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2020


Walking Control Based on Step Timing Adaptation
Walking Control Based on Step Timing Adaptation

Khadiv, M., Herzog, A., Moosavian, S. A. A., Righetti, L.

IEEE Transactions on Robotics, 36, pages: 629 - 643, IEEE, June 2020 (article)

Abstract
Step adjustment can improve the gait robustness of biped robots; however, the adaptation of step timing is often neglected as it gives rise to nonconvex problems when optimized over several footsteps. In this article, we argue that it is not necessary to optimize walking over several steps to ensure gait viability and show that it is sufficient to merely select the next step timing and location. Using this insight, we propose a novel walking pattern generator that optimally selects step location and timing at every control cycle. Our approach is computationally simple compared to standard approaches in the literature, yet guarantees that any viable state will remain viable in the future. We propose a swing foot adaptation strategy and integrate the pattern generator with an inverse dynamics controller that does not explicitly control the center of mass nor the foot center of pressure. This is particularly useful for biped robots with limited control authority over their foot center of pressure, such as robots with point feet or passive ankles. Extensive simulations on a humanoid robot with passive ankles demonstrate the capabilities of the approach in various walking situations, including external pushes and foot slippage, and emphasize the importance of step timing adaptation to stabilize walking.

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link (url) DOI [BibTex]

2020


link (url) DOI [BibTex]


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Visual-Inertial Mapping with Non-Linear Factor Recovery

Usenko, V., Demmel, N., Schubert, D., Stückler, J., Cremers, D.

IEEE Robotics and Automation Letters (RA-L), 5, 2020, accepted for presentation at IEEE International Conference on Robotics and Automation (ICRA) 2020, to appear, arXiv:1904.06504 (article)

Abstract
Cameras and inertial measurement units are complementary sensors for ego-motion estimation and environment mapping. Their combination makes visual-inertial odometry (VIO) systems more accurate and robust. For globally consistent mapping, however, combining visual and inertial information is not straightforward. To estimate the motion and geometry with a set of images large baselines are required. Because of that, most systems operate on keyframes that have large time intervals between each other. Inertial data on the other hand quickly degrades with the duration of the intervals and after several seconds of integration, it typically contains only little useful information. In this paper, we propose to extract relevant information for visual-inertial mapping from visual-inertial odometry using non-linear factor recovery. We reconstruct a set of non-linear factors that make an optimal approximation of the information on the trajectory accumulated by VIO. To obtain a globally consistent map we combine these factors with loop-closing constraints using bundle adjustment. The VIO factors make the roll and pitch angles of the global map observable, and improve the robustness and the accuracy of the mapping. In experiments on a public benchmark, we demonstrate superior performance of our method over the state-of-the-art approaches.

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[BibTex]

[BibTex]


Safe and Fast Tracking on a Robot Manipulator: Robust MPC and Neural Network Control
Safe and Fast Tracking on a Robot Manipulator: Robust MPC and Neural Network Control

Nubert, J., Koehler, J., Berenz, V., Allgower, F., Trimpe, S.

IEEE Robotics and Automation Letters, 2020 (article) Accepted

Abstract
Fast feedback control and safety guarantees are essential in modern robotics. We present an approach that achieves both by combining novel robust model predictive control (MPC) with function approximation via (deep) neural networks (NNs). The result is a new approach for complex tasks with nonlinear, uncertain, and constrained dynamics as are common in robotics. Specifically, we leverage recent results in MPC research to propose a new robust setpoint tracking MPC algorithm, which achieves reliable and safe tracking of a dynamic setpoint while guaranteeing stability and constraint satisfaction. The presented robust MPC scheme constitutes a one-layer approach that unifies the often separated planning and control layers, by directly computing the control command based on a reference and possibly obstacle positions. As a separate contribution, we show how the computation time of the MPC can be drastically reduced by approximating the MPC law with a NN controller. The NN is trained and validated from offline samples of the MPC, yielding statistical guarantees, and used in lieu thereof at run time. Our experiments on a state-of-the-art robot manipulator are the first to show that both the proposed robust and approximate MPC schemes scale to real-world robotic systems.

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arXiv PDF DOI [BibTex]

arXiv PDF DOI [BibTex]

2008


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Learning to control in operational space

Peters, J., Schaal, S.

International Journal of Robotics Research, 27, pages: 197-212, 2008, clmc (article)

Abstract
One of the most general frameworks for phrasing control problems for complex, redundant robots is operational space control. However, while this framework is of essential importance for robotics and well-understood from an analytical point of view, it can be prohibitively hard to achieve accurate control in face of modeling errors, which are inevitable in com- plex robots, e.g., humanoid robots. In this paper, we suggest a learning approach for opertional space control as a direct inverse model learning problem. A first important insight for this paper is that a physically cor- rect solution to the inverse problem with redundant degrees-of-freedom does exist when learning of the inverse map is performed in a suitable piecewise linear way. The second crucial component for our work is based on the insight that many operational space controllers can be understood in terms of a constrained optimal control problem. The cost function as- sociated with this optimal control problem allows us to formulate a learn- ing algorithm that automatically synthesizes a globally consistent desired resolution of redundancy while learning the operational space controller. From the machine learning point of view, this learning problem corre- sponds to a reinforcement learning problem that maximizes an immediate reward. We employ an expectation-maximization policy search algorithm in order to solve this problem. Evaluations on a three degrees of freedom robot arm are used to illustrate the suggested approach. The applica- tion to a physically realistic simulator of the anthropomorphic SARCOS Master arm demonstrates feasibility for complex high degree-of-freedom robots. We also show that the proposed method works in the setting of learning resolved motion rate control on real, physical Mitsubishi PA-10 medical robotics arm.

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link (url) DOI [BibTex]

2008


link (url) DOI [BibTex]


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Adaptation to a sub-optimal desired trajectory

M. Mistry, E. A. G. L. T. Y. S. S. M. K.

Advances in Computational Motor Control VII, Symposium at the Society for Neuroscience Meeting, Washington DC, 2008, 2008, clmc (article)

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PDF [BibTex]

PDF [BibTex]


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Operational space control: A theoretical and emprical comparison

Nakanishi, J., Cory, R., Mistry, M., Peters, J., Schaal, S.

International Journal of Robotics Research, 27(6):737-757, 2008, clmc (article)

Abstract
Dexterous manipulation with a highly redundant movement system is one of the hallmarks of hu- man motor skills. From numerous behavioral studies, there is strong evidence that humans employ compliant task space control, i.e., they focus control only on task variables while keeping redundant degrees-of-freedom as compliant as possible. This strategy is robust towards unknown disturbances and simultaneously safe for the operator and the environment. The theory of operational space con- trol in robotics aims to achieve similar performance properties. However, despite various compelling theoretical lines of research, advanced operational space control is hardly found in actual robotics imple- mentations, in particular new kinds of robots like humanoids and service robots, which would strongly profit from compliant dexterous manipulation. To analyze the pros and cons of different approaches to operational space control, this paper focuses on a theoretical and empirical evaluation of different methods that have been suggested in the literature, but also some new variants of operational space controllers. We address formulations at the velocity, acceleration and force levels. First, we formulate all controllers in a common notational framework, including quaternion-based orientation control, and discuss some of their theoretical properties. Second, we present experimental comparisons of these approaches on a seven-degree-of-freedom anthropomorphic robot arm with several benchmark tasks. As an aside, we also introduce a novel parameter estimation algorithm for rigid body dynamics, which ensures physical consistency, as this issue was crucial for our successful robot implementations. Our extensive empirical results demonstrate that one of the simplified acceleration-based approaches can be advantageous in terms of task performance, ease of parameter tuning, and general robustness and compliance in face of inevitable modeling errors.

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link (url) [BibTex]

link (url) [BibTex]


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Efficient inverse kinematics algorithms for highdimensional movement systems

Tevatia, G., Schaal, S.

CLMC Technical Report: TR-CLMC-2008-1, 2008, clmc (techreport)

Abstract
Real-time control of the endeffector of a humanoid robot in external coordinates requires computationally efficient solutions of the inverse kinematics problem. In this context, this paper investigates methods of resolved motion rate control (RMRC) that employ optimization criteria to resolve kinematic redundancies. In particular we focus on two established techniques, the pseudo inverse with explicit optimization and the extended Jacobian method. We prove that the extended Jacobian method includes pseudo-inverse methods as a special solution. In terms of computational complexity, however, pseudo-inverse and extended Jacobian differ significantly in favor of pseudo-inverse methods. Employing numerical estimation techniques, we introduce a computationally efficient version of the extended Jacobian with performance comparable to the original version. Our results are illustrated in simulation studies with a multiple degree-offreedom robot, and were evaluated on an actual 30 degree-of-freedom full-body humanoid robot.

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link (url) [BibTex]

link (url) [BibTex]


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A library for locally weighted projection regression

Klanke, S., Vijayakumar, S., Schaal, S.

Journal of Machine Learning Research, 9, pages: 623-626, 2008, clmc (article)

Abstract
In this paper we introduce an improved implementation of locally weighted projection regression (LWPR), a supervised learning algorithm that is capable of handling high-dimensional input data. As the key features, our code supports multi-threading, is available for multiple platforms, and provides wrappers for several programming languages.

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link (url) [BibTex]

link (url) [BibTex]


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Frequency analysis with coupled nonlinear oscillators

Buchli, J., Righetti, L., Ijspeert, A.

Physica D: Nonlinear Phenomena, 237(13):1705-1718, August 2008 (article)

Abstract
We present a method to obtain the frequency spectrum of a signal with a nonlinear dynamical system. The dynamical system is composed of a pool of adaptive frequency oscillators with negative mean-field coupling. For the frequency analysis, the synchronization and adaptation properties of the component oscillators are exploited. The frequency spectrum of the signal is reflected in the statistics of the intrinsic frequencies of the oscillators. The frequency analysis is completely embedded in the dynamics of the system. Thus, no pre-processing or additional parameters, such as time windows, are needed. Representative results of the numerical integration of the system are presented. It is shown, that the oscillators tune to the correct frequencies for both discrete and continuous spectra. Due to its dynamic nature the system is also capable to track non-stationary spectra. Further, we show that the system can be modeled in a probabilistic manner by means of a nonlinear Fokker–Planck equation. The probabilistic treatment is in good agreement with the numerical results, and provides a useful tool to understand the underlying mechanisms leading to convergence.

mg

link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Optimization strategies in human reinforcement learning

Hoffmann, H., Theodorou, E., Schaal, S.

Advances in Computational Motor Control VII, Symposium at the Society for Neuroscience Meeting, Washington DC, 2008, 2008, clmc (article)

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PDF [BibTex]

PDF [BibTex]

2007


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Relative Entropy Policy Search

Peters, J.

CLMC Technical Report: TR-CLMC-2007-2, Computational Learning and Motor Control Lab, Los Angeles, CA, 2007, clmc (techreport)

Abstract
This technical report describes a cute idea of how to create new policy search approaches. It directly relates to the Natural Actor-Critic methods but allows the derivation of one shot solutions. Future work may include the application to interesting problems.

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PDF link (url) [BibTex]

2007


PDF link (url) [BibTex]


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The new robotics - towards human-centered machines

Schaal, S.

HFSP Journal Frontiers of Interdisciplinary Research in the Life Sciences, 1(2):115-126, 2007, clmc (article)

Abstract
Research in robotics has moved away from its primary focus on industrial applications. The New Robotics is a vision that has been developed in past years by our own university and many other national and international research instiutions and addresses how increasingly more human-like robots can live among us and take over tasks where our current society has shortcomings. Elder care, physical therapy, child education, search and rescue, and general assistance in daily life situations are some of the examples that will benefit from the New Robotics in the near future. With these goals in mind, research for the New Robotics has to embrace a broad interdisciplinary approach, ranging from traditional mathematical issues of robotics to novel issues in psychology, neuroscience, and ethics. This paper outlines some of the important research problems that will need to be resolved to make the New Robotics a reality.

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link (url) [BibTex]

link (url) [BibTex]


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iCub - The Design and Realization of an Open Humanoid Platform for Cognitive and Neuroscience Research

Tsagarakis, N., Metta, G., Sandini, G., Vernon, D., Beira, R., Becchi, F., Righetti, L., Santos-Victor, J., Ijspeert, A., Carrozza, M., Caldwell, D.

Advanced Robotics, 21(10):1151-1175, 2007 (article)

Abstract
The development of robotic cognition and the advancement of understanding of human cognition form two of the current greatest challenges in robotics and neuroscience, respectively. The RobotCub project aims to develop an embodied robotic child (iCub) with the physical (height 90 cm and mass less than 23 kg) and ultimately cognitive abilities of a 2.5-year-old human child. The iCub will be a freely available open system which can be used by scientists in all cognate disciplines from developmental psychology to epigenetic robotics to enhance understanding of cognitive systems through the study of cognitive development. The iCub will be open both in software, but more importantly in all aspects of the hardware and mechanical design. In this paper the design of the mechanisms and structures forming the basic 'body' of the iCub are described. The papers considers kinematic structures dynamic design criteria, actuator specification and selection, and detailed mechanical and electronic design. The paper concludes with tests of the performance of sample joints, and comparison of these results with the design requirements and simulation projects.

mg

link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Learning an Outlier-Robust Kalman Filter

Ting, J., Theodorou, E., Schaal, S.

CLMC Technical Report: TR-CLMC-2007-1, Los Angeles, CA, 2007, clmc (techreport)

Abstract
We introduce a modified Kalman filter that performs robust, real-time outlier detection, without the need for manual parameter tuning by the user. Systems that rely on high quality sensory data (for instance, robotic systems) can be sensitive to data containing outliers. The standard Kalman filter is not robust to outliers, and other variations of the Kalman filter have been proposed to overcome this issue. However, these methods may require manual parameter tuning, use of heuristics or complicated parameter estimation procedures. Our Kalman filter uses a weighted least squares-like approach by introducing weights for each data sample. A data sample with a smaller weight has a weaker contribution when estimating the current time step?s state. Using an incremental variational Expectation-Maximization framework, we learn the weights and system dynamics. We evaluate our Kalman filter algorithm on data from a robotic dog.

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PDF [BibTex]

PDF [BibTex]

2004


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Discovering optimal imitation strategies

Billard, A., Epars, Y., Calinon, S., Cheng, G., Schaal, S.

Robotics and Autonomous Systems, 47(2-3):68-77, 2004, clmc (article)

Abstract
This paper develops a general policy for learning relevant features of an imitation task. We restrict our study to imitation of manipulative tasks or of gestures. The imitation process is modeled as a hierarchical optimization system, which minimizes the discrepancy between two multi-dimensional datasets. To classify across manipulation strategies, we apply a probabilistic analysis to data in Cartesian and joint spaces. We determine a general metric that optimizes the policy of task reproduction, following strategy determination. The model successfully discovers strategies in six different imitative tasks and controls task reproduction by a full body humanoid robot.

am

[BibTex]

2004


[BibTex]


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Rhythmic movement is not discrete

Schaal, S., Sternad, D., Osu, R., Kawato, M.

Nature Neuroscience, 7(10):1137-1144, 2004, clmc (article)

Abstract
Rhythmic movements, like walking, chewing, or scratching, are phylogenetically old mo-tor behaviors found in many organisms, ranging from insects to primates. In contrast, discrete movements, like reaching, grasping, or kicking, are behaviors that have reached sophistication primarily in younger species, particularly in primates. Neurophysiological and computational research on arm motor control has focused almost exclusively on dis-crete movements, essentially assuming similar neural circuitry for rhythmic tasks. In con-trast, many behavioral studies focused on rhythmic models, subsuming discrete move-ment as a special case. Here, using a human functional neuroimaging experiment, we show that in addition to areas activated in rhythmic movement, discrete movement in-volves several higher cortical planning areas, despite both movement conditions were confined to the same single wrist joint. These results provide the first neuroscientific evi-dence that rhythmic arm movement cannot be part of a more general discrete movement system, and may require separate neurophysiological and theoretical treatment.

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link (url) [BibTex]

link (url) [BibTex]


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Learning from demonstration and adaptation of biped locomotion

Nakanishi, J., Morimoto, J., Endo, G., Cheng, G., Schaal, S., Kawato, M.

Robotics and Autonomous Systems, 47(2-3):79-91, 2004, clmc (article)

Abstract
In this paper, we introduce a framework for learning biped locomotion using dynamical movement primitives based on non-linear oscillators. Our ultimate goal is to establish a design principle of a controller in order to achieve natural human-like locomotion. We suggest dynamical movement primitives as a central pattern generator (CPG) of a biped robot, an approach we have previously proposed for learning and encoding complex human movements. Demonstrated trajectories are learned through movement primitives by locally weighted regression, and the frequency of the learned trajectories is adjusted automatically by a novel frequency adaptation algorithmbased on phase resetting and entrainment of coupled oscillators. Numerical simulations and experimental implementation on a physical robot demonstrate the effectiveness of the proposed locomotioncontroller.

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link (url) [BibTex]

link (url) [BibTex]


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Feedback error learning and nonlinear adaptive control

Nakanishi, J., Schaal, S.

Neural Networks, 17(10):1453-1465, 2004, clmc (article)

Abstract
In this paper, we present our theoretical investigations of the technique of feedback error learning (FEL) from the viewpoint of adaptive control. We first discuss the relationship between FEL and nonlinear adaptive control with adaptive feedback linearization, and show that FEL can be interpreted as a form of nonlinear adaptive control. Second, we present a Lyapunov analysis suggesting that the condition of strictly positive realness (SPR) associated with the tracking error dynamics is a sufficient condition for asymptotic stability of the closed-loop dynamics. Specifically, for a class of second order SISO systems, we show that this condition reduces to KD^2 > KP; where KP and KD are positive position and velocity feedback gains, respectively. Moreover, we provide a ÔpassivityÕ-based stability analysis which suggests that SPR of the tracking error dynamics is a necessary and sufficient condition for asymptotic hyperstability. Thus, the condition KD^2>KP mentioned above is not only a sufficient but also necessary condition to guarantee asymptotic hyperstability of FEL, i.e. the tracking error is bounded and asymptotically converges to zero. As a further point, we explore the adaptive control and FEL framework for feedforward control formulations, and derive an additional sufficient condition for asymptotic stability in the sense of Lyapunov. Finally, we present numerical simulations to illustrate the stability properties of FEL obtained from our mathematical analysis.

am

link (url) [BibTex]

link (url) [BibTex]

1996


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A Kendama learning robot based on bi-directional theory

Miyamoto, H., Schaal, S., Gandolfo, F., Koike, Y., Osu, R., Nakano, E., Wada, Y., Kawato, M.

Neural Networks, 9(8):1281-1302, 1996, clmc (article)

Abstract
A general theory of movement-pattern perception based on bi-directional theory for sensory-motor integration can be used for motion capture and learning by watching in robotics. We demonstrate our methods using the game of Kendama, executed by the SARCOS Dextrous Slave Arm, which has a very similar kinematic structure to the human arm. Three ingredients have to be integrated for the successful execution of this task. The ingredients are (1) to extract via-points from a human movement trajectory using a forward-inverse relaxation model, (2) to treat via-points as a control variable while reconstructing the desired trajectory from all the via-points, and (3) to modify the via-points for successful execution. In order to test the validity of the via-point representation, we utilized a numerical model of the SARCOS arm, and examined the behavior of the system under several conditions.

am

link (url) [BibTex]

1996


link (url) [BibTex]


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One-handed juggling: A dynamical approach to a rhythmic movement task

Schaal, S., Sternad, D., Atkeson, C. G.

Journal of Motor Behavior, 28(2):165-183, 1996, clmc (article)

Abstract
The skill of rhythmic juggling a ball on a racket is investigated from the viewpoint of nonlinear dynamics. The difference equations that model the dynamical system are analyzed by means of local and non-local stability analyses. These analyses yield that the task dynamics offer an economical juggling pattern which is stable even for open-loop actuator motion. For this pattern, two types of pre dictions are extracted: (i) Stable periodic bouncing is sufficiently characterized by a negative acceleration of the racket at the moment of impact with the ball; (ii) A nonlinear scaling relation maps different juggling trajectories onto one topologically equivalent dynamical system. The relevance of these results for the human control of action was evaluated in an experiment where subjects performed a comparable task of juggling a ball on a paddle. Task manipulations involved different juggling heights and gravity conditions of the ball. The predictions were confirmed: (i) For stable rhythmic performance the paddle's acceleration at impact is negative and fluctuations of the impact acceleration follow predictions from global stability analysis; (ii) For each subject, the realizations of juggling for the different experimental conditions are related by the scaling relation. These results allow the conclusion that for the given task, humans reliably exploit the stable solutions inherent to the dynamics of the task and do not overrule these dynamics by other control mechanisms. The dynamical scaling serves as an efficient principle to generate different movement realizations from only a few parameter changes and is discussed as a dynamical formalization of the principle of motor equivalence.

am

link (url) [BibTex]

link (url) [BibTex]

1993


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Design concurrent calculation: A CAD- and data-integrated approach

Schaal, S., Ehrlenspiel, K.

Journal of Engineering Design, 4, pages: 71-85, 1993, clmc (article)

Abstract
Besides functional regards, product design demands increasingly more for further reaching considerations. Quality alone cannot suffice anymore to compete in the market; design for manufacturability, for assembly, for recycling, etc., are well-known keywords. Those can largely be reduced to the necessity of design for costs. This paper focuses on a CAD-based approach to design concurrent calculation. It will discuss how, in the meantime well-established, tools like feature technology, knowledge-based systems, and relational databases can be blended into one coherent concept to achieve an entirely CAD- and data-integrated cost information tool. This system is able to extract data from the CAD-system, combine it with data about the company specific manufacturing environment, and subsequently autonomously evaluate manufacturability aspects and costs of the given CAD-model. Within minutes the designer gets quantitative in-formation about the major cost sources of his/her design. Additionally, some alternative methods for approximating manu-facturing times from empirical data, namely neural networks and local weighted regression, are introduced.

am

[BibTex]

1993


[BibTex]