Inverse Kinematics

One of the primary difficulties is that the number of degrees of freedom is larger than the number of inputs, since deformable materials have conceptually infinite degrees of freedom. One approach applies spatially varying electric fields generated by multiple electrodes. Another approach, which is proposed in this 

The conceptual joints of the gel manipulator are constrained and calculated with equation (2.23) and equation (2.26). The above equations are typical 

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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. 

Target desired angles as shown in Figure4 using measured position of eq.(5) are provided by inverse kinematics ... 

Y. T. l ai and D. E. Orin. A Strictly Caiveigent Real-Time Solution for Inverse Kinematics of Robot Manipulators. Journal of Robotic Systems, (4) 477-501,1987. 

The discovery of an odd-even effect in the (again, very asymmetric) fission of lighter odd-Z fissioning systems studied in inverse kinematics (Steinhauser et al. 1998) has confirmed the findings obtained in thermal-neutron-induced fission. 

Position-based impedance controller, x is the robot actual pose in the task space computed from the actual joint configuration q with the FK block, Xj is the desired pose in the task space, x, is the equiUbritim pose of the environment, K, is the net stiffness of the sensor and of the environment, f, is the external environment forces expressed in the task space, fj is the desired force vector, is the desired joint configuration computed with the inverse kinematic (IK) block, and is the commanded motor torque vector. The command trajectory x is defined as s.x,. = Z" (fj - O, where Z is the admittance matrix and s is the argument of the Laplace transform. 

Articulated arm model for implementing inverse-kinematics equations. 

Memi oglu, A., Human Motion Control Using Inverse Kinematics. Bilkent University, 2003. 

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. 

This chapter was adapted from in part, by permission, M. Otake, Y. Kagami, Y. Ku-niyoshi, M. Inaba, and H. Inoue, Inverse Kinematics of Gel Robots made of Electro-Active Polymer Gel , Proceedings of IEEE International Conference on Robotics and Automation, pp.3224-3229, 2002 M. Otake, Y. Nakamura, and H. Inoue, Pattern Formation Theory for Electroactive Polymer Gel Robots , Proceedings of IEEE International Conference on Robotics and Automation, pp.2782-2787, 2004 M. Otake, Y. Nakamura, M. Inaba, and H. Inoue. Wave-shape Pattern Control of Electroactive Polymer Gel Robots. Proceedings of the 9th International Symposium on Experimental Robotics, 1D178, 2004. 

The purpose of this section is to propose an inverse kinematics method which could ultimately be used to control the shape of the gel robot such as tentacle control of octopus-shaped gel robot which was prototyped (Figure 7.2). It was focused on tip (end-effector) position control of a gel manipulator as a first step (Figure 7.3). This will form a foundation for shape control of gel robots. 

In this section, it was shown that a method to solve inverse kinematics of gel robots made of electro-active polymer gel. As a first step, a method was proposed to control the tip position of a manipulator entirely made of electro-active... 

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... 

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. 

The automated placement of electronic components on MID is described in Chapter 4. As in the case of structuring and metallization processes, a CAD/CAM chain is an objective the comments below are no more than a brief outlook on the general procedure. In a CAD/CAM chain, the positions and orientations of the components, consisting of the x, y, and z coordinates and rotations about the three axes, should be read out and converted, if possible automatically, into the data required by the control software of system in question. This necessitates coordinate transformations between the coordinate systems of MID product, part carrier, and system. If position and orientation of a component inside the machine are known, the corresponding axis configuration for the placement head can be determined by inverse kinematic calculation of the handler. This has to be converted into system-specific syntax and made available to the system controller. CAD/CAM chains for 3D assembly are being developed by the system manufacturers and are also the subject of university-level research. 

This reseairch f ollow the common practice of calculating manipulator required joint torques. First the desired manipulator end-effector path is specified, then based on this Cartesian path the required joint angles are calculated by using robot nominal inverse kinematics (use nominal kinematic values). The trajectory planner is used based on linear function with parabolic blends, then a trajectory generator is applied to generate a smooth path. Finally, the iterative Newton-Euler dynamic equations are employed to compute the require torques at each joints. Because the nominal kinematic parameter values used in the calculation, these set of required manipulator torques are considered as nominal torques. 

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. 

Ideally, the calibration process would reach its maximum usefulness when implemented in a system which utilized off-line programming of parts to be machined. A CAD system would provide the necessary position information for the part by the assignment of locations relative to a part coordinate frame. This information would necessarily include the type of tools needed for specific operations (i.e..drilling, cleaning) and the orientation of the tool relative to the part for operations such as deburring. When the part is placed in a fixture, the manipulator arm could be equipped with a sensor to locate the part relative to the fixture. Then, the calibrated inverse kinematic solution of the robot arm would be used to generate the required joint angles and trajectories needed to machine the part. 

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