A strictly convergent real‐time solution for inverse kinematics of robot manipulators

Abstract

Inverse Kinematics has been recognized as an important problem in robotics applications. A robot independent solution can only be obtained through numerical methods, but most solutions which use this approach have problems with convergence especially near singularity points. This article develops a strictly convergent algorithm and a special‐purpose Inverse Kinematics Processor (IKP) to obtain the solution in real time. While the algorithm is based on open‐loop integration of rates, the absolute position deviation is used as a criterion to control the iteration, and a feedback mechanism has been especially designed to eliminate problems with long‐term drift or with initial errors in the solution. The architecture of the IKP is based on a high‐speed floating‐point arithmetic processor and is designed to perform the common matrix‐vector operations efficiently with a minimum processor cycle time. The algorithm has been simulated on the proposed architecture, and the results show its robustness and real‐time capability. For a six degree‐of‐freedom robot manipulator (for which no closed‐form solution exist), the Inverse Kinematics solution may be obtained at an approximate 2 khz rate with an error which is within standard repeatability limits.

Local SVD inverse of robot Jacobians

“…The inverse kinematics algorithms are supposed to compute q such that the robot end effector translates along a linear path with a desired velocity oḟ Since a robot loses one or more degrees of freedom at its singularities, its actual movement will inevitably lag behind the desired trajectory no matter what algorithms are used to compute q, as observed in references [15,16]. In this study, both algorithms apply the feedback error correction by replacing ẋ with ẋ d + Ke where ẋ d is the desired Cartesian velocity, K = 20I and e defined in reference 8.…”

Review of the damped least-squares inverse kinematics with experiments on an industrial robot manipulator

“…Equation (19) can be solved using the weighted damped least-squares technique [7], that is (20) Again, the singular value decomposition of the matrix J is helpful, i.e.…”

Kinematic control of redundant robot manipulators: A tutorial

“…This is implemented on the computer, of course, in discrete-time and thus unavoidably causes numerical drifts in the task space. In order to overcome this drawback, a closed-loop algorithmic version of the solution (3) can be obtained if the task space vector ~ is replaced by ~ = ~d + Ae, where e = x d -x denotes the error between the desired task trajectory xu and the actual task trajectory x which can be computed from current joint variables via Equation (1), and A is a positive definite (diagonal) matrix that suitably shapes the error convergence (Sciavicco and Siciliano, 1987b;Tsai and Orin, 1987). Notice that the current joint variables are not to be confused with the real robot joint sensor measurements used by the dynamic control.…”