LiDAR-based Control of Autonomous Rotorcraft for the Inspection of Pier-like Structures: Proofs

TL;DR

This paper presents a LiDAR-based control strategy for autonomous rotorcraft, utilizing a novel kinematic model and LPV control techniques to enable precise trajectory tracking during structural inspections.

Contribution

It introduces a LiDAR measurement-based kinematic model and a gain-scheduling control approach for rotorcraft trajectory tracking, with detailed proofs of the theoretical results.

Findings

Successful formulation of a LiDAR-based error dynamic model

Implementation of LPV control with piecewise affine dependence

Validation of control approach through theoretical proofs

Abstract

This is a complementary document to the paper presented in [1], to provide more detailed proofs for some results. The main paper addresses the problem of trajectory tracking control of autonomous rotorcraft in operation scenarios where only relative position measurements obtained from LiDAR sensors are possible. The proposed approach defines an alternative kinematic model, directly based on LiDAR measurements, and uses a trajectory-dependent error space to express the dynamic model of the vehicle. An LPV representation with piecewise affine dependence on the parameters is adopted to describe the error dynamics over a set of predefined operating regions, and a continuous-time $H_2$ control problem is solved using LMIs and implemented within the scope of gain-scheduling control theory.