A New Motion Planning Framework based on the Quantized LQR Method for Autonomous Robots

Onur Sencan,Hakan Temeltas

doi:10.14569/ijacsa.2018.090150

Abstract

This study addresses an argument on the disconnection between the computational side of the robot navigation problem with the control problem including concerns on stability. We aim to constitute a framework that includes a novel approach of using quantizers for occupancy grids and vehicle control systems concurrently. This representation allows stability concerned with the navigation structure through input and output quantizers in the framework. We have given the theoretical proofs of qLQR in the sense of Lyapunov stability alongside with the implementation details. The experimental results demonstrate the effectiveness of the qLQR controller and quantizers in the framework with realtime data and offline simulations.

Highlights

Systems that contain both continuous dynamics and discrete events are called hybrid or discontinuous dynamical systems
The near-optimal solutions around discontinuity surfaces induce chattering problem, which is high-frequency switching between various controllers that designed for different set points originated by neglected effects of actuator and system dynamics [7]
We proposed a new framework for robot navigation problem concerning the asymptotical stability of the system with input and output quantizers

Summary

Introduction

Systems that contain both continuous dynamics and discrete events are called hybrid or discontinuous dynamical systems. After the widespread usage of the pulse width modulation signals in electric drives at the beginning of the 90s, sliding mode control techniques [3,4] use this nonlinear switching behavior as a control method for stabilizing nonlinear systems with an on-off(bang-bang) controller. Sliding mode control frameworks define the switching regions as discontinuity surfaces and aim to design feedback controllers that direct the optimal solutions of system states to settle around these surfaces. The near-optimal solutions around discontinuity surfaces induce chattering problem, which is high-frequency switching between various controllers that designed for different set points originated by neglected effects of actuator and system dynamics [7]

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Conclusion