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Computational Numerical Methods
Published in Timothy Bower, ®, 2023
A common application of fminsearch is to define a function handle that computes an error function that we wish to minimize. For example, we can define an error function as the distance between a desired robot end effector location and a forward kinematics calculation. Then fminsearch can calculate the inverse kinematics problem to find the joint angles needed to position the robot end effector at the specified location. The forward kinematics calculation uses matrix multiplication to calculate the end position of a serial-link robotic arm. For robots with only a few joints, it may be possible to find an analytic inverse kinematic solution, but more complex robots often require numerical methods to find the desired joint angles. The starting point value is critical for finding the desired joint angles because multiple joint angle sets can position the robot arm at the same location. For example, we can consider either elbow-up or elbow-down configurations. So it is important to pass a starting point to fminsearch such that the nearest set of correct joint angles puts the robot in the desired configuration.
Nonlinear Control Design
Published in Jitendra R. Raol, Ramakalyan Ayyagari, Control Systems, 2020
Jitendra R. Raol, Ramakalyan Ayyagari
Most mechanical systems, robotic examples in this chapter and aerospace examples in Chapter 14, are governed by second order differential equations and evolve on nonlinear manifolds. At a superficial level, with more linear theory behind, typical control techniques for these systems rely on the introduction of local coordinates so as to set up a smooth one-to-one correspondence between the actual state space and Cartesian space within an admissible range. Although this converts control on a manifold to control in Cartesian space, the engineer would have enjoyed the intuition. The issue of singularity exists for any choice of local coordinates on certain nonlinear manifolds, such as the special orthogonal group SO(3). We have purposefully avoided the kinematics, inverse kinematics, and the possibility of singularities in this text, while placing emphasis on touching upon the controller desgin. Interested readers may look into books [17–24] on dynamics and control.
Mathematical Models of Robot Motion
Published in Jitendra R. Raol, Ajith K. Gopal, Mobile Intelligent Autonomous Systems, 2016
In order to specify and adjust the robot’s controller, the kinematic and dynamic mathematical models of the robot are needed. The kinematics is the study and analysis of the robot’s movements with respect to a chosen reference coordinate system. It is an analytic specification and description of the spatial movement of the robot. This is a relationship between the position and the orientation of the robot’s links and the joint coordinates. It is possible to determine the position and the orientation of the robot’s end links based on its geometric relations. The inverse kinematics is the process of determining each joint coordinates from the specified position/orientation of the robot end links. Table 2.1 and Figure 2.5 show the functionality of the robot’s kinematics. The kinematic model of a robot is represented by the HTM as discussed in Section 2.2.4. This HTM process is necessary for a robot with more than 2DoF. A robot of n-DoF is formed by n-links assembled by n-articulations in such way that each articulation-link constitutes one DoF. To each of these links a reference system is associated and the homogeneous transformations are used to represent the rotations/relative translations from the different links which compose the robot. It is thus possible to represent the translations and relative rotations between the different links.
Teams of robots in additive manufacturing: a review
Published in Virtual and Physical Prototyping, 2023
Abdullah Alhijaily, Zekai Murat Kilic, A. N. Paulo Bartolo
Workspace utilisation: the efficient use of the workspace is a generic challenge in AM, as some regions within the workspace of the machine may not be usable or optimum to work on due to different factors such as singularities, vibrations, and accuracy fluctuations (Liu, Wu, and Wang 2019). Singularities avoidance is critical in the path planning of robotic arms. The configuration in which a robot is unable to move in certain directions is called a singular configuration (Lynch and Park 2017). If the robot is near a singular configuration several problems may arise, such as the velocity and torque of the joints may be unbounded, and a unique solution of the inverse kinematics cannot be achieved (Spong, Hutchinson, and Vidyasagar 2006). The presence of multiple robots in a cooperative AM system can be exploited to avoid singularities. For example, a printing area that is near a singular configuration of a robotic arm can be assigned to another arm in the system that is far from singularities in that region. The same strategy can be used to avoid configuration exhibiting high vibrations or regions with high accuracy fluctuations.
Design and Development of a Low-Cost Vision-Based 6 DoF Assistive Feeding Robot for the Aged and Specially-Abled People
Published in IETE Journal of Research, 2023
Priyam Parikh, Reena Trivedi, Jatin Dave, Keyur Joshi, Dipak Adhyaru
Main contributions: Designed and developed an indigenous 3D printed feeding serial manipulator for the aged Indian patients.Applied product of exponential based forward kinematics method to find the intermediate points in the C-space.Face recognition and depth measurement using a 3D depth camera.Applied derivative based inverse kinematics algorithm to achieve the singularity free motion.Simulated an entire robotic system against step and cubic input signal using PID, FC, FPID and GA: FOPID controller. Interpreted the results based on overshoot, settling time, error and derivative error.Based on the simulated results, the robot is controlled using FC for the first two intermediate points, from intermediate point 3–5, the robot is controlled using FPOID and the last intermediate point was controlled using FPID.Real-time testing of the robotic arm on multiple users.
Numerical method for inverse kinematics using an extended angle-axis vector to avoid deadlock caused by joint limits*
Published in Advanced Robotics, 2021
Masanori Sekiguchi, Naoyuki Takesue
To automate work using an articulated robot, such as an industrial robot arm, it is necessary to generate joint displacement commands that can achieve the required motions. In most cases, the requirements given to the robot during the teaching process are assigned in task space. Therefore, inverse kinematics is required to convert a point in task space to a corresponding point in joint space. Inverse kinematics methods can be divided into two categories: analytical methods for obtaining solutions by geometrical consideration or algebraic transformation [1–3], and numerical methods that perform iterative calculations [4]. If the robot mechanism meets certain conditions, the inverse kinematics problem can be solved analytically; otherwise, numerical methods are used.