Inverse kinematic problem

M.M. Lavrentiev, V.G. Romanov, and V.G. Vasiliev (1970) [15] considered the linearized inverse kinematic problem ... 

R.G. Mukhometov (1975, 1977) [16] proved global uniqueness results for 2D inverse kinematic problem with full data ... 

A.L. Bukhgeim (1983) [4] proved necessary and sufficient conditions for the solvability of the two-dimensional inverse kinematic problem with partial local data in class of real analytic functions, and... 

Moreover, in Section 3 we construct a Newton-type algorithm for finding the 3D velocity distribution from 3D travel time measurements for the local inverse kinematic problem. Initially, as a first approximation, we choose a sound velocity that increases linearly with the depth. This is since it was shown in [5] that with this choice of linearization our problem reduces to a sequence of 2D Radon transforms in discs. Om case is much harder, since we consider solving a nonlinear problem, and therefore we need to solve a direct 3D problem on each iteration. However, we can show that, in our case, already the second iteration is often much better than the solution from the linearized approximation. 

In order to find the most stable three-dimensional (local) inverse kinematic problem it is appropriate to start from the simpler one-dimensional case. The following considerations are made along the lines of [21, pp. 102-103], Let us consider a ray propagation in a layer of thickness H with a sound velocity V over a half-space of velocity V > V, see Figure 1. 

A.L. Bukhgeim (1983) On one algorithm of solving the inverse kinematic problem of seismology. Numerical Methods in Seismic Investigations, Nauka, Novosibirsk (in Russian), 152-155. 

Equation (3) represents the solution to the inverse kinematic problem in the sense that for a given Cartesian configuration, composed of the position and orientation specified by b,- and R, respectively, the actuator lengths /, for i=l,2,..., 6, can be computed using (3). 

An alternative route to implement local MC moves is provided by the literature on (inverse) kinematics, such as on control systems for robotic arms composed of flexible joints [27,87]. Here, the problem is transformed to either a set of linear equations [27] or finding the roots of a high-order polynomial [87] at comparable computational expense. One of the benefits of such an approach is the ability to introduce arbitrary stiff segments into the loop, that is, the degrees of freedom used for chain closure do not have to be consecutive. Conversely,... 

Kolodny, R., Guibas, L., Levitt, M., Koehl, P. Inverse kinematics in biology the protein loop closure problem. Int. J. Robot. Res. 2005, 24, 151-63. 

This chapter proposes a foundation to control shape of deformable machines consisting of actively deformable materials. If the problem is stated in inverse kinematics form, the required method is to control joint angles, in this case, curvatures, of arbitrary points to fulfill some condition. It is difficult to control every part of the body directly since the numbers of input is smaller than degrees of freedom of the machines. 

The method generates subset of possible workspace and moves the tip of the gel in the plane. From the viewpoint of problem solving algorithm, it is evaluated that this inverse kinematic model as practical approach efficiency is in high... 

The inversion algorithm for the 2D kinematic problem in a layer is fully... 

The inverse kinematics solution for the SCARA manipulator is used to determine the Joint variables for a desired position and orientation of the end effector with reference to the base frame. A geometric approach was used to break down the spatial geometry of the manipulator into several plane geometry problems. This is a simple operation if o( - O. By using the link/Joint geometric parameters as well as the equations determined, an inverse kinematics solution can be obtained. 

A different solution of the problem consists in first approximating independently functions /,(t), on the grounds of above mentioned observational subsets for given i — th element of the network, and then constituting approximative function X t) as the result of pseudo-inverse operation (Kadaj,1990). In this paper we deal with developing this way of solution for three-dimensional kinematic network. 

The mathematical justification for the assumption of coherent concentration fronts proceeds via the inverse of this argument. It has been shown that, in a system governed by the kinematic wave equation [Eq. (9.12)] involving a transition between two constant states (a Riemann problem), if a unique solution exists it is always a function of the combined variable the... 

The application of the kinematic modelling in the mechanical systems of connected bodies is most often related to the solution of the direct and the inverse problems of kinematics. But at the stages of dynamics the kinematic modelling is connected with the determination of the... 

Similar to the PDF model, and in contrast to some of the more complex nonUnear models, all three models (monoexponential, logistic, and kinematic) for isovolumic relaxation characterization can generate parameters by fitting the pressures, the equivalent of solving the inverse problem. The clear advantage of invertible (i.e., linear) models is their ability to provide unique quantitative parameters. 

---