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Machining contours on a large thin-walled part is a difficult task due to inevitable deformation of the actual part. The deformation of the contour can significantly influence the rigidity of the thin-walled part; thus, it is of importance to minimize the deformation of the contour compared with the design contour. This paper proposes a novel method to adaptively calculate the optimal contour on the deformed surface based on optimized parallel projection. The geometry data of free-form surface is obtained by on-machine measurement (OMM), and then, the actual surface is reconstructed using the measurement data. The reconstructed surface is matched with the design surface, and then, the design contour was projected onto the reconstructed surface to obtain the locating contour. The iterative nearest point (ICP) algorithm is used to adjust the design contour to match the locating contour. Finally, the projection direction is optimized to minimize contour deformation, and the adjusted contour is projected onto the reconstructed surface along the optimal direction to obtain the new contour. The effectiveness of this method is verified by machining and measuring experiments. [ABSTRACT FROM AUTHOR]

Free-form surfaces have been widely used in aerospace, automotive and other fields. Due to its complex geometry, free-form surface inspection is generally conducted by touch-trigger or measuring probe-based Coordinate Measurement Machines or On-machine Measurement. Sampling strategy plays a decisive role in improving both measurement accuracy and efficiency, which is determined by sample size and distribution of sample points. However, it is difficult to simultaneously take the surface curvature, sampling density and approximation error into account, considering the complexity of surface geometry. In this paper, triangle mesh simplification is innovatively adopted in sampling planning to achieve multi-geometric constraints. As triangle mesh has outstanding advantages in representing the surface features, strong stability and is easy to modify its structure, free-form surface is converted to a dense triangle mesh. Triangle mesh simplification is implemented by iteratively contracting triangle edges. An improved quadric error metric is established to decide contraction order and optimal target vertices under discrete curvature constraint. Sampling density is controlled by limiting the triangle edge length. Detailed adaptive sampling algorithm under multi-geometric constraints is then developed. Both simulation and experiment are conducted to validate feasibility and robustness of the proposed method. The results are compared with uniform sampling and existing adaptive sampling strategy to show that the proposed method can prominently reduce sampling error when sample size is small. • Free-form surface sampling method under multi-geometric constraints can improve sampling accuracy. • Both surface curvature and sampling density are necessary in surface sampling. • Triangle mesh simplification is firstly used for multi-geometric constraints-based surface sampling. [ABSTRACT FROM AUTHOR]

The design of a globally convergent position observer for feature points from visual information is a challenging problem, especially for the case with only inertial measurements and without assumptions of uniform observability, which remained open for a long time. We give a solution to the problem in this paper assuming that only the bearing of a feature point, and biased linear acceleration and rotational velocity of a robot – all in the body-fixed frame – are available. Further, in contrast to existing related results, we do not need the value of the gravitational constant either. The proposed approach builds upon the parameter estimation-based observer recently developed in Ortega et al. (2015) and its extension to matrix Lie groups in our previous work. Conditions on the robot trajectory under which the observer converges are given, and these are strictly weaker than the standard persistency of excitation and uniform complete observability conditions. Finally, as an illustration, we apply the proposed design to the visual inertial navigation problem. [ABSTRACT FROM AUTHOR]