Closed-Loop Inverse Kinematics Algorithm with Implicit Numerical Integration

doi:10.12700/aph.14.1.2017.1.10

Cited by 5 publications

(2 citation statements)

References 6 publications

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“…Desperate attempts were invented in the early nineties of the past century to tackle the problem of singularities as considering 2 nd order differential inverse kinematics [59] or the complex extension of the real generalizes coordinates in [60]. In [61] D. Drexler suggested a witty idea of "action point transformation" for the regularization of the Jacobian, and in [62] an implicit 2 nd order integration was suggested.…”

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

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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.

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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

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“…Human driver models and models of the closed-loop system based on a control theory (e.g., [8][9][10]) approach have been considered in [11]. A human model based on fractional order calculus has also been presented [12].…”

Section: Introductionmentioning

confidence: 99%

Handover Process of Autonomous Vehicles – Technology and Application Challenges

Drexler¹,

Takács²,

Nagy³

et al. 2019

ACTA POLYTECH HUNG

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Self-driving technologies introduced new challenges to the control engineering community. Autonomous vehicles with limited automation capabilities require constant human supervision, and human drivers have to be able to take back control at any time, which is called handover. This is a critical process in terms of safety, thus appropriate handover modeling is fundamental in design, simulation and education related to selfdriving cars. This article reviews the literature of handover processes, situation awareness and control-oriented human driver models. It unifies the psychological and physiological control theory models to create a parameterized engineering tool to quantify the handover processes.

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A Novel QP-Based Kinematic Redundancy Resolution Method With Joint Constraints Satisfaction

Woliński

Wojtyra

2022

IEEE Access

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Kinematically redundant manipulators are advantageous for their increased dexterity and ability to fulfill some secondary requirements along with their primary task to follow the prescribed trajectory. The redundancy results in a non-trivial inverse kinematics problem (IK). Standard methods of redundancy resolution are based on the pseudoinverse of the Jacobian matrix of the manipulator. The excessive degrees of freedom are utilized to perform secondary tasks that are projected onto the null space of the Jacobian matrix. However, the joint constraints satisfaction cannot be easily ensured in this way-even though methods that account for the joint position limits are known, the constraints for joint velocities and especially accelerations are not straightforward to include. In this paper, a novel redundancy resolution method based on a less common quadratic programming (QP) approach is described. The proposed velocity-level IK method allows fulfilment of the joint constraints at the position, velocity, and acceleration levels. In the derived formulas, accelerations instead of the usual velocities are used-the discretized joint state equations allow the use of joint accelerations as decision variables in the QP problem. The developed algorithm is investigated in a series of numerical tests in which the kinematics of the KUKA LWR4+ redundant 7-DOF manipulator is exploited. The newly elaborated QP-based IK method is firstly compared with the classic pseudoinverse-based approach and then tested for its ability to keep the joint accelerations within the prescribed bounds. The prospects of the proposed approach are discussed in the concluding section.

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Closed-Loop Inverse Kinematics Algorithm with Implicit Numerical Integration

Abstract: The closed-loop inverse kinematics algorithm is a numerical approximation of

Cited by 5 publications

References 6 publications

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

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

Handover Process of Autonomous Vehicles – Technology and Application Challenges

A Novel QP-Based Kinematic Redundancy Resolution Method With Joint Constraints Satisfaction

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