Condition analysis of a multicopter carried with passive skid for rough terrain landing

This paper describes the condition analysis of a multicopter carried with a proposed device for rough terrain landing. Based on a multicopter carried with an electrical robot arm for grasping, we proposed a method to determine whether the skid-carried multicopter can land on an arbitrary slope or not. We established the static model of the entire device, and analyzed the conditions under which the arm and skid can contact the arbitrary plane and the COG (Center of Gravity), which includes the mass of passive skid, multicopter body and each link of the robot arm. Further, we proposed a method to analyze whether the entire device can land stably. By analyzing that the projection of the entire device’s COG is inside or outside the triangle, that comprises the contact point between the device and the uneven ground, we can determine whether the device can land successfully and the condition for capable landing is concluded. After the numerical analysis, the verification experiment is conducted, and by comparing the result of analysis with the experiment, the accuracy of the analysis can be demonstrated.

Shortest paths in arbitrary plane domains

Let $\Omega $ be a connected open set in the plane and $\gamma : [0,1] \to \overline {\Omega }$ a path such that $\gamma ((0,1)) \subset \Omega $ . We show that the path $\gamma $ can be “pulled tight” to a unique shortest path which is homotopic to $\gamma $ , via a homotopy h with endpoints fixed whose intermediate paths $h_t$ , for $t \in [0,1)$ , satisfy $h_t((0,1)) \subset \Omega $ . We prove this result even in the case when there is no path of finite Euclidean length homotopic to $\gamma $ under such a homotopy. For this purpose, we offer three other natural, equivalent notions of a “shortest” path. This work generalizes previous results for simply connected domains with simple closed curve boundaries.

Algorithmic Complex for Solving of Problems with Quadrics Using Imaginary Geometric Images

The paper is devoted to the consideration of a number of issues related to the creation of an algorithmic complex designed to solve positional and metric problems with quadrics on a projection model . A feature of the complex is the active use of geometric schemes and algorithms involving imaginary geometric images. In the paper has been presented a detailed description of constructive geometric algorithms for constructing of conics, quadrics and associated geometric images in a system of constructive geometric modeling – Simplex. All the discussed algorithms are available for independent repetition by the reader. In the paper have been presented and implemented algorithms for constructing conic from a point, a polar, and three points; constructing conic from two pairs of complex conjugate points and one real point; determination of a point on a quadric’s surface; setting a quadric by nine points in three-dimensional space. A new alternative frame of the quadric has been considered, based on which have been solved problems of constructing a tangent and a normal to the quadric, finding an intersection line of an arbitrary plane with the quadric, and performing polar and inverse transformations with respect to the quadric. Have been proposed algorithms for constructing an autopolar tetrahedron with respect to the quadric, and for constructing a conic from an autopolar triangle and two points. Have been considered problems of determining a collinear transformation in three-dimensional space and control the quadric through it. The implementation of the algorithms considered in the paper allowed conclude that there is an urgent need to develop tools for modeling imaginary conics, without which the complex of solving problems with quadrics cannot be taken for the complete one.

Hybrid calibration and detection approach for mobile robotic manufacturing systems

Purpose The purpose of this paper is to present a visual detection approach to predict the poses of target objects placed in arbitrary positions before completing the corresponding tasks in mobile robotic manufacturing systems. Design/methodology/approach A hybrid visual detection approach that combines monocular vision and laser ranging is proposed based on an eye-in-hand vision system. The laser displacement sensor is adopted to achieve normal alignment for an arbitrary plane and obtain depth information. The monocular camera measures the two-dimensional image information. In addition, a robot hand-eye relationship calibration method is presented in this paper. Findings First, a hybrid visual detection approach for mobile robotic manufacturing systems is proposed. This detection approach is based on an eye-in-hand vision system consisting of one monocular camera and three laser displacement sensors and it can achieve normal alignment for an arbitrary plane and spatial positioning of the workpiece. Second, based on this vision system, a robot hand-eye relationship calibration method is presented and it was successfully applied to a mobile robotic manufacturing system designed by the authors’ team. As a result, the relationship between the workpiece coordinate system and the end-effector coordinate system could be established accurately. Practical implications This approach can quickly and accurately establish the relationship between the coordinate system of the workpiece and that of the end-effector. The normal alignment accuracy of the hand-eye vision system was less than 0.5° and the spatial positioning accuracy could reach 0.5 mm. Originality/value This approach can achieve normal alignment for arbitrary planes and spatial positioning of the workpiece and it can quickly establish the pose relationship between the workpiece and end-effector coordinate systems. Moreover, the proposed approach can significantly improve the work efficiency, flexibility and intelligence of mobile robotic manufacturing systems.

Rigid body dynamics using equimomental systems of point-masses

The inertia matrix of any rigid body is the same as the inertia matrix of some system of four point-masses. In this work, the possible disposition of these point-masses is investigated. It is found that every system of possible point-masses with the same inertia matrix can be parameterised by the elements of the orthogonal group in four-dimensional modulo-permutation of the points. It is shown that given a fixed inertia matrix, it is possible to find a system of point-masses with the same inertia matrix but where one of the points is located at some arbitrary point. It is also possible to place two point-masses on an arbitrary line or three of the points on an arbitrary plane. The possibility of placing some of the point-masses at infinity is also investigated. Applications of these ideas to rigid body dynamics are considered. The equation of motion for a rigid body is derived in terms of a system of four point-masses. These turn out to be very simple when written in a 6-vector notation.

Full Thermal Simulation of an Arbitrary, Plane Axisymmetric Residual Stress Field

In this paper, numerical formulations are presented; these permit full thermal simulation of an arbitrary plane axisymmetric residual stress field encompassing hoop, radial, and axial stresses. Earlier formulations were based upon the determination of a temperature profile within the tube that could only replicate radial and hoop stresses; in general, axial stresses were incorrect. This new thermal simulation provides all three stresses and is achieved by incorporating orthotropic coefficients of thermal expansion that themselves vary with radius. Results are generally highly accurate. Crucial near-bore hoop and axial stresses can be replicated within 1%. Near-bore behavior is discussed in detail. These formulations will permit subsequent determination of stress intensity factors (SIF) for arbitrarily orientated cracks within pressure vessels in the presence of pre-existing residual stresses. Note that these thermal solutions mimic known, residual stress profiles; they do not predict residual stress profiles.