predictive models. In this paper, we show that pattern recognition techniques can be applied to realize model-free execution monitoring by classifying observed behavioral patterns into normal or faulty execution. We investigate the use of several such techniques and verify their utility in a number of experiments involving the navigation of a mobile robot in indoor environments.

Olfaction is a challenging new sensing modality for intelligent systems. With the emergence of electronic noses it is now possible to detect and recognise a range of different odours for a variety of applications. An existing application is to use electronic olfaction on mobile robots for the purpose of odour based navigation. In this work, we introduce a new application where electronic olfaction is used in cooperation with other types of sensors on a mobile robot in order to acquire the odour property of objects. The mobility of the robot facilitates the execution of specific perceptual actions, such as moving closer to objects to acquire odour properties. Additional sensing modalities provides the spatial detection of objects and electronic olfaction then acquires the odour property which can be used for discrimination and recognition of the object being considered. We examine the problem of deciding when, how and where the e-nose should be activated by planning for active perception. We investigate the use of symbolic reasoning techniques in this context and consider the problem of integrating the information provided by the e-nose with both prior information and information from other sensors (e.g., vision). Finally, experiments are performed on a mobile robot equipped with an e-nose together with a variety of sensors that can perform decision making tasks in realistic environments.

An intelligent physical agent must incorporate motor and perceptual processes to interface with the physical world, and abstract cognitive processes to reason about the world and the options available. One crucial aspect of incorporating cognitive processes into a physically embedded reasoning system is the integration between the symbols used by the reasoning processes to denote physical objects, and the perceptual data corresponding to these objects. We treat this integration aspect by proposing a fuzzy computational theory of anchoring. Anchoring is the process of creating and maintaining the correspondence between symbols and percepts that refer to the same physical objects. Modeling this process using fuzzy set-theoretic notions enables dealing with perceptual data that can be affected by uncertainty/imprecision and imprecise/vague linguistic descriptions of objects.

In this paper we present TAL-C, a logic of action and change for worlds with action concurrency. TAL-C has a first-order semantics and proof theory. It builds on an existing logic TAL, which includes the use of dependency laws for dealing with ramification. It is demonstrated how TAL-C can represent a number of phenomena related to action concurrency: action duration, how the effects of one action interferes with or enables another action, synergistic effects of concurrent actions, conflicting and cumulative effect interactions, and resource conflicts. A central idea is that actions are not described as having effects that directly alter the world state. Instead, actions produce influences, and the way these influences alter the world state are described in specialized influence laws. Finally, we address how TAL-C narratives can be written to support modularity.