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Forschung 2019
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Forschungsbericht 2016
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A basic task in the design of an industrial robot application
is the relative placement of robot and workpiece. Process points are defined in Cartesian coordinates relative to the workpiece coordinate system, and the workpiece has to be located such that the robot can reach all points. Finding such a location is still an iterative procedure based on the developers' intuition. One difficulty is the choice of one of the several solutions of the backward transform of a typical 6R robot.
We present a novel algorithm that simultaneously optimizes the workpiece location and the robot configuration at all process points using higher order optimization algorithms. A key ingredient is the extension of the robot with a virtual prismatic axis. The practical feasibility of the approach is shown with an example using a commercial industrial robot.
A basic task in the design of an industrial robot application is the relative placement of robot and workpiece. Process points are defined in Cartesian coordinates relative to the workpiece coordinate system, and the workpiece has to be located such that the robot can reach all points. Finding such a location is still an iterative procedure based on the developers’ intuition. One difficulty is the choice of one of the several solutions of the backward transform of a typical 6R robot. We present a novel algorithm that simultaneously optimizes the workpiece location and the robot configuration at all process points using higher order optimization algorithms. A key ingredient is the extension of the robot with a virtual prismatic axis. The practical feasibility of the approach is shown with an example using a commercial industrial robot.
A basic task in the design of a robotic production cell is the relative placement of robot and workpiece. The fundamental requirement is that the robot can reach all process positions; only then one can think further optimization. Therefore an algorithm that automatically places an object into the workspace is very desirable. However many iterative optimization algorithms cannot guarantee that all intermediate steps are reachable, resulting in complicated procedures. We present a novel approach which extends a robot by a virtual prismatic joint - which measures the distance to the workspace - such that any TCP frames are reachable. This allows higher order nonlinear programming algorithms to be used for placement of an object alone as well as the optimal placement under some differentiable criterion.
Adaptive Moment Estimation (ADAM) is a very popular training algorithm for deep neural networks and belongs to the family of adaptive gradient descent optimizers. However to the best of the authors knowledge no complete convergence analysis exists for ADAM. The contribution of this paper is a method for the local convergence analysis in batch mode for a deterministic fixed training set, which gives necessary conditions for the hyperparameters of the ADAM algorithm. Due to the local nature of the arguments the objective function can be non-convex but must be at least twice continuously differentiable. Then we apply this procedure to other adaptive gradient descent algorithms and show for most of them local convergence with hyperparameter bounds.
Adaptive Moment Estimation (Adam) is a very popular training algorithm for deep neural networks, implemented in many machine learning frameworks. To the best of the authors knowledge no complete convergence analysis exists for Adam. The contribution of this paper is a method for the local convergence analysis in batch mode for a deterministic fixed training set, which gives necessary conditions for the hyperparameters of the Adam algorithm. Due to the local nature of the arguments the objective function can be non-convex but must be at least twice continuously differentiable.
The main issues in many image processing applications are
object recognition and detection of objects, which answers the questions whether an object is present and if it is present, where it is located. Popular object detection algorithms like YOLO use a regression formulation for the whole problem, especially for the bounding box parameters. In production industry the setting usually is different: One usually knows the object type and rather wants to know with high precision where the object is. We study a prototype application in this area where we identify the rotation of an object in a plane. To solve this problem use a regression approach with a CNN architecture as a function approximator. We compare our results to standard image processing algorithms, which do not use neural networks, and present quantitative results on the accuracy.
CNNs seem at least competitive to classical image processing.
One of the most popular training algorithms for deep neural networks is the Adaptive Moment Estimation (Adam) introduced by Kingma and Ba. Despite its success in many applications there is no satisfactory convergence analysis: only local convergence can be shown for batch mode under some restrictions on the hyperparameters, counterexamples exist for incremental mode. Recent results show that for simple quadratic objective functions limit cycles of period 2 exist in batch mode, but only for atypical hyperparameters, and only for the algorithm without bias correction. We extend the convergence analysis to all choices of the hyperparameters for quadratic functions. This finally answers the question of convergence for Adam in batch mode to the negative. We analyze the stability of these limit cycles and relate our analysis to other results where approximate convergence was shown, but under the additional assumption of bounded gradients which does not apply to quadratic functions. The investigation heavily relies on the use of computer algebra due to the complexity of the equations.