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Sökning: WFRF:(Palm Rainer)

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1.
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2.
  • Asl, Reza Mohammadi, et al. (författare)
  • Fuzzy-Based Parameter Optimization of Adaptive Unscented Kalman Filter : Methodology and Experimental Validation
  • 2020
  • Ingår i: IEEE Access. - : IEEE. - 2169-3536. ; 8, s. 54887-54904
  • Tidskriftsartikel (refereegranskat)abstract
    • This study introduces a fuzzy based optimal state estimation approach. The new method is based on two principles: Adaptive Unscented Kalman filter, and Fuzzy Adaptive Grasshopper Optimization Algorithm. The approach is designed for the optimization of an adaptive Unscented Kalman Filter. To find the optimal parameters for the filter, a fuzzy based evolutionary algorithm, named Fuzzy Adaptive Grasshopper Optimization Algorithm, is developed where its efficiency is verified by application to different benchmark functions. The proposed optimal adaptive unscented Kalman filter is applied to two nonlinear systems: a robotic manipulator, and a servo-hydraulic system. Different simulation tests are conducted to verify the performance of the filter. The results of simulations are presented and compared with a previous version of the unscented Kalman filter. For a realistic test, the proposed filter is applied on the practical servo-hydraulic system. Practical results are discussed, and presented results approve the capability of the presented method for practical applications.
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3.
  • Asl, Reza Mohammadi, et al. (författare)
  • Integral Non-Singular Terminal Sliding Mode Controller for nth-Order Nonlinear Systems
  • 2019
  • Ingår i: IEEE Access. - : Institute of Electrical and Electronics Engineers (IEEE). - 2169-3536. ; 7, s. 102792-102802
  • Tidskriftsartikel (refereegranskat)abstract
    • In this study, a new integral non-singular terminal sliding mode control method for nonlinear systems is introduced. The proposed controller is designed by defining a new sliding surface with an additional integral part. This new manifold is first introduced into the second-order system and then expanded to nth-order systems. The stability of the control system is demonstrated for both second-order and nth-order systems by using the Lyapunov stability theory. The proposed controller is applied to a robotic manipulator as a case study for second-order systems, and a servo-hydraulic system as a case study for third-order systems. The results are presented and discussed.
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4.
  • Berglund, Erik, et al. (författare)
  • Mapping between different kinematic structures without absolute positioning during operation
  • 2012
  • Ingår i: Electronics Letters. - : Institution of Engineering and Technology (IET). - 0013-5194 .- 1350-911X. ; 48:18, s. 1110-1112
  • Tidskriftsartikel (refereegranskat)abstract
    • When creating datasets for modelling of human skills based on training examples from human motion, one can encounter the problem that the kinematics of the robot does not match the human kinematics. Presented is a simple method of bypassing the explicit modelling of the human kinematics based on a variant of the self-organising map (SOM) algorithm. While the literature contains instances of SOM-type algorithms used for dimension reduction, this reported work deals with the inverse problem: dimension increase, as we are going from 4 to 5 degrees of freedom.
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5.
  • Bergsten, Pontus, 1971-, et al. (författare)
  • Fuzzy Observers
  • 2001
  • Ingår i: The 10th IEEE International Conference on Fuzzy Systems (Volym:3). - New York, USA : IEEE conference proceedings. - 078037293X ; , s. 700-703
  • Konferensbidrag (refereegranskat)abstract
    • We consider the analysis and design of three different types of nonlinear observers for dynamic Takagi-Sugeno fuzzy systems. Our approach is based on extending existing nonlinear observer schemes, namely Thau-Luenberger and sliding mode observers, to the case of interpolated multiple local affine linear models. Then linear matrix inequality based techniques are used for observer analysis and design.
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6.
  • Bergsten, Pontus, 1971-, et al. (författare)
  • Observers for Takagi-Sugeno fuzzy systems
  • 2002
  • Ingår i: IEEE transactions on systems, man and cybernetics. Part B. Cybernetics. - : IEEE Journals & Magazines. - 1083-4419 .- 1941-0492. ; 32:1, s. 114-121
  • Tidskriftsartikel (refereegranskat)abstract
    • We focus on the analysis and design of two different sliding mode observers for dynamic Takagi-Sugeno (TS) fuzzy systems. A nonlinear system of this class is composed of multiple affine local linear models that are smoothly interpolated by weighting functions resulting from a fuzzy partitioning of the state space of a given nonlinear system subject to observation. The Takagi-Sugeno fuzzy system is then an accurate approximation of the original nonlinear system. Our approach to the analysis and design of observers for Takagi-Sugeno fuzzy systems is based on extending sliding mode observer schemes to the case of interpolated multiple local affine linear models. Thus, our main contribution is nonlinear observer analysis and design methods that can effectively deal with model/plant mismatches. Furthermore, we consider the difficult case when the weighting functions in the Takagi-Sugeno fuzzy system depend on the estimated state
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7.
  • Chadalavada, Ravi Teja, 1989-, et al. (författare)
  • Accessing your navigation plans! Human-Robot Intention Transfer using Eye-Tracking Glasses
  • 2018
  • Ingår i: Advances in Manufacturing Technology XXXII. - Amsterdam, Netherlands : IOS Press. - 9781614999010 - 9781614999027 ; , s. 253-258
  • Konferensbidrag (refereegranskat)abstract
    • Robots in human co-habited environments need human-aware task and motion planning, ideally responding to people’s motion intentions as soon as they can be inferred from human cues. Eye gaze can convey information about intentions beyond trajectory and head pose of a person. Hence, we propose eye-tracking glasses as safety equipment in industrial environments shared by humans and robots. This paper investigates the possibility of human-to-robot implicit intention transference solely from eye gaze data.  We present experiments in which humans wearing eye-tracking glasses encountered a small forklift truck under various conditions. We evaluate how the observed eye gaze patterns of the participants related to their navigation decisions. Our analysis shows that people primarily gazed on that side of the robot they ultimately decided to pass by. We discuss implications of these results and relate to a control approach that uses human eye gaze for early obstacle avoidance.
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8.
  • Chadalavada, Ravi Teja, 1989-, et al. (författare)
  • Bi-directional navigation intent communication using spatial augmented reality and eye-tracking glasses for improved safety in human-robot interaction
  • 2020
  • Ingår i: Robotics and Computer-Integrated Manufacturing. - : Elsevier. - 0736-5845 .- 1879-2537. ; 61
  • Tidskriftsartikel (refereegranskat)abstract
    • Safety, legibility and efficiency are essential for autonomous mobile robots that interact with humans. A key factor in this respect is bi-directional communication of navigation intent, which we focus on in this article with a particular view on industrial logistic applications. In the direction robot-to-human, we study how a robot can communicate its navigation intent using Spatial Augmented Reality (SAR) such that humans can intuitively understand the robot's intention and feel safe in the vicinity of robots. We conducted experiments with an autonomous forklift that projects various patterns on the shared floor space to convey its navigation intentions. We analyzed trajectories and eye gaze patterns of humans while interacting with an autonomous forklift and carried out stimulated recall interviews (SRI) in order to identify desirable features for projection of robot intentions. In the direction human-to-robot, we argue that robots in human co-habited environments need human-aware task and motion planning to support safety and efficiency, ideally responding to people's motion intentions as soon as they can be inferred from human cues. Eye gaze can convey information about intentions beyond what can be inferred from the trajectory and head pose of a person. Hence, we propose eye-tracking glasses as safety equipment in industrial environments shared by humans and robots. In this work, we investigate the possibility of human-to-robot implicit intention transference solely from eye gaze data and evaluate how the observed eye gaze patterns of the participants relate to their navigation decisions. We again analyzed trajectories and eye gaze patterns of humans while interacting with an autonomous forklift for clues that could reveal direction intent. Our analysis shows that people primarily gazed on that side of the robot they ultimately decided to pass by. We discuss implications of these results and relate to a control approach that uses human gaze for early obstacle avoidance.
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9.
  • Currie, Bronwen, et al. (författare)
  • Living dangerously: implications of hydrogen sulphide events for marine life along the Namibian coast : A.G.V. Salvanes6, R. Bahlo5
  • 2008
  • Ingår i: International Symposium on Eastern Boundary Upwelling Ecosystems: Spain.
  • Konferensbidrag (populärvet., debatt m.m.)abstract
    • Hypoxia, anoxia and free hydrogen sulphide in the water column are characteristic of the inner shelf coastal upwelling system off central Namibia. Biogeochemical monitoring of the diatomaceous sediments along the central coast over a 3-year period, coupled with acoustic studies and ROV video coverage, indicated a major role played by the seafloor in the generation and control of H2S into the water column. We determined the sedimentary processes resulting in the generation and dispersal of hydrogen sulphide, and its effect on some of the locally important fishes and invertebrates.Marked interannual variability with no obvious seasonal trends was apparent in methane contents of sediments even over the short three-year period, whilst sulphate reduction rates in the sediment showed little change. The large sulphur bacteria Thiomargarita namibiensis and Beggiatoa spp. form dense mats over extensive areas of mud and oxidize sulphide at the sediment-water interface, thereby regulating its flux into the overlying water. During episodic events however, hydrogen sulphide pervades the entire water column, followed by severe hypoxia. Under experimental conditions, the survival of juvenile horse mackerel Trachurus trachurus capensis was limited to less than two hours in water containing <0.7ml.l-1 dissolved oxygen. If sulphide was also present survival time was reduced to less than 30 minutes. In contrast, pelagic gobies Sufflogobius bibarbatus survive exposure to extended periods of anoxia and water containing sulphide. Gobies are found abundantly on the muddy seafloor where they evidently possess both physiological and behavioural strategies to survive sulphide and anoxia, accounting for the success of this species in Namibian waters and its importance as a key diet species for predatory fish, seabirds and marine mammals.
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10.
  • Driankov, Dimiter, 1952-, et al. (författare)
  • A Takagi-Sugeno fuzzy gain-scheduler
  • 1996
  • Ingår i: Proceedings of the Fifth IEEE International Conference on Fuzzy Systems. - New York, USA : IEEE conference proceedings. - 0780336453 ; , s. 1053-1059
  • Konferensbidrag (refereegranskat)abstract
    • In the present paper we describe the design of a fuzzy gain scheduler for tracking a reference trajectory of a nonlinear autonomous system. The proposed fuzzy gain scheduling method has two major advantages over the existing crisp gain scheduling methods. First, it provides a general and formally motivated method for the interpolation of available local control laws into a global gain scheduling control law. Second, the method for determining the weights of the local control laws in the global gain scheduling control law is general and computationally efficient. It is shown that a fuzzy gain scheduler can be designed such that robust asymptotic stability is met. Finally, an LQR control design based method is presented
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11.
  • Driankov, Dimiter, 1952-, et al. (författare)
  • An Introduction to Fuzzy Control
  • 1996. - 2nd revised
  • Bok (refereegranskat)abstract
    • Fuzzy controllers are a class of knowledge based controllers using artificial intelligence techniques with origins in fuzzy logic. They can be found either as stand-alone control elements or as integral parts of a wide range of industrial process control systems and consumer products. Applications of fuzzy controllers are an established practice for Japanese manufacturers, and are spreading in Europe and America. The main aim of this book is to show that fuzzy control is not totally ad hoc, that there exist formal techniques for the analysis of a fuzzy controller, and that fuzzy control can be implemented even when no expert knowledge is available. The book is mainly oriented to control engineers and theorists, although parts can be read without any knowledge of control theory and may interest AI people. This 2nd, revised edition incorporates suggestions from numerous reviewers and updates and reorganizes some of the material.
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12.
  • Driankov, Dimiter, 1952-, et al. (författare)
  • Fuzzy control with fuzzy inputs: the need for new rule semantics
  • 1994
  • Ingår i: Proceedings of the Third IEEE Conference on Fuzzy Systems, 1994. IEEE World Congress on Computational Intelligence, VOLS I-III. - : IEEE conference proceedings. - 078031896X ; , s. 111-114
  • Konferensbidrag (refereegranskat)abstract
    • The standard computation taking place in a fuzzy logic controller proceeds from crisp inputs and via the consecutive steps of fuzzification, inference, and defuzzification computes a crisp control output. However, this computational practice simplifies to an extent the actual developments taking place in the closed loop. In reality, the knowledge about the current values of the controller input is very often available via sensory measurements. In this case, one has to take into account the negative side effects that come up with the use of sensors, in particular the presence of noisy measurements. In the paper the authors consider one particular way of dealing with noisy controller inputs, namely transforming the noise-distribution into a fuzzy set and then feeding back the so obtained fuzzy signal to the controller input. Adopting this approach requires that the shape of the input fuzzy signal should be reflected as much as possible in the output fuzzy signal so that important noise characteristics are preserved. In the paper the authors describe the requirements on the shape of the fuzzy output signal given a certain fuzzy input signal and show that the existing semantics for fuzzy IF-THEN rules do not satisfy these requirements. The authors propose new semantics for such rules which together with max-min composition produces the desired results.
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13.
  • Driankov, Dimiter, 1952-, et al. (författare)
  • Towards a systematic analysis of fuzzy observers
  • 1999
  • Ingår i: Proceedings of the  18th International Conference of the North American   Fuzzy Information Processing Society, 1999. NAFIPS.. - : IEEE conference proceedings. - 0780352114 ; , s. 179-183
  • Konferensbidrag (refereegranskat)abstract
    • The paper deals with the analysis of local fuzzy observers for nonlinear plants. The plant is approximated by a TS fuzzy model for which a local linear fuzzy observer is designed. This type of fuzzy observer reconstructs the non-measurable states if the parameters of the locally linearized plant are given. Matched uncertainties in the plant model can be eliminated by an additional nonlinear fuzzy sliding mode observer. Conditions are given under which the combination of the linear and the nonlinear observer lead to a reconstruction of non-measurable states                                                                                                                                                      
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14.
  • Hanson, Lars, et al. (författare)
  • Annie, a Tool for Integrating Ergonomics in the Design of Car Interiors
  • 1999
  • Ingår i: Journal of Materials & Manufacturing. ; 108:5, s. 1114-1124
  • Tidskriftsartikel (refereegranskat)abstract
    • In this ANNIE project – Applications of Neural Networks to Integrated Ergonomics – BE96-3433, a tool for integrating ergonomics into the design process is developed. This paper presents some features in the current ANNIE as applied to the design of car interiors. A variant of the ERGOMan mannequin with vision is controlled by a hybrid system for neuro-fuzzy simulation. It is trained by using an Elite system for registration of movements. An example of a trajectory generated by the system is shown. A fuzzy model is used for comfort evaluation. An experiment was performed to test its feasibility and it showed very promising results.
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15.
  • Hanson, Lars, et al. (författare)
  • ANNIE, a Tool for Integrating Ergonomics in the Design of Car Interiors
  • 2000
  • Ingår i: SAE Transactions – Journal of Materials and Manufacturing. Technical Paper 1999-01-3372. Reprinted From: Proceedings of the 1999 SAE Southern Automotive Manufacturing.. ; , s. 1-11
  • Konferensbidrag (refereegranskat)abstract
    • An example of a result from a long-term cooperation with Lund University (together with professor Roland Akselsson at the Department for Work Environment) there some of the authors (Engström) gained extensive grants (Wallenberg Stifelsen regarding equipment as well as other founding from e.g. the Swedish Work Environment Found). In this case the just mentioned EU-financing.
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16.
  • Hanson, Lars, et al. (författare)
  • ANNIE, a Tool for Integrating Ergonomics in the Design of Car Interiors
  • 1999
  • Ingår i: SAE technical paper series. - 400 Commonwealth Drive, Warrendale, PA, United States : SAE International. - 0148-7191. ; 108:5, s. 1114-1124
  • Tidskriftsartikel (refereegranskat)abstract
    • In the ANNIE project - Applications of Neural Networks to Integrated Ergonomics - BE96-3433, a tool for integrating ergonomics into the design process is developed. This paper presents some features in the current ANNIE as applied to the design of car interiors. A variant of the ERGOMan mannequin with vision is controlled by a hybrid system for neuro-fuzzy simulation. It is trained by using an Elite system for registration of movements. An example of a trajectory generated by the system is shown. A fuzzy model is used for comfort evaluation. An experiment was performed to test its feasibility and it showed very promising results.
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17.
  • Iliev, Boyko, et al. (författare)
  • Interpretation of human demonstrations using mirror neuron system principles
  • 2007
  • Ingår i: IEEE 6th international conference on development and learning, ICDL 2007. - New York : IEEE. - 9781424411160 ; , s. 128-133
  • Konferensbidrag (refereegranskat)abstract
    • In this article we suggest a framework for programming by demonstration of robotic grasping based on principles of the Mirror Neuron System (MNS) model. The approach uses a hand-state representation inspired by neurophysiological models of human grasping. We show that such a representation not only simplifies the grasp recognition but also preserves the essential part of the reaching motion associated with the grasp. We show that if the hand state trajectory of a demonstration can be reconstructed, the robot is able to replicate the grasp. This can be done using motion primitives, derived by fuzzy time-clustering from the demonstrated reach-and grasp motions. To illustrate the approach we show how human demonstrations of cylindrical grasps can be modeled, interpreted and replicated by a robot in this framework.
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18.
  • Kadmiry, Bourhane, et al. (författare)
  • Autonomous Helicopter Control Using Gradient Descent Optimization Method
  • 2001
  • Ingår i: Proceedings of the Asian Conference on Robotic &amp; Automation (ACRA).
  • Konferensbidrag (refereegranskat)abstract
    • The work reported in this paper is aimed at designing a velocityyaltitude and position controllers for the unmanned helicopter APID MK-III by Scandicraft AB in Sweden. The controllers are able of regulating high velocities via stabilization of the attitude angles within much larger ranges than currently available. We use a novel approach to the design consisting of two steps: rst, a gradient descent optimization method i s u s e d t o c ompute for each desired horizontal velocityyaltitude or position the corresponding desired values for the attitude angles and the main rotor col-lective pitch; second, a linear control scheme is used to regulate the attitude angles so that the helicopter achieves its desired horizontal velocity at the desired altitude, or its desired position. The performance of the controllers is evaluated in simulation and shows that the proposed design method achieves its intended purpose.
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19.
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20.
  • Modin, Hanna, et al. (författare)
  • Leaching test using samples from a modern, carbon-poor landfill
  • 2011
  • Ingår i: [Host publication title missing].
  • Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
    • Landfilling of organic waste is prohibited in Sweden. Modern Swedish landfills differ from landfills containing municipal solid waste rich in organic matter. As a first step to understanding long-term leaching from modern landfills, a leaching test was performed. The leaching of heavy metals was small compared to the total contents. At a liquid to solid ratio of 10 more than 99 % of most heavy metals remained in the waste. The degradation potential measured as respiration during four days was below 1 mg O2•g-1 dry waste and it decreased during the leaching. Due to the low degradability of this waste it does not seem motivated to keep the landfill moist to enhance degradation during the active phase. The contaminants of concern in a modern landfill are largely non-degradable, e.g. heavy metals, and they must be disposed of somewhere once removed from the leachate. A reasonable management option, therefore, could be to keep the landfill as dry as possible in an attempt to keep the metals in the landfill for as long time as possible.
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21.
  • Palm, Rainer, et al. (författare)
  • Crossing-Point Estimation in Human-Robot Navigation-Statistical Linearization versus Sigma-Point Transformation
  • 2024
  • Ingår i: Sensors. - : MDPI. - 1424-8220. ; 24:11
  • Tidskriftsartikel (refereegranskat)abstract
    • Interactions between mobile robots and human operators in common areas require a high level of safety, especially in terms of trajectory planning, obstacle avoidance and mutual cooperation. In this connection, the crossings of planned trajectories and their uncertainty based on model fluctuations, system noise and sensor noise play an outstanding role. This paper discusses the calculation of the expected areas of interactions during human-robot navigation with respect to fuzzy and noisy information. The expected crossing points of the possible trajectories are nonlinearly associated with the positions and orientations of the robots and humans. The nonlinear transformation of a noisy system input, such as the directions of the motion of humans and robots, to a system output, the expected area of intersection of their trajectories, is performed by two methods: statistical linearization and the sigma-point transformation. For both approaches, fuzzy approximations are presented and the inverse problem is discussed where the input distribution parameters are computed from the given output distribution parameters.
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22.
  • Palm, Rainer, 1942-, et al. (författare)
  • Fluid mechanics for path planning and obstacle avoidance of mobile robots
  • 2014
  • Ingår i: ICINCO 2014 proceedings of the 11th International Conference on Informatics in Control Automation and Robotics. - : SciTePress. - 9789897580406 ; , s. 231-238
  • Konferensbidrag (refereegranskat)abstract
    • Obstacle avoidance is an important issue for off-line path planning and on-line reaction to unforeseen appearance of obstacles during motion of a non-holonomic mobile robot along apredefined trajectory. Possible trajectories for obstacle avoidance are modeled by the velocity potential using a uniform flow plus a doublet representing a cylindrical obstacle. In the case of an appearance of an obstacle in the sensor cone of the robot a set of streamlines is computed from which a streamline is selected that guarantees a smooth transition from/to the planned trajectory. To avoid collisions with other robots a combination of velocity potential and force potential and/or the change of streamlines during operation (lane hopping) are discussed.
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23.
  • Palm, Rainer, 1942-, et al. (författare)
  • Fuzzy Geometric Approach to Collision Estimation Under Gaussian Noise in Human-Robot Interaction
  • 2021
  • Ingår i: Computational Intelligence. - Cham : Springer. - 9783030705930 - 9783030705947 - 9783030705961 ; , s. 191-221
  • Bokkapitel (refereegranskat)abstract
    • Humans and mobile robots while sharing the same work areas require a high level of safety especially at possible intersections of trajectories. An issue of the human-robot navigation is the computation of the intersection point in the presence of noisy measurements or fuzzy information. For Gaussian distributions of positions/orientations (inputs) of robot and human agent and their parameters the corresponding parameters at the intersections (outputs) are computed by analytical and fuzzy methods.This is done both for the static and the dynamic case using Kalman filters for robot/human positions and orientations and thus for the estimation of the intersection positions. For the overdetermined case (6 inputs, 2 outputs) a so-called ’energetic’ approach is used for the estimation of the point of intersection. The inverse task is discussed, specifying the parameters of the output distributions and looking for the parameters of the input distributions. For larger standard deviations (stds) mixed Gaussian models are suggested as approximation of non-Gaussian distributions.
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24.
  • Palm, Rainer, 1942-, et al. (författare)
  • Fuzzy logic and control in Human-Robot Systems : geometrical and kinematic considerations
  • 2018
  • Ingår i: WCCI 2018. - : IEEE. - 9781509060207 ; , s. 827-834
  • Konferensbidrag (refereegranskat)abstract
    • The interaction between humans and mobile robots in shared areas requires adequate control for both humans and robots.The online path planning of the robot depending on the estimated or intended movement of the person is crucial for the obstacle avoidance and close cooperation between them. The velocity obstacles method and its fuzzification optimizes the relationship between the velocities of a robot and a human agent during the interaction. In order to find the estimated intersection between robot and human in the case of positions/orientations disturbed by noise, analytical and fuzzified versions are presented. The orientation of a person is estimated by eye tracking, with the help of which the intersection area is calculated. Eye tracking leads to clusters of fixations that are condensed into cluster centers by fuzzy-time clustering to detect the intention and attention of humans.
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25.
  • Palm, Rainer, 1942-, et al. (författare)
  • Fuzzy Modeling and Control for Intention Recognition in Human-Robot Systems
  • 2016
  • Ingår i: Proceedings of the 8th International Joint Conference on Computational Intelligence (IJCCI 2016). - Setúbal, Portugal : SciTePress. - 9789897582011 ; , s. 67-74
  • Konferensbidrag (refereegranskat)abstract
    • The recognition of human intentions from trajectories in the framework of human-robot interaction is a challenging field of research. In this paper some control problems of the human-robot interaction and their intentions to compete or cooperate in shared work spaces are addressed and the time schedule of the information flow is discussed. The expected human movements relative to the robot are summarized in a so-called "compass dial" from which fuzzy control rules for the robot's reactions are derived. To avoid collisions between robot and human very early the computation of collision times at predicted human-robot intersections is discussed and a switching controller for collision avoidance is proposed. In the context of the recognition of human intentions to move to certain goals, pedestrian tracks are modeled by fuzzy clustering, lanes preferred by human agents are identified, and the identification of degrees of membership of a pedestrian track to specific lanes are discussed. Computations based on simulated and experimental data show the applicability of the methods presented.
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26.
  • Palm, Rainer, 1942-, et al. (författare)
  • Fuzzy Modeling, Control and Prediction in Human-Robot Systems
  • 2019
  • Ingår i: Computational Intelligence. - Switzerland : Springer Publishing Company. - 9783319992822 - 9783319992839 ; , s. 149-177
  • Bokkapitel (refereegranskat)abstract
    • A safe and synchronized interaction between human agents and robots in shared areas requires both long distance prediction of their motions and an appropriate control policy for short distance reaction. In this connection recognition of mutual intentions in the prediction phase is crucial to improve the performance of short distance control.We suggest an approach for short distance control inwhich the expected human movements relative to the robot are being summarized in a so-called “compass dial” from which fuzzy control rules for the robot’s reactions are derived. To predict possible collisions between robot and human at the earliest possible time, the travel times to predicted human-robot intersections are calculated and fed into a hybrid controller for collision avoidance. By applying the method of velocity obstacles, the relation between a change in robot’s motion direction and its velocity during an interaction is optimized and a combination with fuzzy expert rules is used for a safe obstacle avoidance. For a prediction of human intentions to move to certain goals pedestrian tracks are modeled by fuzzy clustering, and trajectories of human and robot agents are extrapolated to avoid collisions at intersections. Examples with both simulated and real data show the applicability of the presented methods and the high performance of the results.
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27.
  • Palm, Rainer, 1942-, et al. (författare)
  • Fuzzy switched hybrid systems : modeling and identification
  • 1998
  • Ingår i: Proceedings of the 1998 IEEE Intelligent Control (ISIC)/CIRA/ISAS Joint Conference, Gaithersburg, MD, September 14-17, 1998. - : IEEE conference proceedings. - 0780344235 ; , s. 130-135
  • Konferensbidrag (refereegranskat)abstract
    • The combination of hybrid systems and fuzzy multiple model systems is described. Further, a hierarchical identification of the resulting fuzzy switched hybrid system is outlined. The behavior of the discrete component is identified by black box fuzzy clustering and subsequent parameter identification taking into account some prior-knowledge about the discrete states. The identification of the continuous models for each discrete state is done based on local linear fuzzy models
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28.
  • Palm, Rainer, 1942-, et al. (författare)
  • Gaussian Noise and the Intersection Problem in Human-Robot Systems : Analytical and Fuzzy Approach
  • 2019
  • Ingår i: 2019 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE). - : IEEE. - 9781538617298 ; , s. 1-6
  • Konferensbidrag (refereegranskat)abstract
    • In this paper the intersection problem in humanrobot systems with respect to noisy information is discussed. The interaction between humans and mobile robots in shared areas requires a high level of safety especially at the intersections of trajectories. We discuss the intersection problem with respect to noisy information on the basis of an analytic geometrical model and its TS fuzzy version. The transmission of a 2-dimensional Gaussian noise signal, in particular information on human and robot orientations, through a non-linear static system and its fuzzy version, will be described. We discuss the problem: Given the parameters of the input distributions, find the parameters of the output distributions.
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29.
  • Palm, Rainer, et al. (författare)
  • Grasp recognition by fuzzy modeling and hidden Markov models
  • 2010
  • Ingår i: Robot intelligence. - New York : Springer. - 9781849963282 ; , s. 25-47
  • Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
    • Grasp recognition is a major part of the approach for Programming-by-Demonstration (PbD) for five-fingered robotic hands. This chapter describes three different methods for grasp recognition for a human hand. A human operator wearing a data glove instructs the robot to perform different grasps. For a number of human grasps the finger joint angle trajectories are recorded and modeled by fuzzy clustering and Takagi-Sugeno modeling. This leads to grasp models using time as input parameter and joint angles as outputs. Given a test grasp by the human operator the robot classifies and recognizes the grasp and generates the corresponding robot grasp. Three methods for grasp recognition are compared with each other. In the first method, the test grasp is compared with model grasps using the difference between the model outputs. The second method deals with qualitative fuzzy models which used for recognition and classification. The third method is based on Hidden-Markov-Models (HMM) which are commonly used in robot learning.
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30.
  • Palm, Rainer, et al. (författare)
  • Improving the global performance of a fuzzy gain-scheduler by supervision
  • 1999
  • Ingår i: Engineering Applications of Artificial Intelligence. - : Elsevier. - 0952-1976. ; 12:3, s. 297-307
  • Tidskriftsartikel (refereegranskat)abstract
    • The fundamental issue in gain scheduling along a desired reference trajectory is the question of guaranteed stability of the overall gain-scheduled closed-loop system. Since the gain-scheduled design is based on linear-time-invariant approximation of the open-loop system, and since this system is actually nonlinear, the design guarantees only local stability. This requires a further restriction, namely that the desired reference trajectory should vary slowly. The design of a fuzzy gain scheduler requires a conventional model of the nonlinear system under control and a partition of the state space into a ®nite number of fuzzy regions. The nonlinear system is Lyapunov-linearized at the center of each fuzzy region. Then linear controllers intended to locally stabilize the linearized system, and consequently the original nonlinear system, at the center of a fuzzy region are designed. In that way, gain-scheduling control of the original nonlinear system can be designed to cope with any (unknown in advance) slowly time-varying desired trajectory. This paper shows how the stability and robustness analysis of the gainscheduled closed-loop sysem in terms of sliding-mode control techniques can be used for the design of a supervisory system which avoids unstable behavior outside the region in which local stability is guaranteed.
  •  
31.
  • Palm, Rainer, 1942-, et al. (författare)
  • Learning and adaptation of robot skills using fuzzy models
  • 2010
  • Ingår i: 2010 IEEE International Conference on Fuzzy Systems (FUZZ). - : IEEE conference proceedings. - 9781424469192 ; , s. 1-8
  • Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
    • Robot skills can be taught and recognized by a Programming-by-Demonstration technique where first a human operator demonstrates a set of reference skills. The operator's motions are then recorded by a data-capturing system and modeled via fuzzy clustering and a Takagi-Sugeno modeling technique. The resulting skill models use the time as input and the operator's actions as outputs. During the recognition phase, the robot recognizes which skill has been used by the operator in a novel demonstration. This is done by comparison between the time clusters of the test skill and those of the reference skills. Finally, the robot executes the recognized skill by using the corresponding reference skill model. Drastic differences between learned and real world conditions which occur during the execution of skills by the robot are eliminated by using the Broyden update formula for Jacobians. This method was extended for fuzzy models especially for time cluster models. After the online training of a skill model the updated model is used for further executions of the same skill by the robot.
  •  
32.
  • Palm, Rainer, 1942-, et al. (författare)
  • Long distance prediction and short distance control in Human-Robot Systems
  • 2017
  • Ingår i: 2017 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE). - : Institute of Electrical and Electronics Engineers (IEEE). - 9781509060344 - 9781509060351 - 9781509060337
  • Konferensbidrag (refereegranskat)abstract
    • The study of the interaction between autonomous robots and human agents in common working areas is an emerging field of research. Main points thereby are human safety, system stability, performance and optimality of the whole interaction process. Two approaches to deal with human-robot interaction can be distinguished: Long distance prediction which requires the recognition of intentions of other agents, and short distance control which deals with actions and reactions between agents and mutual reactive control of their motions and behaviors. In this context obstacle avoidance plays a prominent role. In this paper long distance prediction is represented by the identification of human intentions to use specific lanes by using fuzzy time clustering of pedestrian tracks. Another issue is the extrapolation of parts of both human and robot trajectories in the presence of scattered/uncertain measurements to guarantee a collision-free robot motion. Short distance control is represented by obstacle avoidance between agents using the method of velocity obstacles and both analytical and fuzzy control methods.
  •  
33.
  • Palm, Rainer, et al. (författare)
  • Market-based algorithms and fuzzy methods for the navigation of mobile robots
  • 2012
  • Konferensbidrag (refereegranskat)abstract
    • An important aspect of the navigation of mobile robots is the avoidance of static and dynamic obstacles. This paper deals with obstacle avoidance using artificial potential fields and selected traffic rules. The potential field method is optimized by a mixture of fuzzy methods and market-based optimization (MBO) between competing potential fields of mobile robots. Here, depending on the local situation, some potential fields are strengthened and some are weakened. The optimization takes place especially when several mobile robots act in a small area. In addition, to avoid an undesired behavior of the mobile platform in the vicinity of obstacles, central symmetrical potential fields are `deformed' by using fuzzy rules.
  •  
34.
  • Palm, Rainer, et al. (författare)
  • Model Based Fuzzy Control Fuzzy Gain Schedulers and Sliding Mode Fuzzy Controllers : Fuzzy Gain Schedulers and Sliding Mode Fuzzy Controllers
  • 1997
  • Bok (refereegranskat)abstract
    • Model Based Fuzzy Control uses a given conventional or fuzzy open loop model of the plant under control to derive the set of fuzzy rules for the fuzzy controller. Of central interest are the stability, performance, and robustness of the resulting closed loop system. The major objective of model based fuzzy control is to use the full range of linear and nonlinear design and analysis methods to design such fuzzy controllers with better stability, performance, and robustness properties than non-fuzzy controllers designed using the same techniques. This objective has already been achieved for fuzzy sliding mode controllers and fuzzy gain schedulers - the main topics of this book. The primary aim of the book is to serve as a guide for the practitioner and to provide introductory material for courses in control theory.
  •  
35.
  • Palm, Rainer, 1942- (författare)
  • Multiple-step-ahead prediction in control systems with Gaussian process models and TS-fuzzy models
  • 2007
  • Ingår i: Engineering applications of artificial intelligence. - : Elsevier BV. - 0952-1976 .- 1873-6769. ; 20:8, s. 1023-1035
  • Tidskriftsartikel (refereegranskat)abstract
    • In this paper one-step-ahead and multiple-step-ahead predictions of time series in disturbed open loop and closed loop systems using Gaussian process models and TS-fuzzy models are described. Gaussian process models are based on the Bayesian framework where the conditional distribution of output measurements is used for the prediction of the system outputs. For one-step-ahead prediction a local process model with a small past horizon is built online with the help of Gaussian processes. Multiple-step-ahead prediction requires the knowledge of previous outputs and control values as well as the future control values. A "naive" multiple-step-ahead prediction is a successive one-step-ahead prediction where the outputs in each consecutive step are used as inputs for the next step of prediction. A global TS-fuzzy model is built to generate the nominal future control trajectory for multiple-step-ahead prediction. In the presence of model uncertainties a correction of the so computed control trajectory is needed. This is done by an internal feedback between the two process models. The method is tested on disturbed time invariant and time variant systems for different past horizons. The combination of the TS-fuzzy model and the Gaussian process model together with a correction of the control trajectory shows a good performance of the multiple-step-ahead prediction for systems with uncertainties. © 2007 Elsevier Ltd. All rights reserved.
  •  
36.
  • Palm, Rainer, 1942-, et al. (författare)
  • Navigation in Human-Robot and Robot-Robot Interaction using Optimization Methods
  • 2016
  • Ingår i: SMC 2016. - : IEEE. - 9781509018970 ; , s. 4489-4494
  • Konferensbidrag (refereegranskat)abstract
    • Human-robot interaction and robot-robot interaction and cooperation in shared spatial areas is a challenging field of research regarding safety, stability and performance. In this paper the collision avoidance between human and robot by extrapolation of human intentions and a suitable optimization of tracking velocities is discussed. Furthermore for robot-robot interactions in a shared area traffic rules and artificial force potential fields and their optimization by market-based approach are applied for obstacle avoidance. For testing and verification, the navigation strategy is implemented and tested in simulation of more realistic vehicles. Extensive simulation experiments are performed to examine the improvement of the traditional potential field (PF) method by the MBO strategy.
  •  
37.
  • Palm, Rainer, et al. (författare)
  • Navigation of mobile robots by potential field methods and market-based optimization
  • 2011
  • Ingår i: Proceedings of the 5th European Conference on Mobile Robots ECMR 2011. ; , s. 207-212
  • Konferensbidrag (refereegranskat)abstract
    • Mobile robots play an increasing role in everyday life, be it for industrial purposes, military missions, or for health care and for the support of handicapped people. A prominent aspect is the multi-robot planning, and autonomous navigation of a team of mobile robots, especially the avoidance of static and dynamic obstacles. The present paper deals with obstacle avoidance using artificial potential fields and selected traffic rules. As a novelty, the potential field method is enhanced by a decentralized market-based optimization (MBO) between competing potential fields of mobile robots. Some potential fields are strengthened and others are weakened depending on the local situation. In addition to that, circular potential fields are ’deformed’ by using fuzzy rules to avoid an undesired behavior of a robot in the vicinity of obstacles.
  •  
38.
  • Palm, Rainer, et al. (författare)
  • Particle swarm against market-based optimisation for obstacle avoidance
  • 2013
  • Ingår i: Electronics Letters. - : Institution of Engineering and Technology (IET). - 0013-5194 .- 1350-911X. ; 49:22, s. 1378-1379
  • Tidskriftsartikel (refereegranskat)abstract
    • A comparison of particle swarm optimisation (PSO) and market-based optimisation (MBO) is presented when applied to obstacle avoidance by mobile robots using artificial potential fields and special traffic rules. Most notably, PSO and MBO are applied to optimise the motion of mobile robots when acting in a common confined workspace. Simulation results show that both methods perform equally well with slight advantage for PSO.
  •  
39.
  • Palm, Rainer, et al. (författare)
  • Particle swarm optimization of potential fields for obstacle avoidance
  • 2013
  • Ingår i: Scientific cooperations Intern. Conf. in Electrical and Electronics Engineering. ; , s. 117-123
  • Konferensbidrag (refereegranskat)abstract
    • This paper addresses the safe navigation of multiple nonholonomic mobile robots in shared areas. Obstacle avoidance for mobile robots is performed by artificial potential fields and special traffic rules. In addition, the behavior of mobile robots is optimized by particle swarm optimization (PSO). The control of non-holonomic vehicles is performed using the virtual leader principle together with a local linear controller.
  •  
40.
  • Palm, Rainer, 1942-, et al. (författare)
  • Programming-by-Demonstration and Adaptation of Robot Skills by Fuzzy Time Modeling
  • 2014
  • Ingår i: International Journal of Humanoid Robotics. - Singapore : World Scientific. - 0219-8436 .- 1793-6942. ; 11:1
  • Tidskriftsartikel (refereegranskat)abstract
    • Robot skills are motion or grasping primitives from which a complicated robot task consists. Skills can be directly learned and recognized by a technique named programming-bydemonstration. A human operator demonstrates a set of reference skills where his motions are recorded by a data-capturing system and modeled via fuzzy clustering and a Takagi–Sugeno modeling technique. The skill models use time instants as input and operator actions as outputs. In the recognition phase, the robot identi¯es the skill shown by the operator in a novel test demonstration. Finally, using the corresponding reference skill model the robot executes the recognized skill. Skill models can be updated online where drastic di®erences between learned and real world conditions are eliminated using the Broyden update formula. This method was extended for fuzzy models especially for time cluster models.
  •  
41.
  • Palm, Rainer, et al. (författare)
  • Programming-by-Demonstration of Robot Skills using Fuzzy-Time-Modeling
  • 2010
  • Ingår i: IEEE International Conference on Systems, Man and Cybernetics (SMC 2010). - New York, USA : IEEE. - 9781424465880
  • Konferensbidrag (refereegranskat)abstract
    • Robot skills are motion or grasping primitives from which a complicated robot task consists. Skills can be directly learned and recognized by a technique named Programming-by-Demonstration. A human operator demonstrates a set of reference skills where his motions are recorded by a data-capturing system and modeled via fuzzy clustering and a Takagi-Sugeno modeling technique. The skill models use the time instants as input and the actions of the operator as outputs. In the recognition phase, the robot identifies the skill that has been shown by the operator in a novel test demonstration. The recognition is done by comparing of the time clusters of the test skill and the reference skills. Finally, using the corresponding reference skill model the robot executes the recognized skill. Skill models can be updated on-line where drastic differences between learned and real world conditions during the execution of skills by the robot are eliminated using the Broyden update formula. This method was extended for fuzzy models especially for time cluster models. The updated model is used for further executions of the same skill by the robot.
  •  
42.
  • Palm, Rainer, et al. (författare)
  • Recognition and teaching of robot skills by fuzzy time-modeling
  • 2009
  • Ingår i: Proceedings of the Joint 2009 international fuzzy systems association world congress and 2009 European society of fuzzy logic and technology conference. - Linz, Austria : Johannes Kepler university. - 9789899507968 ; , s. 7-12
  • Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
    • Robot skills are low-level motion and/or grasping capabilities that constitute the basic building blocks from which tasks are built. Teaching and recognition of such skills can be done by Programming-by-Demonstration approach. A human operator demonstrates certain skills while his motions are recorded by a data-capturing device and modeled in our case via fuzzy clustering and Takagi-Sugeno modeling technique. The resulting skill models use the time as input and the operator's actions and reactions as outputs. Given a test skill by the human operator the robot control system recognizes the individual phases of skills and generates the type of skill shown by the operator.
  •  
43.
  • Palm, Rainer, et al. (författare)
  • Recognition of human grasps by time-clustering and fuzzy modeling
  • 2009
  • Ingår i: Robotics and Autonomous Systems. - Amsterdam : Elsevier. - 0921-8890 .- 1872-793X. ; 57:5, s. 484-495
  • Tidskriftsartikel (refereegranskat)abstract
    • In this paper we address the problem of recognition of human grasps for five-fingeredrobotic hands and industrial robots in the context of programming-by-demonstration. The robot isinstructed by a human operator wearing a data glove capturing the hand poses. For a number ofhuman grasps, the corresponding fingertip trajectories are modeled in time and space by fuzzyclustering and Takagi-Sugeno (TS) modeling. This so-called time-clustering leads to grasp modelsusing time as input parameter and fingertip positions as outputs. For a sequence of grasps thecontrol system of the robot hand identifies the grasp segments, classifies the grasps andgenerates the sequence of grasps shown before. For this purpose, each grasp is correlated with atraining sequence. By means of a hybrid fuzzy model the demonstrated grasp sequence can bereconstructed.
  •  
44.
  • Palm, Rainer, 1942-, et al. (författare)
  • Recognition of Human-Robot Motion Intentions by Trajectory Observation
  • 2016
  • Ingår i: 2016 9th International Conference on Human System Interactions, HSI 2016. - New York : Institute of Electrical and Electronics Engineers (IEEE). - 9781509017294 ; , s. 229-235
  • Konferensbidrag (refereegranskat)abstract
    • The intention of humans and autonomous robots to interact in shared spatial areas is a challenging field of research regarding human safety, system stability and performance of the system's behavior. In this paper the intention recognition between human and robot from the control point of view are addressed and the time schedule of the exchanged signals is discussed. After a description of the kinematic and geometric relations between human and robot a so-called 'compass dial' with the relative velocities is presented from which suitable fuzzy control rules are derived. The computation of the collision times at intersections and possible avoidance strategies are further discussed. Computations based on simulated and experimental data show the applicability of the methods presented.
  •  
45.
  • Palm, Rainer, et al. (författare)
  • Segmentation and recognition of human grasps for programming-by-demonstration using time-clustering and fuzzy modeling
  • 2007
  • Ingår i: IEEE international fuzzy systems conference, FUZZ-IEEE 2007. - New York : IEEE. - 1424412099 ; , s. 1-6
  • Konferensbidrag (refereegranskat)abstract
    • In this article we address the problem of programming by demonstration (PbD) of grasping tasks for a five-fingered robotic hand. The robot is instructed by a human operator wearing a data glove capturing the hand poses. For a number of human grasps, the corresponding fingertip trajectories are modeled in time and space by fuzzy clustering and Takagi-Sugeno modeling. This so-called time-clustering leads to grasp models using the time as input parameter and the fingertip positions as outputs. For a test sequence of grasps the control system of the robot hand identifies the grasp segments, classifies the grasps and generates the sequence of grasps shown before. For this purpose, each grasp is correlated with a training sequence. By means of a hybrid fuzzy model the demonstrated grasp sequence can be reconstructed.
  •  
46.
  • Palm, Rainer, 1942-, et al. (författare)
  • Uncertainty and Fuzzy Modeling in Human-Robot Navigation
  • 2019
  • Ingår i: Proceedings of the 11th International Joint Conference on Computational Intelligence. - : SciTePress. - 9789897583841 ; , s. 296-305
  • Konferensbidrag (refereegranskat)abstract
    • The interaction between humans and mobile robots in shared areas requires a high level of safety especially at the crossings of the trajectories of humans and robots. We discuss the intersection calculation and its fuzzy version in the context of human-robot navigation with respect to noise information. Based on known parameters of the Gaussian input distributions at the orientations of human and robot the parameters of the output distributions at the intersection are to be found by analytical and fuzzy calculation. Furthermore the inverse task is discussed where the parameters of the output distributions are given and the parameters of the input distributions are searched. For larger standard deviations of the orientation signals we suggest mixed Gaussian models as approximation of nonlinear distributions.
  •  
47.
  • Palm, Rainer, 1942-, et al. (författare)
  • Velocity potentials and fuzzy modeling of fluid streamlines for obstacle avoidance of mobile robots
  • 2015
  • Ingår i: 2015 IEEE International Conference on Fuzzy Systems, (FUZZ-IEEE). - : IEEE Press. - 9781467374286 ; , s. 1-8
  • Konferensbidrag (refereegranskat)abstract
    • The use of the velocity potential of an incompressible fluid is an important and elegant tool for obstacle avoidance of mobile robots. Obstacles are modeled as cylindrical objects - combinations of cylinders can also form super obstacles. Possible trajectories of a vehicle are given by a set of streamlines around the obstacle computed by the velocity potential. Because of the number of streamlines and of data points involved therein, models of sets of streamlines for different sizes of obstacles are created first using dataset models and finally fuzzy models of streamlines. Once an obstacle appears in the sensor cone of the robot the set of streamlines is computed from which that streamline is selected that guarantees a smooth transition from/to the planned trajectory. Collisions with other robots are avoided by a combination of velocity potential and force potential and/or the change of streamlines during operation (lane hopping).
  •  
48.
  • Palm, Rainer, et al. (författare)
  • Grasp recognition by time-clustering, fuzzy modeling, and Hidden Markov Models (HMM) : a comparative study
  • 2008
  • Ingår i: IEEE international conference on fuzzy systems, FUZZ-IEEE 2008. (IEEE World Congress on Computational Intelligence). - NewYork : IEEE. - 9781424418183 ; , s. 599-605
  • Konferensbidrag (refereegranskat)abstract
    • This paper deals with three different methodsfor grasp recognition for a human hand. Grasp recognitionis a major part of the approach for Programming-by-Demonstration (PbD) for five-fingered robotic hands. A humanoperator instructs the robot to perform different grasps wearinga data glove. For a number of human grasps, the finger jointangle trajectories are recorded and modeled by fuzzy clusteringand Takagi-Sugeno modeling. This leads to grasp models usingthe time as input parameter and the joint angles as outputs.Given a test grasp by the human operator the robot classifiesand recognizes the grasp and generates the corresponding robotgrasp. Three methods for grasp recognition are presented andcompared. In the first method the test grasp is comparedwith model grasps using the difference between the modeloutputs. In the second one, qualitative fuzzy models are usedfor recognition and classification. The third method is based onHidden-Markov-Models (HMM) which are commonly used inrobot learning
  •  
49.
  • Robertsson, Linn, et al. (författare)
  • Perception modeling for human-like artificial sensor systems
  • 2007
  • Ingår i: International journal of human-computer studies. - Amsterdam : Elsevier. - 1071-5819 .- 1095-9300. ; 65:5, s. 446-459
  • Tidskriftsartikel (refereegranskat)abstract
    • In this article we present an approach to the design of human-like artificial systems. It uses a perception model to describe how sensory information is processed for a particular task and to correlate human and artificial perception. Since human-like sensors share their principle of operation with natural systems, their response can be interpreted in an intuitive way. Therefore, such sensors allow for easier and more natural human–machine interaction. The approach is demonstrated in two applications. The first is an “electronic tongue”, which performs quality assessment of food and water. In the second application we describe the development of an artificial hand for dexterous manipulation. We show that human-like functionality can be achieved even if the structure of the system is not completely biologically inspired.
  •  
50.
  • Skoglund, Alexander, et al. (författare)
  • A Hand State Approach to Imitation with a Next-State-Planner for Industrial Manipulators
  • 2008
  • Ingår i: Proceedings of the 2008 International Conference on Cognitive Systems. ; , s. 130-137
  • Konferensbidrag (refereegranskat)abstract
    •   In this paper we present an approach to reproduce human demonstrations in a reach-to-grasp context. The demonstration is represented in hand state space. By using the distance to the target object as a scheduling variable, the way in which the robot approaches the object is controlled. The controller that we deploy to execute the motion is formulated as a nextstateplanner. The planner produces an action from the current state instead of planning the whole trajectory in advance which can be error prone in non-static environments. The results have a direct application in Programming-by-Demonstration. It also contributes to cognitive systems since the ability to reach-tograsp supports the development of cognitive abilities.  
  •  
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