Trajectory tracking performance comparison of kinematic bicycle model with LQR and Lyapunov-based controllers on a circular trajectory

Abstract

This paper focuses on comparative results of two different controllers applied to kinematic bicycle model with rear wheel contact point to the ground as the reference point. The wide range of representation of different types of robots and vehicles of kinematic bicycle model is the main reason for this model selection. This paper has three main sections. The first section of the paper is mathematical modeling of the model. The second section is describing the utilized control techniques. The last section shares results of the simulations. The simulations have been carried out with pure feedback signals in absence of noise. The compared two controllers are an (Linear Quadratic Regulator)LQR controller and a Lyapunov based controller. The objective in the simulations is to track and complete a given constant radius trajectory. Last section includes comparison of results by analyzing statistical values of a defined error signal.

Keywords

• Wheeled mobile robot
• LQR
• Lyapunov
• Kinematic bicycle model
• Trajectory tracking

LQR ve Lyapunov temelli iki kontrolcünün kinematik bisiklet tipi model için güzergah izleme performansı karşılaştırması

Abstract

Bu makale farklı kontrol tekniklerinin arka tekerleğinin yere temas noktasını referans alan kinematik bisiklet tipi robot üzerine uygulamasının karşılaştırmalı sonuçlarına odaklanmıştır. Kinematik bisiklet tipi modelin seçilmesinin ardında yatan asıl sebep, bu modelin günümüzde kullanılan birçok robot modelini ve aracı temsil edebilmesidir. Çalışma üç ana bölümden oluşmaktadır. İlk bölüm robotun modellenmesini içermekte. İkinci bölüm uygulanan kontrol teknikleri ile ilgili çalışmaları barındırmakta. Son bölüm ise simülasyon sonuçlarını paylaşmaktadır. Kullanılan sinyaller gürültüsüz ortamda bir geribesleme sinyali için oluşturulmuştur. Karşılaştırılan kontrolcüler (Linear Quadratic Regulator)LQR ve bir Lyapunov temelli kontrolcülerdir. Simülasyonların ana amacı modelin verilen sabit yarıçaplı güzergahı takip ederek tamamlamasıdır. Son bölüm içerisinde tanımlanan hata sinyalinin istatistiksel olarak değerlendirmesini içerir.

Keywords

• Mobil robot
• LQR
• Lyapunov
• Kinematik bisiklet modeli
• Güzergah takibi

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