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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS2019

Implementation and Testing of Inverse Kinematics on Robotic Arm

COSIE (Coronal Spectrographic Imager in the Extreme Ultraviolet) is a proposed solar tracking ISS imaging payload that will help bridge the theoretical gap between the physics of the low corona and the heliosphere. This scientific instrument requires high pointing accuracy, on the order of arc seconds. The instrument is mounted on to a three revolute joint robotic arm in order to track the roll, pitch and yaw motion of the Sun. The goal of this project is to construct a prototype model of the robotic arm and implement the proposed analytical inverse kinematics algorithm. In robotics, the inverse kinematics problem is solving for the set of joint angles that achieve the desired end effect or location and/or orientation. In this case, orientation is the focus. Depending on the configuration, multiple sets of joint angle solutions may exist. Due to the complexity of robotics, typically iterative methods are used to solve for the joint angle solution sets. However, in this case, an analytical solution exists. A small robotic arm representative of the full size hardware was constructed. The inverse kinematics algorithm, originally in MATLAB/Simulink, was converted into C in order to interface with the motors. This C software was implemented on a Windows PC and micro-controller, and serial communication between the two was established, allowing the motors to be directly controlled by the inverse kinematics algorithm. Testing the inverse kinematics on a physical system will allow the validity and accuracy of the analytic solution to be verified.

Franz, Carter↗
NASA NTRS1990

Automatic generation of forward and inverse kinematics for a reconfigurable modular manipulator system

An algorithm is proposed for automatically generating both the forward and inverse kinematics of a serial-link N-degree-of-freedom reconfigurable manipulator (RM). Generation of the kinematic equations that govern a modular manipulator starts with geometric descriptions of the units, or modules, as well as their sequence in the manipulator. This geometric information is used to obtain the Denavit-Hartenberg (DH) parameters of an RM. The DH kinematic parameters are then used to obtain the forward kinematic transformation of the system. The problem of obtaining the inverse kinematics of RMs is addressed, and the idea of scaling an RM to automate the inverse kinematics and make the procedure as general as possible is proposed.

Kelmar, Laura↗
NASA NTRS1989

Real-time neuromorphic algorithms for inverse kinematics of redundant manipulators

The paper presents an efficient neuromorphic formulation to accurately solve the inverse kinematics problem for redundant manipulators. The approach involves a dynamical learning procedure based on a novel formalism in neural network theory: the concept of 'terminal' attractors. Topographically mapped terminal attractors are used to define a neural network whose synaptic elements can rapidly encapture the inverse kinematics transformations, and, subsequently generalize to compute joint-space coordinates required to achieve arbitrary end-effector configurations. Unlike prior neuromorphic implementations, this technique can also systematically exploit redundancy to optimize kinematic criteria, e.g., torque optimization. Simulations on 3-DOF and 7-DOF redundant manipulators, are used to validate the theoretical framework and illustrate its computational efficacy.

Barhen, Jacob↗
NASA NTRS2004

Direct and Inverse Kinematics of a Novel Tip-Tilt-Piston Parallel Manipulator

Closed-form direct and inverse kinematics of a new three degree-of-freedom (DOF) parallel manipulator with inextensible limbs and base-mounted actuators are presented. The manipulator has higher resolution and precision than the existing three DOF mechanisms with extensible limbs. Since all of the manipulator actuators are base-mounted; higher payload capacity, smaller actuator sizes, and lower power dissipation can be obtained. The manipulator is suitable for alignment applications where only tip, tilt, and piston motions are significant. The direct kinematics of the manipulator is reduced to solving an eighth-degree polynomial in the square of tangent of half-angle between one of the limbs and the base plane. Hence, there are at most 16 assembly configurations for the manipulator. In addition, it is shown that the 16 solutions are eight pairs of reflected configurations with respect to the base plane. Numerical examples for the direct and inverse kinematics of the manipulator are also presented.

Tahmasebi, Farhad↗
NASA NTRS1986

Inverse kinematic solution for near-simple robots and its application to robot calibration

This paper provides an inverse kinematic solution for a class of robot manipulators called near-simple manipulators. The kinematics of these manipulators differ from those of simple-robots by small parameter variations. Although most robots are by design simple, in practice, due to manufacturing tolerances, every robot is near-simple. The method in this paper gives an approximate inverse kinematics solution for real time applications based on the nominal solution for these robots. The validity of the results are tested both by a simulation study and by applying the algorithm to a PUMA robot.

Hayati, Samad A.↗
NASA NTRS1992

Inverse kinematics problem in robotics using neural networks

In this paper, Multilayer Feedforward Networks are applied to the robot inverse kinematic problem. The networks are trained with endeffector position and joint angles. After training, performance is measured by having the network generate joint angles for arbitrary endeffector trajectories. A 3-degree-of-freedom (DOF) spatial manipulator is used for the study. It is found that neural networks provide a simple and effective way to both model the manipulator inverse kinematics and circumvent the problems associated with algorithmic solution methods.

Choi, Benjamin B.↗
NASA NTRSDate not supplied

Efficient and Singularity-Aware Inverse Kinematics for 6-DOF and 7-DOF Revolute Manipulators

Inverse kinematics (IK) for 6-DOF and 7-DOF revolute robot manipulators may be decomposed into canonical subproblems which find the angles on circles where they intersect with other geometric objects. We present new algebraic solutions and geometric interpretations for six subproblems. We demonstrate significant performance improvements over existing IK methods. 7-DOF manipulators have one redundant DOF to parameterize, so we introduce the general SEW angle, which generalizes the conventional SEW angle but with an arbitrary reference direction function. One special choice, the stereographic SEW angle, has a singularity when the wrist is on a half-line instead of a full line.

Computational Geometry↗
NASA NTRS1989

Computational neural learning formalisms for manipulator inverse kinematics

An efficient, adaptive neural learning paradigm for addressing the inverse kinematics of redundant manipulators is presented. The proposed methodology exploits the infinite local stability of terminal attractors - a new class of mathematical constructs which provide unique information processing capabilities to artificial neural systems. For robotic applications, synaptic elements of such networks can rapidly acquire the kinematic invariances embedded within the presented samples. Subsequently, joint-space configurations, required to follow arbitrary end-effector trajectories, can readily be computed. In a significant departure from prior neuromorphic learning algorithms, this methodology provides mechanisms for incorporating an in-training skew to handle kinematics and environmental constraints.

Gulati, Sandeep↗
NASA NTRS1989

An inverse kinematics algorithm for a highly redundant variable-geometry-truss manipulator

A new class of robotic arm consists of a periodic sequence of truss substructures, each of which has several variable-length members. Such variable-geometry-truss manipulator (VGTMs) are inherently highly redundant and promise a significant increase in dexterity over conventional anthropomorphic manipulators. This dexterity may be exploited for both obstacle avoidance and controlled deployment in complex workspaces. The inverse kinematics problem for such unorthodox manipulators, however, becomes complex because of the large number of degrees of freedom, and conventional solutions to the inverse kinematics problem become inefficient because of the high degree of redundancy. A solution is presented to this problem based on a spline-like reference curve for the manipulator's shape. Such an approach has a number of advantages: (1) direct, intuitive manipulation of shape; (2) reduced calculation time; and (3) direct control over the effective degree of redundancy of the manipulator. Furthermore, although the algorithm was developed primarily for variable-geometry-truss manipulators, it is general enough for application to a number of manipulator designs.

Naccarato, Frank↗
NASA NTRS1990

An adaptive inverse kinematics algorithm for robot manipulators

An adaptive algorithm for solving the inverse kinematics problem for robot manipulators is presented. The algorithm is derived using model reference adaptive control (MRAC) theory and is computationally efficient for online applications. The scheme requires no a priori knowledge of the kinematics of the robot if Cartesian end-effector sensing is available, and it requires knowledge of only the forward kinematics if joint position sensing is used. Computer simulation results are given for the redundant seven-DOF robotics research arm, demonstrating that the proposed algorithm yields accurate joint angle trajectories for a given end-effector position/orientation trajectory.

Colbaugh, R.↗
NASA NTRS1994

Robust inverse kinematics using damped least squares with dynamic weighting

This paper presents a general method for calculating the inverse kinematics with singularity and joint limit robustness for both redundant and non-redundant serial-link manipulators. Damped least squares inverse of the Jacobian is used with dynamic weighting matrices in approximating the solution. This reduces specific joint differential vectors. The algorithm gives an exact solution away from the singularities and joint limits, and an approximate solution at or near the singularities and/or joint limits. The procedure is here implemented for a six d.o.f. teleoperator and a well behaved slave manipulator resulted under teleoperational control.

Schinstock, D. E.↗
NASA NTRS1987

Recursive inverse kinematics for robot arms via Kalman filtering and Bryson-Frazier smoothing

This paper applies linear filtering and smoothing theory to solve recursively the inverse kinematics problem for serial multilink manipulators. This problem is to find a set of joint angles that achieve a prescribed tip position and/or orientation. A widely applicable numerical search solution is presented. The approach finds the minimum of a generalized distance between the desired and the actual manipulator tip position and/or orientation. Both a first-order steepest-descent gradient search and a second-order Newton-Raphson search are developed. The optimal relaxation factor required for the steepest descent method is computed recursively using an outward/inward procedure similar to those used typically for recursive inverse dynamics calculations. The second-order search requires evaluation of a gradient and an approximate Hessian. A Gauss-Markov approach is used to approximate the Hessian matrix in terms of products of first-order derivatives. This matrix is inverted recursively using a two-stage process of inward Kalman filtering followed by outward smoothing. This two-stage process is analogous to that recently developed by the author to solve by means of spatial filtering and smoothing the forward dynamics problem for serial manipulators.

Rodriguez, G.↗
NASA NTRS2024

Redundancy Parameterization and Inverse Kinematics of 7-DOF Revolute Manipulators

Seven degree-of-freedom (DOF) robot arms have one redundant DOF for obstacle and singularity avoidance. This DOF does not change the end effector motion and must be parameterized to fully specify the joint angles for a given end effector pose. For 7-DOF revolute (7R) manipulators, we introduce the generalized shoulder-elbow-wrist (SEW) angle, a generalization of the widely-used conventional SEW angle but with an arbitrary reference direction function, along with Jacobian expressions and singularity analysis. Other redundancy parameterizations including the conventional SEW angle encounter an algorithmic singularity along a line in the workspace. We introduce a reference direction function choice called the stereographic SEW angle which has a singularity only along a half-line and can be placed out of reach. We prove such a singularity is unavoidable for any parameterization. Finally, using the general SEW angle and the subproblem decomposition method, we provide efficient singularity-robust inverse kinematics solutions for 7R manipulators which are often closed-form but may involve a 1D or (in general) 2D search. Search-based solutions may be converted to finding polynomial roots. Examples are available in a publicly accessible repository.

Kinematics↗
NASA NTRSDate not supplied

Adjusting a Full Body Model to Mitigate Inverse Kinematics Artifacts in Opensim

BACKGROUND: In support of Vibration Isolation and Stabilization (VIS) system development for Human Health Countermeasures (HHC) exercise systems in space, such as the European Enhanced Exploration Exercise Device (E4D) [1], dynamic quantities required to model the response of a proposed VIS while considering the effect of VIS motion on the forces between the human and VIS platform were obtained using motion capture data [2]. On occasion, large-amplitude oscillatory spikes were found in the subject’s linear and angular momentum derivatives, affecting analyses that depend on forces and moments derived from motion capture. The purpose of this investigation was to identify causes of these artifacts and techniques for their resolution. METHODS AND RESULTS: To obtain the required human dynamic quantities to drive the VIS simulation, motion capture data was collected containing recorded trajectories of passive retroreflective markers on body landmarks of an exercising subject. Since the full body Rajagopal model [3] was originally used to enhance gait analysis, upper body joints did not require large Ranges of Motion (ROM). We thus modified the Rajagopal model [4, 5] to allow it to be used for upper body intensive exercises like those common to the E4D. OpenSim Inverse Kinematics (IK) [6] was performed using these scaled subject models to generate the joint angles throughout the exercise while minimizing marker error. At times, the arms were observed to ‘snap’ from one configuration to another, causing spike artifacts. Following IK, a custom OpenSim plugin [7] was used to determine the required dynamic quantities including the rates of change of the linear and angular momenta of the human. Since motion capture is recorded at a larger time step than required by the VIS simulation, the human center of mass location was fit with splines and a second derivative taken to obtain the momentum derivative, allowing the VIS simulation to maintain conservation of momentum when appropriate. In a few cases during this stage, artifacts much larger than the expected noise of the second derivatives were introduced. Investigation of cases containing artifacts revealed several modifications that could be made to the OpenSim model to improve IK results. Since OpenSim models use Euler angles and rotation sequences, ‘gimbal lock’ would be encountered in the arms when raised 90 degrees to the side (e.g., T-pose, some hang clean exercise, etc.). This was resolved by reorienting the horizontal axes at the shoulder joint by 45 degrees, placing ‘gimbal lock’ outside common arm ROM, with the arm ROMs adjusted following this change. Elbow and wrist ROMs could also be adjusted to allow realistic motion while at the same time limiting the likelihood of unrealistic orientations. On occasion, the arms flipped backwards when raised above the head. This was prevented by using medial elbow markers in scaling and IK. When medial markers were not available, the acromial joint location in the unscaled model was shifted before model scaling to better align the arm with available markers. Lastly, artifacts which became apparent after taking the second derivatives of spline-fit data were found to occur in cases when the pelvis rotation limit prevented the full range of motion of an exercise. These issues were resolved by unclamping the pelvis rotation limit. Through this investigation, an understanding of conditions leading to IK artifacts was acquired allowing the automation of artifact detection. These artifact detection and mitigation techniques can be applied toward modeling of upper body motions in aerospace and other fields for improved IK results.

C A Bell↗
NASA NTRS1991

Forward and inverse kinematics of double universal joint robot wrists

A robot wrist consisting of two universal joints can eliminate the wrist singularity problem found on many individual robots. Forward and inverse position and velocity kinematics are presented for such a wrist having three degrees of freedom. Denavit-Hartenberg parameters are derived to find the transforms required for the kinematic equations. The Omni-Wrist, a commercial double universal joint robot wrist, is studied in detail. There are four levels of kinematic parameters identified for this wrist; three forward and three inverse maps are presented for both position and velocity. These equations relate the hand coordinate frame to the wrist base frame. They are sufficient for control of the wrist standing alone. When the wrist is attached to a manipulator arm; the offset between the two universal joints complicates the solution of the overall kinematics problem. All wrist coordinate frame origins are not coincident, which prevents decoupling of position and orientation for manipulator inverse kinematics.

Williams, Robert L., II↗