Tracking a Planar Target Using Image-Based Visual Servoing Technique

In this paper, we design and validate a kinematic controller for a quadrotor tracking a planar moving target using image-based visual servoing (IBVS). Most of the current literature on IBVS for moving targets often consider restrictive assumptions on the target dynamics that limits its generalizability for any arbitrary motion. We propose a model-free target velocity estimator augmented kinematic controller based on appropriately derived feature dynamics in a virtual image plane. We show how the inner-loop mismatch affects the kinematic controller performance through a comprehensive theoretical analysis based on the Lyapunov direct method. We prove that the system errors converge exponentially to an ultimate bound in general and asymptotically to zero for the purely translational and constant target motions and vanishing inner-loop mismatch. Extensive simulations, including model-in-the-loop and software-in-the-loop settings, along with experimental validation in an outdoor environment, confirm the utility of the proposed visual servoing technique.

I. Introduction

Quadrotors have become immensely popular due to their autonomous capabilities and exceptional maneuverability, making them well-suited for various applications such as search and rescue, object transportation, inspection, surveillance, and mapping, among others [1], [2]. In scenarios that require high precision, such as tracking and landing on a moving target using quadrotors [3], [4], [5], [6], visual servoing techniques have shown promise as visual measurement provides good tracking performance. The two main visual servoing approaches are (1) position-based visual servoing (PBVS), which performs position reconstruction based on visual information for control laws, and (2) image-based visual servoing (IBVS), where control calculations are performed directly in the image plane [7], [8]. Achieving the necessary precision in position reconstruction parameters such as target model depth, intrinsic parameters, and 3D geometry can be challenging in position-based visual servoing (PBVS) [9], [10]. As a result, many researchers prefer to use image-based visual servoing (IBVS) methods owing to their relatively simple control formulation and robustness to camera calibration, and depth estimation errors [11]. Since quadrotors are underactuated systems, the formulation based on IBVS often results in a coupled Image Jacobian, posing difficulties in control design. Authors in [12] address this issue by employing feature sets based on spherical image projection and perspective image moments. In a comparative study, the authors of [13] noted that the spherical feature-based methods do not have proper stabilization during vertical motion. In contrast, the image moment-based methods performed better when the image plane was parallel to the target plane. Motivated by the requirement of a parallel image plane to the target plane for image moment-based features, researchers in [14] presented the notion of a virtual image plane invariant to the pitch and roll motion of the quadrotor. The above literature considers a static target.