An Efficient Egocentric Regulator for Continuous Targeting Problems of the Underactuated Quadrotor

TL;DR

The paper tackles the problem of continuously targeting a moving animal with an underactuated quadrotor, where nonlinear, strongly coupled dynamics hinder real-time tracking. It introduces the Efficient Egocentric Regulator (EER), which recasts the tracking problem in a body-centered, egocentric frame, decouples key nonlinearities, and solves a linear-quadratic problem for a virtual input that maps analytically to the real control. The main contributions are the coordinate-mapping theorems, the analytic control law, and extensive validation through mimic biological experiments and simulations, showing orders-of-magnitude speedups on onboard hardware (approximately 0.3 ms per update, about 350× faster than generic nonlinear optimizers) and the ability to operate at thousands of hertz. This approach significantly improves real-time feasibility for autonomous wildlife health management and sensor placement, enabling robust, high-frequency targeting in challenging, dynamic environments.

Abstract

Flying robots such as the quadrotor could provide an efficient approach for medical treatment or sensor placing of wild animals. In these applications, continuously targeting the moving animal is a crucial requirement. Due to the underactuated characteristics of the quadrotor and the coupled kinematics with the animal, nonlinear optimal tracking approaches, other than smooth feedback control, are required. However, with severe nonlinearities, it would be time-consuming to evaluate control inputs, and real-time tracking may not be achieved with generic optimizers onboard. To tackle this problem, a novel efficient egocentric regulation approach with high computational efficiency is proposed in this paper. Specifically, it directly formulates the optimal tracking problem in an egocentric manner regarding the quadrotor's body coordinates. Meanwhile, the nonlinearities of the system are peeled off through a mapping of the feedback states as well as control inputs, between the inertial and body coordinates. In this way, the proposed efficient egocentric regulator only requires solving a quadratic performance objective with linear constraints and then generate control inputs analytically. Comparative simulations and mimic biological experiment are carried out to verify the effectiveness and computational efficiency. Results demonstrate that the proposed control approach presents the highest and stablest computational efficiency than generic optimizers on different platforms. Particularly, on a commonly utilized onboard computer, our method can compute the control action in approximately 0.3 ms, which is on the order of 350 times faster than that of generic nonlinear optimizers, establishing a control frequency around 3000 Hz.

Figures (11)

• Figure 1: A free body diagram of the quadrotor. $\boldsymbol{e}^{\mathcal{I}}$ is the inertial coordinates and $\boldsymbol{e}^{\mathcal{B}}$ is the body fixed coordinates
• Figure 2: A schematic diagram for the targeting problem. Desired-point is the desired hit point of the anethesia gun in the animal; targeted plane denotes the plane which is parallel to the $\boldsymbol{e}_2^\mathcal{I}\boldsymbol{e}_3^\mathcal{I}$ plane while passing through the desired-point; targeted-point is the intersection of the anesthesia gun's extension line and the targeted plane.
• Figure 3: The illustration of the EER. As shown in the right part, a virtual coordinate $\mathcal{V}$ parallel to the quadrotor's instantaneous body coordinate $\boldsymbol{e}^{\mathcal{B}}$ is established while taking the desired-point as the origin. Based on this, a virtual system model is established, where the virtual state $\boldsymbol{x}_e$ is obtained by mapping $\boldsymbol{x}$ from the inertial coordinate $\boldsymbol{e}^{\mathcal{I}}$ to the virtual coordinate. Then, a linear quadratic optimization problem is built up to generate the virtual optimal control input $\boldsymbol{u}_e$ analytically. Finally, the real control input $\boldsymbol{u}$ can be derived by mapping $\boldsymbol{u}_e$ back to $\boldsymbol{e}^{\mathcal{I}}$.
• Figure 4: The schematic diagram of system structure in simulation
• Figure 5: Case 1 in simulation: the animal moves by constant speed

Theorems & Definitions (3)

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