Singularity-robust Inverse Kinematics Research Articles

Singularity-Robust Inverse Kinematics for Serial Manipulators

This paper is a practical~guideline how to analyze and evaluate literature algorithms of singularity-robust inverse kinematics or to construct new ones. Additive, multiplicative and based on the Singularity ValueDecomposition (SVD) methods are examined to retrieve well conditioning of a matrix to be inverted in the Newton algorithm of inverse kinematics. It is shown that singularity avoidance can be performedin two different, but equivalent, ways: either via properly modified manipulability matrix or not allowing to decreese the minimal singular value below a given threshold. It is discussed which method can always be used and which only when some pre-conditions are met. Selected methods are compared to with respect to the efficiency of coping with singularities based on a theoretical analysis as well as simulation results. Also some questions important for mathematically and/or practically oriented roboticians are stated and answered.

A neuro-dynamic walking engine for humanoid robots

Using tools from artificial intelligence, mainly artificial neural networks, this paper presents an walking-engine for humanoid robots. This engine uses dynamic neural networks with feedback for gait generation, a modified Zhang neural network for a singularity-robust inverse kinematics solver, and feedforward neural networks for neuro-adaptive control. The Atlas humanoid robot model in simulation is used to test and verify the capabilities of the neuro-dynamic walking engine. Results show that the engine is capable of generating conventional ZMP stable walking gaits and executing them using the Atlas robot in simulation.

A whole-body rescue motion control with task-priority strategy for a rescue robot

This paper introduces a new rescue robot consisting of dual-manipulator and variable configuration mobile platform for multi-purpose such as casualty extraction and hazardous goods transport. A specific rescue motion strategy using a whole-body is suggested to tackle characteristics of the robot configuration and balancing issue. In order to take into account safety and stability of the robot during the rescue motions, some restrictions are reflected into redundant domain of the robot with different priority. For stable motion control in various scenarios, a singularity-robust inverse kinematics is adopted and modified to induce smoother robot movement. The robustness of the control approach is checked numerically by comparing other method and experiments for the rescue motion strategy are carried out by using a small-scaled simulator in place of the rescue robot under development.

Minimum infinity-norm joint velocity solutions for singularity-robust inverse kinematics

In this paper, a new method based on minimum infinity-norm joint velocity solutions for a redundant manipulator is proposed to lead it pass through singularities without excessive joint velocities. The infinity-norm is used to overcome the limitations of the minimum 2-norm solutions. In order to make a continuous transition from undamped phase to damped phase in the vicinity of a singular point and to avoid discontinuities in trajectory planning, a new mixing rate is adopted by using sigmoid function with Gaussian distribution. The effectiveness of our approach is compared with other methods in a redundant manipulator by simulation results.

Singularity-Robust Inverse Kinematics Using Lagrange Multiplier for Redundant Manipulators

In this paper, a singularity-robust inverse kinematics is newly suggested by using a Lagrange multiplier for redundant manipulator systems. Two tasks are considered with priority orders under the assumption that a primary task has no singularity. First, an inverse kinematics problem is formulated to be an optimization one subject to an equality constraint, in other words, to be a minimization problem of secondary task error subject to an equality constraint for primary task execution. Second, in the procedure of minimization for a given objective function, a new inverse kinematics algorithm is derived. Third, since nonzero Lagrange multiplier values appear in the neighborhood of a singular configuration of a robotic manipulator, we choose them as a natural choice of the dampening factor to alleviate the ill-conditioning of matrix inversion, ultimately for singularity-robust inverse kinematics. Finally, the effectiveness of the suggested singularity-robust inverse kinematics is shown through a numerical simulation about deburring and conveyance tasks of a dual arm manipulator system.

Damped least square based genetic algorithm with Ggaussian distribution of damping factor for singularity-robust inverse kinematics

Robot inverse kinematics based on Jacobian inversion encounters critical issues of kinematic singularities. In this paper, several techniques based on damped least squares are proposed to lead robot pass through kinematic singularities without excessive joint velocities. Unlike other work in which the same damping factor is used for all singular vectors, this paper proposes a different damping coefficient for each singular vector based on corresponding singular value of the Jacobian. Moreover, a continuous distribution of damping factor following Gaussian function guarantees the continuous in joint velocities. A genetic algorithm is utilized to search for the best maximum damping factor and singular region, which used to require ad hoc searching in other works. As a result, end effector tracking error, which is inherited from damped least squares by introducing damping factors, is minimized. The effectiveness of our approach is compared with other methods in both non-redundant robot and redundant robot.

Development of an Anthropomorphic Telemanipulation System (Entwicklung eines anthropomorphen Telemanipulationssystems)

Abstract This article describes the development of a dual arm robotic manipulator with anthropomorphic kinematics. The goal of this work is mimicking the functionality of the human arms for the purpose of teleoperation. Two main issues are discussed. First, the kinematic control of the manipulators, including redundancy resolution and singularity robust inverse kinematics, is presented. Second issue is the comparative study of compliant control methods aiming at securing stable contact with unknown environments. As a practical benchmark an assembly experiment for a case of a negligible time delay was successfully performed.