[Paper Review] Discussions on Inverse Kinematics based on Levenberg-Marquardt Method and Model-Free Adaptive (Predictive) Control

Feilong Zhang|arXiv (Cornell University)|Sep 30, 2020

Iterative Learning Control Systems18 references4 citations

TL;DR

This paper proposes a novel Model-Free Adaptive Predictive Control (MFAPC) approach for solving inverse kinematics in robotic systems by reinterpreting the Levenberg-Marquardt method through control theory. By minimizing predictive tracking error, MFAPC achieves superior convergence and robustness in computational error, demonstrating excellent control performance and efficient inverse kinematic solution acquisition in simulation.

ABSTRACT

In this brief, the current robust numerical solution to the inverse kinematics based on Levenberg-Marquardt (LM) method is reanalyzed through control theory instead of numerical method. Compared to current works, the robustness of computation and convergence performance of computational error are analyzed much more clearly by analyzing the control performance of the corrected model free adaptive control (MFAC). Then mainly motivated by minimizing the predictive tracking error, this study suggests a new method of model free adaptive predictive control (MFAPC) to solve the inverse kinematics problem. At last, we apply the MFAPC as a controller for the robotic kinematic control problem in simulation. It not only shows an excellent control performance but also efficiently acquires the solution to inverse kinematic.

Motivation & Objective

• To reanalyze the Levenberg-Marquardt method for inverse kinematics through control theory rather than numerical analysis.
• To improve computational robustness and convergence performance of inverse kinematics solutions.
• To develop a new predictive control framework—Model-Free Adaptive Predictive Control (MFAPC)—targeted at minimizing predictive tracking error.
• To demonstrate the effectiveness of MFAPC in solving inverse kinematics and controlling robotic kinematics in simulation.

Proposed method

• Reinterprets the Levenberg-Marquardt method as a control problem, analyzing its performance through control-theoretic principles.
• Proposes a new control strategy, Model-Free Adaptive Predictive Control (MFAPC), designed to minimize predictive tracking error.
• Applies MFAPC as a controller for robotic kinematic systems, treating inverse kinematics as a real-time control task.
• Uses a corrected model-free adaptive control (MFAC) framework to enhance stability and convergence.
• Employs predictive control design to anticipate and reduce future tracking errors in the inverse kinematic solution process.
• Validates the method through simulation-based robotic kinematic control, assessing performance and solution efficiency.

Experimental results

Research questions

• RQ1 How can the Levenberg-Marquardt method for inverse kinematics be reinterpreted using control theory to improve robustness and convergence?
• RQ2 What are the control-theoretic performance characteristics of the corrected model-free adaptive control (MFAC) in solving inverse kinematics?
• RQ3 Can a predictive control approach significantly enhance the accuracy and efficiency of inverse kinematic solutions?
• RQ4 How does the proposed MFAPC method compare to conventional approaches in terms of computational error convergence and robustness?
• RQ5 What is the effectiveness of MFAPC in controlling robotic kinematic systems in simulation?

Key findings

• The control-theoretic reinterpretation of the Levenberg-Marquardt method provides clearer analysis of computational robustness and convergence performance.
• MFAPC effectively minimizes predictive tracking error, leading to improved solution accuracy in inverse kinematics.
• The proposed MFAPC controller demonstrates excellent control performance in robotic kinematic simulation.
• MFAPC efficiently acquires inverse kinematic solutions with enhanced convergence and robustness compared to standard methods.
• The simulation results confirm that MFAPC is a viable and high-performing alternative for real-time robotic control applications.