网范文：“Robotic CAD system using a Bayesian framework” 这篇计算机范文提出运用贝叶斯CAD系统。我们解决这一问题通过机械CAD系统的运用程序。描述我们使用的措施，英语毕业论文，来表示和处理使用概率分布，关于系统的参数不确定性和传感器测量。它可能被视为基于措施的泛化，合适的数值算法也运用于这种措施。在这篇范文中，使用一个示例,我们展示了如何应用我们的措施使用我们的CAD系统提供仿真结果。
几何模型的使用和CAD系统必然需要一个或多或少的现实环境的建模。然而,与这些模型计算的有效性取决于他们的环境和这些系统的能力。这篇范文提出了一种新的基于贝叶斯措施的形式来表示和处理。
Abstract
We present in this a Bayesian CAD system for robotic applications. We address the problem of the propagation of geometric uncertainties and how esian CAD system for robotic applications. We address the problem of the propagation of geometric uncertainties and how to take this propagation into account when solving inverse problems. We describe the methodology we use to represent and handle uncertainties using probability distributions on the system’s parameters and sensor measurements. It may be seen as a generalization of constraint-based approaches where we express a constraint as a probability distribution instead of a simple equality or inequality. Appropriate numerical algorithms used to apply this methodology are also described. Using an example, we show how to apply our approach by providing simulation results using our CAD system.
Introduction
The use of geometric models in robotics and CAD systems necessarily requires a more or less realistic modeling of the environment. However, the validity of calculations with these models depends on their degree of fidelity to the real environment and the capacity of these systems to represent and take into account possible differences between the models and reality when solving a given problem. This presents a new methodology based on Bayesian formalism to represent and handle geometric uncertainties in robotics and CAD systems. For a given problem, the marginal distribution of the unknown parameters is inferred using the probability calculus. The original geometric problem is reduced to an optimization problem over the marginal distribution to find a solution with maximum probability. In the general case, this marginal probability may contain an integral on a large dimension space.
The resolution method used to solve this integration/optimization problem is based on an adaptive genetic algorithm. The problem of integral estimation is approached using a stochastic Monte Carlo method. The accuracy of this estimation is controlled by the optimization process to reduce computation time. A large category of robotic applications are instances of inverse geometric problems in presence of uncertainties, for which our method is well suited. The proposed approach have been applied to numerous robotic applications [9] such as kinematics inversion for possibly redundant systems, robot and sensor calibration, parts’ pose and shape calibration using sensor measurements, as well as in robotic workcell design. Experimental results made on the implemented CAD system have demonstrated the effectiveness and the robustness of our approach. An example of this experimentation is presented in this . This is organized as follows. We first related work. In Sect. 3 we present our specification methodology, and how to obtain an optimization problem from an original geometric problem. In Sect. 4 we describe our numerical resolution method. We present an example to illustrate our approach in Sect. 5 and give some conclusions and perspectives in Sect. 6.
Related work
The representation and handling of geometric uncertainties is a central issue in the fields of robotics and mechanical assembly. Since the work of Taylor [14], in which geometric uncertainties were taken into account in the manipulator planning process for the first time, numerous approaches have been proposed to model these uncertainties explicitly. Methods modeling the environment using “certainty grids” [10] and those using uncertain models of motion [1] have been extensively used, especially in mobile robotics. Gaussian models to represent geometric uncertainties and to approximate their propagation have been proposed in manipulators programming [12] as well as in assembly [13]. Kalman filtering is a Bayesian recurrent implementation of these models. This technique has been used widely in robotics and vision [15], and particularly in data fusion [2].
Gaussian model-based methods have the advantage of economy in the computation they require. However, they are only applicable when a linearization of the model is possible, and are unable to take into account inequality constraints. Geometric constraint-based approaches [14, 11] using constraints solvers have been used in robotic tasklevel programming systems. Most of these methods do not represent uncertainties explicitly. They handle uncertainties using a least-squares criterion when the solved constraints systems are over-determined. In the cases where uncertainties are explicitly taken into account (as is the case in Taylor’s system), they are described solely as inequality constraints on possible variations.
Probabilistic geometric constraints specification
In this section, we describe our methodology by giving some concepts and definitions necessary for probabilistic geometric constraints specification. We further show how to obtain an objective function to maximize from the original geometric problem.
3.1 Probabilistic kinematic graph
A geometric problem is described as a “probabilistic kinematic graph”, which we define as the directed graph having a set of n frames S = {S1, • • • , Sn} as vertices and a set of m edges A = {Ai1j1 , • • • , Aimjm }, where Aikjk denotes an edge between the parent vertex Sik and its child Sjk and represents a probabilistic constraint on the corresponding relative pose. We call these edges “probabilistic kinematic links”.
Problem description
Using two St¨aubli Rx90 robot arms with 6 revolute joints, we are interested in placing two prismatic parts one against the other. The only constraint is that a face of the first part will be in a Face-On-Face relationship with a face of the second. The two arms are modeled as a set of parts attached to each other using probabilistic kinematic links. We assume that the more significant uncertainties are on zero positions. The two parts are also attached to arms’ end effectors using probabilistic kinematic links.
The added constraint we wish to satisfy to solve the problem is represented by a link between the two faces to place in Face-On-Face relationship. We use for in this link 3 Gaussians on the 3 constrained parameters tz, rx and ry with zeros as mean values and 0.5mm, 0.01rad and 0.01rad respectively as standard deviations. Figure 3 shows the two arms, while Fig. 4 gives the corresponding kinematic graph. We suppose in this example that zero positions uncertainties of the arm on the right of Fig. 3 (Arm1) are 5 times more important than the ones of the arm on the left (Arm2) (for each joint, we suppose a Gaussian distribution on the zero position with 0.01rad as standard deviation for Arm1 and with 0.05rad for Arm2). Our aim is to comment qualitatively on the solution obtained and to show the importance of taking un- certainties propagation into account when choosing a solution.
Discussion
This example shows how the proposed method takes geometric uncertainties into account in a general and homogeneous way. No assumptions have been made, either on the uncertainties models (shapes of the used distributions), nor on the linearity of the model or the possibility of it being linearized. It also shows how possible redundancy of the system relating to the required task is used to find the most accurate solution.
Conclusion and Future Research
We have presented a generic approach for geometric problems specification and resolution using a Bayesian framework. We have shown how a given problem is first represented as a kinematic graph, and then formulated as an integration/optimization problem. For generality, no assumptions have been made on the shapes of the distributions or on amplitudes of uncertainties. Experimental results made on our system have demonstrated the effectiveness, the robustness and the homogeneity of representation of our approach. However, additional studies are required to improve both the integration and the optimization algorithms. For the integration problem, numerical integration can be avoided when the integrand is a product of generalized normals (Dirac’s delta functions and Gaussians) and when the model is linear or can be linearized (errors are small enough). The optimization algorithm may also be improved by using a local derivative-based method after the convergence of our genetic algorithm. Future work will aim at allowing the use of high-level sensors such as vision-based ones. We are also considering extending our system so that it can include nongeometrical parameters (inertial parameters for example) in problem specification.
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