Laid down in this paper are the foundations on which the design of engineering systems, in the presence of an uncontrollable changing environment, can be based. The changes in environment conditions are accounted for by means of robustness. To this end, a theoretical framework as well as a general methodology for model-based robust design are proposed. Within this framework, all quantities involved in a design task are classified into three sets: the design variables (DV), grouped in vector x, which are to be assigned values as an outcome of the design task; the design-environment parameters (DEP), grouped in vector p, over which the designer has no control; and the performance functions (PF), grouped in vector f, representing the functional relations among performance, DV, and DEP. A distinction is made between global robust design and local robust design, this paper focusing on the latter. The robust design problem is formulated as the minimization of a norm of the covariance matrix of the variations in PF upon variations in the DEP, aka noise in the literature on robust design. Moreover, one pertinent concept is introduced: design isotropy. We show that isotropic designs lead to robustness, even in the absence of knowledge of the statistical properties of the variations of the DEP. To demonstrate our approach, a few examples are included.
A discrete, non-linear, time-varying, torsional dynamic model of a multi-stage planetary train that is formed by any number of simple planetary stages is proposed in this study. Each planetary stage has a distinct fundamental mesh frequency and any number of planets spaced in any angular positions. The model allows the analysis of the gear train in all possible power flow configurations suitable for various gear drive ratios. It includes periodic variation of gear mesh stiffnesses as well as clearance (backlash) non-linearities that allow tooth separations. Equations of motion for the general case are formulated and solved semi-analytically using a hybrid harmonic balance method (HBM) in conjugate with inverse Fourier transform. Relative mesh displacements along lines of action of individual gear pairs were used as the continuation parameters to pass singular points and ill-conditioned equations in their proximity. At the end, a case study of a two-stage planetary train is used to demonstrate the effectiveness of the model and solution methods. The HBM solutions are compared to those obtained by a direct numerical integration method to assess their accuracy.
Introduced in this paper is a robust algorithm to solve the five-pose planar Burmester problem. The proposed algorithm functions even in the presence of special conditions of the prescribed poses that lead to algorithmic singularities otherwise. In order to show the applicability and to validate the robustness of the proposed algorithm, some examples are included.
Extrinsic calibration of a camera and a 2D laser range finder (lidar) sensors is crucial in sensor data fusion applications; for example SLAM algorithms used in mobile robot platforms. The fundamental challenge of extrinsic calibration is when the camera-lidar sensors do not overlap or share the same field of view. In this paper we propose a novel and flexible approach for the extrinsic calibration of a camera-lidar system without overlap, which can be used for robotic platform self-calibration. The approach is based on the robot–world hand–eye calibration (RWHE) problem; proven to have efficient and accurate solutions. First, the system was mapped to the RWHE calibration problem modeled as the linear relationship boldAX=boldZB, where X and Z are unknown calibration matrices. Then, we computed the transformation matrix B, which was the main challenge in the above mapping. The computation is based on reasonable assumptions about geometric structure in the calibration environment. The reliability and accuracy of the proposed approach is compared to a state-of-the-art method in extrinsic 2D lidar to camera calibration. Experimental results from real datasets indicate that the proposed approach provides better results with an L2 norm translational and rotational deviations of 314 mm and 0.12∘ respectively.
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