Matrix inversion-free quasi-differential approach in solving the inverse kinematic task

Csanadi, Bertalan; Tar, József K.; Bitó, J.F.

doi:10.1109/cinti.2016.7846380

Cited by 16 publications

(2 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…They used different analytical, geometric, and algebraic methods combined with the Paden-Kahan subproblem and the matrix theory. Other works [23][24][25][26][27] proposed conventional tools to discover the robot manipulator's kinematic solutions.…”

Section: Related Workmentioning

confidence: 99%

Algorithm to Generate Trajectories in a Robotic Arm Using an LCD Touch Screen to Help Physically Disabled People

et al. 2021

View full text Add to dashboard Cite

In the last two-decade, robotics has attracted a lot of attention from the biomedical sectors, to help physically disabled people in their quotidian lives. Therefore, the research of robotics applied in the control of an anthropomorphic robotic arm to people assistance and rehabilitation has increased considerably. In this context, robotic control is one of the most important problems and is considered the main part of trajectory planning and motion control. The main solution for robotic control is inverse-kinematics, because it provides the angles of robotic arm joints. However, there are disadvantages in the algorithms presented by several authors because the trajectory calculation needs an optimization process which implies more calculations to generate an optimized trajectory. Moreover, the solutions presented by the authors implied devices where the people are dependent or require help from other people to control these devices. This article proposes an algorithm to calculate an accuracy trajectory in any time of interest using an LCD touch screen to calculate the inverse-kinematics and get the end-point of the gripper; the trajectory is calculated using a novel distribution function proposed which makes an easy way to get fast results to the trajectory planning. The obtained results show improvements to generate a safe and fast trajectory of an anthropomorphic robotic arm using an LCD touch screen allowed calculating short trajectories with minimal fingers moves.

show abstract

Section: Related Workmentioning

confidence: 99%

Algorithm to Generate Trajectories in a Robotic Arm Using an LCD Touch Screen to Help Physically Disabled People

et al. 2021

View full text Add to dashboard Cite

show abstract

“…Realizing the fact that the Moore-Penrose pseudoinverse can simply be generalized by the use of different weights for the quadratic cost function contributions that play similar role as the "joint activation factors" when certain elements of the null space of the Jacobian are mixed into the solution after computing the pseudoinverse, a matrix inversion-free, FPI-based solution of the inverse kinematic task was proposed by Csanádi et al in [63]. The forward kinematic task is expressed by the function f : R n → R m in which n, m ∈ N, and n > m. The "initial position" x ini = f (q ini ) is known, and a function of the scalar variable t ∈ R, q(t) has to be found for which x(t) = f (q(t)), x(t ini ) = x ini , and q(t ini ) = q ini .…”

Section: Delay1mentioning

confidence: 99%

On the Implementation of Fixed Point Iteration-based Adaptive Receding Horizon Control for Multiple Degree of Freedom, Higher Order Dynamical Systems

Khan¹,

Tar²

2019

ACTA POLYTECH HUNG

View full text Add to dashboard Cite

Based on the observation that it is very difficult to combine the mathematical frameworks of the prevailing Lyapunov function-based adaptive controllers and the traditional, optimal control-based "Model Predictive Controllers (MPC)", a novel adaptive solution was introduced to improve the operation of the "Receding Horizon Controllers (RHC)". Because at the local optima the gradient of the auxiliary function is zero, Lagrange's original "Reduced Gradient Method (RGM)" was replaced by a "Fixed Point Iteration (FPI)"-based algorithm that directly drove this gradient toward zero. According to "Banach's Fixed Point Theorem" the convergence of the method was guaranteed by a contractive function that generated the iterative sequence. The greatest modeling burden in this approach was the need for the calculation of the Jacobian of the problem, i.e. the gradient of the gradient of the auxiliary function. In the first simulations only a single "Degree of Freedom (DoF)" 2 nd order nonlinear system, a van der Pol oscillator was investigated. The attempts that were made to evade the calculation of the Jacobian were finished with the conclusion that at least a rough numerical approximation of this Jacobian generally must be utilized. Though the MPC approach allows the use a great variety of cost functions and dynamical models, mathematically well established results are available only for quadratic cost functions and "Linear Time-invariant (LTI)" models. For other cost functions and models careful numerical analysis is needed. In this paper the use of non-quadratic cost functions is numerically investigated in the FPI-based adaptive RHC control of 2 DoF 2 nd order nonlinear system that consists of two, nonlinearly coupled van der Pol oscillators, is considered. To guarantee lucid calculations simple functions are introduced that map the active parts of the horizon under consideration to the elements of the gradient of the auxiliary function that are calculated analytically. For the calculation of the Jacobian only a rough numerical estimation is applied. The simulation results reveal certain limitations of the suggested method.

show abstract

Studying Various Cost Functions by Nonlinear Programming for the Control of an Underactuated Mechanical System

Faitli

Tar

2018

Advances in Service and Industrial Robotics

View full text Add to dashboard Cite

Matrix inversion-free quasi-differential approach in solving the inverse kinematic task

Cited by 16 publications

References 12 publications

Algorithm to Generate Trajectories in a Robotic Arm Using an LCD Touch Screen to Help Physically Disabled People

Algorithm to Generate Trajectories in a Robotic Arm Using an LCD Touch Screen to Help Physically Disabled People

On the Implementation of Fixed Point Iteration-based Adaptive Receding Horizon Control for Multiple Degree of Freedom, Higher Order Dynamical Systems

Studying Various Cost Functions by Nonlinear Programming for the Control of an Underactuated Mechanical System

Contact Info

Product

Resources

About