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Skills can often be performed in many different ways. In order to provide robots with human-like adaptation capabilities, it is of great interest to learn several ways of achieving the same skills in parallel, since eventual changes in the environment or in the robot can make some solutions unfeasible. In this case, the knowledge of multiple solutions can avoid relearning the task. This problem is addressed in this paper within the framework of Reinforcement Learning, as the automatic determination of multiple optimal parameterized policies. For this purpose, a model handling a variable number of policies is built using a Bayesian non-parametric approach. The algorithm is first compared to single policy algorithms on known benchmarks. It is then applied to a typical robotic problem presenting multiple solutions.

RESUMO A cultura da goiaba apresenta perdas em torno de 40 a 60% na pós-colheita relacionadas a problemas fitossanitários, como a antracnose causada pelo fungo Colletotrichum gloeosporioides. Pesquisas com métodos alternativos utilizando indutores de resistência têm sido bastante promissoras na busca de produtos com alto potencial no controle de patógenos em pós-colheita. Assim, o presente trabalho teve como objetivo avaliar os indutores de resistência no controle da antracnose e seus efeitos na qualidade físico-química em frutos de goiabeira ‘Paluma’. Os tratamentos utilizados foram: Agro-mós®, Ecolife®, Fosfitonova K®, Cuprogarb 500®, Rocksil® e testemunha (água destilada esterilizada). Realizou-se o teste in vitro, com discos de colônia de C. gloeosporioides (0,45 cm de diâmetro) com sete dias de cultivo e, postos em meio de cultura BDA acrescidos com os indutores. Foi determinada a porcentagem de inibição do crescimento micelial de C. gloeosporioides. O ensaio in vivo foi realizado com frutos de goiabeira variedade Paluma, desinfestados e tratados com indutores. Em seguida, discos de colônia do C. gloeosporioides foram inoculados e do primeiro ao oitavo dia após a inoculação, foram feitas avaliações do diâmetro das lesões nos frutos. As análises pós-colheita foram realizadas, avaliando a perda de massa fresca, sólidos solúveis totais (SST), acidez titulável (AT), razão SST/AT e potencial hidrogeniônico (pH). Foi utilizado o delineamento inteiramente casualizado, em esquema de parcela subdivididas 6x8 (tratamentos x período de avaliação) e as médias comparadas pelo teste de Tukey a 5% de probabilidade. Os indutores Agro-mos®, Ecolife®, Fosfitonova K®, Cuprogarb 500® e Rocksil® inibiram o crescimento micelial do C. gloeosporioides in vitro, reduziram o diâmetro das lesões e mantiveram a qualidade pós-colheita em frutos de goiabeira ‘Paluma’. ABSTRACT The culture of guava present losses around 40-60% in postharvest related to phytosanitary problems such as anthracnose caused by Colletotrichum gloeosporioides. Research on alternative methods using resistance inductors have been quite promising in the search for products with high potential in the control of pathogens in postharvest. The present study aimed to evaluate the resistance inducers in controlling anthracnose and its effects on physical and chemical quality in fruits of guava ‘Paluma’. The treatments were: Agro-mós®, Ecolife®, Fosfitonova K®, Cuprogarb 500®, Rocksil® and witness (distilled water and sterile). The in vitro test with C. gloeosporioides colony discs (0,45 cm diameter) with seven days of culture and put into PDA culture medium added with elicitors. It was determined the percentage of inhibition of mycelial growth of C. gloeosporioides. And the in vivo test was conducted with fruit variety of guava Paluma, disinfected and treated with elicitors then C. gloeosporioides colony discs were inoculated and the first to the eighth day, evaluations were made of lesions diameter in the fruit sand was also performed post-harvest analysis, assessing the loss of fresh mass, total soluble solids (TSS), titratable acidity (TA), reason TSS/TA and hydrogenic potential (pH). It was used a completely randomized design in a split plot design 6x8 (treatments x evaluation period) and the averages compared by Tukey test at 5% probability. The elicitors Agro-mos®, Ecolife®, Fosfitonova K®, Cuprogarb 500® and Rocksil® inhibited the mycelial growth of C. gloeosporioides in vitro, reduces the lesions diameter and maintained post-harvest quality fruit guava ‘Paluma’.

The Hamiltonian formulation of the theory proposed in [1, 2] is given both in the Hamilton–De Donder and in the multimomentum Hamiltonian geometrical approaches. (3 + 3) Yang–Mills gauge theories are dealt with explicitly in order to restate them in terms of Einstein–Cartan like field theories.

A gauge-independent formulation of the theory developed in J. Phys. A: Math. Gen. 36 8341 (2003) is proposed.

We construct a new geometrical framework for Yang–Mills Lagrangian field theories as an appropriate quotient space of the standard first jet-bundle and investigate the geometrical properties of the resulting mathematical setting. We deduce the field equations from a variational problem formulated through a regular Poincare–Cartan form, thus ensuring the kinematical admissibility of critical sections. We state a generalized Nother theorem and explicitly consider the case of the free Yang–Mills field.

Continuous soft robots are becoming more and more widespread in applications, due to their increased safety and flexibility in critical applications. The possibility of having soft robots that are able to change their stiffness in selected parts can help in situations where higher forces need to be applied. This paper describes a theoretical framework for learning the desired stiffness characteristics of the robot from multiple demonstrations. The framework is based on a statistical mathematical model for encoding the motion of a continuous manipulator, coupled with an optimal control strategy for learning the best impedance parameters of the manipulator.

Human-robot collaboration seeks to have humans and robots closely interacting in everyday situations. For some tasks, physical contact between the user and the robot may occur, originating significant challenges at safety, cognition, perception and control levels, among others. This paper focuses on robot motion adaptation to parameters of a collaborative task, extraction of the desired robot behavior, and variable impedance control for human-safe interaction. We propose to teach a robot cooperative behaviors from demonstrations, which are probabilistically encoded by a task-parametrized formulation of a Gaussian mixture model. Such encoding is later used for specifying both the desired state of the robot, and an optimal feedback control law that exploits the variability in position, velocity and force spaces observed during the demonstrations. The whole framework allows the robot to modify its movements as a function of parameters of the task, while showing different impedance behaviors. Tests were successfully carried out in a scenario where a 7 DOF backdrivable manipulator learns to cooperate with a human to transport an object.

We present a task-parameterized probabilistic model encoding movements in the form of virtual spring-damper systems acting in multiple frames of reference. Each candidate coordinate system observes a set of demonstrations from its own perspective, by extracting an attractor path whose variations depend on the relevance of the frame at each step of the task. This information is exploited to generate new attractor paths in new situations (new position and orientation of the frames), with the predicted covariances used to estimate the varying stiffness and damping of the spring-damper systems, resulting in a minimal intervention control strategy. The approach is tested with a 7-DOFs Barrett WAM manipulator whose movement and impedance behavior need to be modulated in regard to the position and orientation of two external objects varying during demonstration and reproduction.

A new challenge for surgical robotics is placed in the use of flexible manipulators, to perform procedures that are impossible for currently available rigid robots. Since the surgeon only controls the end-effector of the manipulator, new control strategies need to be developed to correctly move its flexible body without damaging the surrounding environment. This paper shows how a positional controller for a new surgical robot (STIFF-FLOP) can be learnt from the demonstrations given by an expert user. The proposed algorithm exploits the variability of the task to comply with the constraints only when needed, by implementing a minimal intervention principle control strategy. The results are applied to scenarios involving movements inside a constrained environment and disturbance rejection.

Robot programming by demonstration encompasses a wide range of learning strategies, from simple mimicking of the demonstrator's actions to the higher level extraction of the underlying intent. By focusing on this last form, we study the problem of extracting the reward function explaining the demonstrations from a set of candidate reward functions, and using this information for self-refinement of the skill. This definition of the problem has links with inverse reinforcement learning problems in which the robot autonomously extracts an optimal reward function that defines the goal of the task. By relying on Gaussian mixture models, the proposed approach learns how the different candidate reward functions are combined, and in which contexts or phases of the task they are relevant for explaining the user's demonstrations. The extracted reward profile is then exploited to improve the skill with a self-refinement approach based on expectation-maximization, allowing the imitator to reach a skill level that goes beyond the demonstrations. The approach can be used to reproduce a skill in different ways or to transfer tasks across robots of different structures. The proposed approach is tested in simulation with a new type of continuum robot (STIFF-FLOP), using kinesthetic demonstrations from a Barrett WAM manipulator.

In minimally invasive surgery, tools go through narrow openings and manipulate soft organs to perform surgical tasks. There are limitations in current robot-assisted surgical systems due to the rigidity of robot tools. The aim of the STIFF-FLOP European project is to develop a soft robotic arm to perform surgical tasks. The flexibility of the robot allows the surgeon to move within organs to reach remote areas inside the body and perform challenging procedures in laparoscopy. This article addresses the problem of designing learning interfaces enabling the transfer of skills from human demonstration. Robot programming by demonstration encompasses a wide range of learning strategies, from simple mimicking of the demonstrator's actions to the higher level imitation of the underlying intent extracted from the demonstrations. By focusing on this last form, we study the problem of extracting an objective function explaining the demonstrations from an over-specified set of candidate reward functions, and using this information for self-refinement of the skill. In contrast to inverse reinforcement learning strategies that attempt to explain the observations with reward functions defined for the entire task (or a set of pre-defined reward profiles active for different parts of the task), the proposed approach is based on context-dependent reward-weighted learning, where the robot can learn the relevance of candidate objective functions with respect to the current phase of the task or encountered situation. The robot then exploits this information for skills refinement in the policy parameters space. The proposed approach is tested in simulation with a cutting task performed by the STIFF-FLOP flexible robot, using kinesthetic demonstrations from a Barrett WAM manipulator.

A gauge-invariant formulation of constrained variational calculus, based on the introduction of the bundle of affine scalars over the configuration manifold, is presented. In the resulting setup, the Lagrangian is replaced by a section of a suitable principal fibre bundle over the velocity space. A geometric rephrasement of Pontryagin's maximum principle, showing the equivalence between a constrained variational problem in the state space and a canonically associated free one in a higher affine bundle, is proved., 21 pages

The paper is devoted to prove the existence of a local solution of the Hamilton-Jacobi equation in field theory, whence the general solution of the field equations can be obtained. The solution is adapted to the choice of the submanifold where the initial data of the field equations are assigned. Finally, a technique to obtain the general solution of the field equations, starting from the given initial manifold, is deduced., 16 pages

Within the geometrical framework developed in [Geometric constrained variational calculus. I: Piecewise smooth extremals, Int. J. Geom. Methods Mod. Phys. 12 (2015) 1550061], the problem of minimality for constrained calculus of variations is analyzed among the class of differentiable curves. A fully covariant representation of the second variation of the action functional, based on a suitable gauge transformation of the Lagrangian, is explicitly worked out. Both necessary and sufficient conditions for minimality are proved, and reinterpreted in terms of Jacobi fields.

A new approach leading to the formulation of the Hamilton-Jacobi equation for field theories is investigated within the framework of jet-bundles and multi-symplectic manifolds. An algorithm associating classes of solutions to given sets of boundary conditions of the field equations is provided. The paper also puts into evidence the intrinsic limits of the Hamilton-Jacobi method as an algorithm to determine families of solutions of the field equations, showing how the choice of the boundary data is often limited by compatibility conditions., 16 pages; submitted to J. Math. Phys

A geometric setup for constrained variational calculus is presented. The analysis deals with the study of the extremals of an action functional defined on piecewise differentiable curves, subject to differentiable, non-holonomic constraints. Special attention is paid to the tensorial aspects of the theory. As far as the kinematical foundations are concerned, a fully covariant scheme is developed through the introduction of the concept of infinitesimal control. The standard classification of the extremals into normal and abnormal ones is discussed, pointing out the existence of an algebraic algorithm assigning to each admissible curve a corresponding abnormality index, related to the co-rank of a suitable linear map. Attention is then shifted to the study of the first variation of the action functional. The analysis includes a revisitation of Pontryagin's equations and of the Lagrange multipliers method, as well as a reformulation of Pontryagin's algorithm in hamiltonian terms. The analysis is completed by a general result, concerning the existence of finite deformations with fixed endpoints., Comment: 30 pages. arXiv admin note: substantial text overlap with arXiv:0705.2362

The formulation of General Relativity presented in math-ph/0506077 and the Hamiltonian formulation of Gauge theories described in math-ph/0507001 are made to interact. The resulting scheme allows to see General Relativity as a constrained Gauge theory., 8 Pages, Submitted to International Journal of Geometric Methods in Modern Physics

In the gauge natural bundle framework a new space is introduced and a first-order purely frame-formulation of General Relativity is obtained., Comment: 9 Pages, Submitted to Classical and Quantum Gravity

A geometrical approach to Lagrangian and Hamiltonian non-holonomic dynamics is proposed. The construction relies on a revisitation of the Poincare–Cartan 1-form, leading to the introduction of the concepts of Lagrangian and Hamiltonian pairs and to the implementation of a non-holonomic Legendre map. The relationship with the standard 'extrinsic' approach is outlined. A unified 'canonical framework', joining both Lagrangian and Hamiltonian aspects, is proposed.

In previous reports it has been demonstrated that jugular compression causes a modification of middle ear acoustic impedance; this phenomenon has been named the jugulotympanic reflex (JTR). The aim of the present study was to contribute to the understanding of the origin of this reflex. We have analyzed the middle-ear impedance modifications induced by unilateral and bilateral jugular compression in 12 normal subjects, in 12 patients afflicted with otosclerosis, in 3 patients with Menière's disease and in 6 patients demonstrating intracranial hypertension. In the latter group, the cerebrospinal fluid (CSF) pressure was simultaneously recorded. The JTR was elicited in each normal subject and in each patient affected by Menière's disease and intracranial hypertension, while it was usually absent or modified in otosclerotic patients. The absence of the JTR in otosclerotic patients and, above all, the correspondence between CSF pressure and the middle-ear impedance modification induced by jugular compression suggest that it is due to the transmission of pressure changes from the CSF to the perilymph through the cochlear aqueduct.

The combination of imitation and exploration strategies is used in this paper to transfer sensory-motor skills to robotic platforms. The aim is to be able to learn very different tasks with good generalization capabilities and starting from a few demonstrations. This goal is achieved by learning a task-parameterized model from demonstrations where a teacher shows the task corresponding to different possible values of preassigned parameters. In this manner, new reproductions can be generated for new situations by assigning new values to the parameters, thus achieving very precise generalization capabilities. In this paper we propose a novel algorithm that is able to learn the model together with its dependence from the task-parameters, without specifying a predefined relationship or structure. The algorithm is able to learn the model starting from a few demonstrations by applying an exploration strategy that refines the learnt model autonomously. The algorithm is tested on a reaching task performed with a Barrett WAM manipulator.

Transferring skills from a biological organism to a hyper-redundant system is a challenging task, especially when the two agents have very different structure/embodiment and evolve in different environments. In this article, we propose to address this problem by designing motion primitives in the form of probabilistic dynamical systems. We take inspiration from invertebrate systems in nature to seek for versatile representations of motion/behavior primitives in continuum robots. We take the perspective that the incredibly varied skills achieved by the octopus can guide roboticists toward the design of robust motor skill encoding schemes and present our ongoing work that aims at combining statistical machine learning, dynamical systems, and stochastic optimization to study the problem of transferring movement patterns from an octopus arm to a flexible surgical robot (STIFF-FLOP) composed of two modules with constant curvatures. The approach is tested in simulation by imitation and self-refinement of an octopus reaching motion.

This paper presents a novel strategy to learn a positional controller for the body of a flexible surgical manipulator used for minimally invasive surgery. The manipulator is developed within the STIFF-FLOP European project and is targeted for a laparoscopic use in remote areas of the abdominal region that are not easily accessible by means of currently available rigid tools. While the surgeon controls the end-effector during the task, the flexible body of the manipulator needs to be displaced to enter inside constrained spaces by efficiently exploiting its flexibility, without touching vital organs and structures. The proposed algorithm exploits the instruments of machine learning within the programming by demonstrations paradigm to produce a statistical model of the natural movements of the surgeon during the task. The gathered information is then reused to determine a controller in the null space of the robot that does not interfere with the surgeon task and displaces the robot body within the available space in a fully automated manner.

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